Some multiplication patterns are given below. You may practise these. If you find any irregularity, you may send suggestions. So, now enjoy the world of multiplication.
v Multiplying two 2-digit numbers
(same 1st digit)
Select two 2-digit numbers with the same first digit.
Multiply their second digits (keep the carry). _ _ _ X
Multiply the sum of the second digits by the first digit,
add the carry (keep the carry). _ _ X _
Multiply the first digits (add the carry). X X _ _
Example:
If the first number is 42, choose 45 as the second number (any 2-digit number with first digit 4).
Multiply the last digits: 2 × 5 = 10 (keep carry)
_ _ _ 0
Multiply the sum of the 2nd digits by the first:
5 + 2 = 7; 7 × 4 = 28; 28 + 1 = 29 (keep carry)
_ _ 9 _
Multiply the first digits (add the carry)
4 × 4 = 16; 16 + 2 = 18
1 8 _ _
So 42 × 45 = 1890.
See the pattern?
If the first number is 62, choose 67 as the second number
(any 2-digit number with first digit 6).
Multiply the last digits: 2 × 7 = 14 (keep carry)
_ _ _ 4
Multiply the sum of the 2nd digits by the first (add carry):
2 + 7 = 9; 6 × 9 = 54; 54 + 1 = 55 (keep carry)
_ _ 5 _
Multiply the first digits (add the carry)
6 × 6 = 36; 36 + 5 = 41
4 1 _ _
So 62 × 67 = 4154.
v Multiplying two 2-digit numbers
(same 1st digit, 2nd digits sum to 10)
Both numbers should have the same first digit.
Choose second digits whose sum is 10.
Multiply the first digit by one number greater than itself; this number will be the first part of the answer:
X X _ _.
Multiply the two second digits together; the product
will be the last part of the answer: _ _ X X.
Note: If the two second digits are 1 and 9 (or, more generally, have a product that is less than ten), insert a 0 (zero) for the first X in step 4.
(Thanks to Michael Richardson, age 10, for this note.)
Example:
If the first number is 47, choose 43 as the second number (same first digit, second digits add to 10).
4 × 5 = 20 (multiply the first digit by one number greater than itself): the first part of the answer is
2 0 _ _.
7 × 3 = 21 (multiply the two second digits together); the last part of the answer is _ _ 2 1.
So 47 × 43 = 2021.
See the pattern?
If the first number is 62, choose 68 as the second number (same first digit, second digits add to 10).
6 × 7 = 42 (multiply the first digit by one greater), the first part of the answer is 4 2 _ _.
2 × 8 = 16 (multiply the two second digits together); the last part of the answer is _ _ 1 6.
So 62 × 68 = 4216.
v Multiplying two 2-digit numbers
(same 2nd digit)
Both numbers should have the same second digit.
Choose first digits whose sum is 10.
Multiply the first digits and add one second: X X _ _.
Multiply the second digits together: _ _ X X.
Example:
If the first number is 67, choose 47 as the second number (same second digit, first digits add to 10).
Multiply the 1st digits, add one 2nd.
6x4 = 24, 24+7 = 31. 3 1 _ _
Multiply the 2nd digits. 7x7 = 49 _ _ 4 9
So 67 × 47 = 3149.
See the pattern?
If the first number is 93, choose 13 as the second number (same second digit, first digits add to 10).
Multiply the 1st digits, add one 2nd. 9x1 = 9, 9+3 = 12.
1 2 _ _
Multiply the 2nd digits. 3x3 = 9 _ _ 0 9
So 93 × 13 = 1209.
v Multiplying two selected 3-digit numbers
(middle digit 0)
Select a 3-digit number with a middle digit of 0.
Choose a multiplier with the same first two digits, whose third digit sums to 10 with the third digit of the first 3-digit number.
The first digit(s) will be the square of the first digit:
X _ _ _ _ or X X _ _ _ _.
The next digit will be the first digit of the numbers:
_ X _ _ _ or _ _ X _ _ _.
The next digit is zero: _ _ 0 _ _ or _ _ _ 0 _ _.
The last two digits will be the product of the third digits:
_ _ _ X X or _ _ _ _ X X.
Example:
If the first number is 407, choose 403 as the second number (same first digits, second digits add to 10).
4 × 4 = 16 (square the first digit): 1 6 _ _ _ _.
The next digit will be the first digit of the numbers:
_ _ 4 _ _ .
The next digit is zero: _ _ 0 _ _ .
7 × 3 = 21 (the last two digits will be the product of the third digits: _ _ _ 2 1.
So 407 × 403 = 164021.
See the pattern?
If the first number is 201, choose 209 as the second number (same first digits, second digits add to 10).
2 × 2 = 4 (square the first digit): 4 _ _ _ _.
The next digit will be the first digit of the numbers:
_ 2 _ _ _ .
The next digit is zero: _ _ 0 _ _ .
1 × 9 = 09 (the last two digits will be the product of the third digits: _ _ _ 0 9.
So 201 × 209 = 42009.
v Multiplying two selected 3-digit numbers
(middle digit 1)
Select a 3-digit number with a middle digit of 1.
Choose a multiplier with the same first two digits, whose third digit sums to 10 with the third digit of the first 3-digit number.
The last two digits will be the product of the first digits:
_ _ _ 0 X or _ _ _ _ X X.
The third digit from the right will be 2:
_ _ 2 _ _ or _ _ _ 2 _ _ .
The next digit to the left will be 3 times the first digit of the number (keep carry):
_ X _ _ _ or _ _ X _ _ _.
The first digits will be the square of the first digit plus the carry:
X _ _ _ _ or X X _ _ _ _.
As you determine the digits in the answer from right to left, repeat them to yourself at each step until you have the whole answer.
Example:
If the first number is 814, choose 816 as the second number (same first digits, second digits add to 10).
4 × 6 = 24 (multiply the first digits) - last two digits:
_ _ _ _ 2 4.
The third digit from the right is 2: _ _ 2 _ _ .
8 × 3 = 24 (the next digit to the left is 3 times the first digit (keep carry 2): _ _ 4 _ _ _ .
8 × 8 = 64; 64 + 2 = 66 ( the first digits are the square of the first digit plus the carry: 6 6 _ _ _ _.
So 814 × 816 = 664224.
See the pattern?
If the first number is 317, choose 313 as the multiplier (same first digits, second digits add to 10).
7 × 3 = 21 (multiply the first digits) - last two digits:
_ _ _ _ 2 1.
The third digit from the right is 2: _ _ 2 _ _ .
3 × 3 = 9 (the next digit to the left is 3 times the first digit (no carry): _ 9 _ _ _ .
3 × 3 = 9 ( the first digits are the square of the first digit: 9 _ _ _ _.
So 317 × 313 = 99221.
v Multiplying two selected 3-digit numbers
(middle digit 2)
Select a 3-digit number with a middle digit of 2.
Choose a multiplier with the same first two digits, whose third digit sums to 10 with the third digit of the first 3-digit number.
The last two digits will be the product of the third digits: _ _ _ _X X.
The third digit from the right will be 6: _ _ 6 _ _.
The next digit to the left will be 5 times the first digit of the number (keep carry): _ _ X _ _ _.
The first digits will be the square of the first digit plus the carry: X X _ _ _ _.
As you determine the digits in the answer from right to left, repeat them to yourself at each step until you have the whole answer.
Example:
If the first number is 622, choose 628 as the second number (same first digits, third digits add to 10).
2 × 8 = 16 (multiply the third digits) - last two digits:
_ _ _ _ 1 6.
The third digit from the right is 6: _ _ 6 _ _ _.
5 × 6 = 30 (the next digit to the left is 5 times the first digit (keep carry 3): _ _ 0 _ _ _ .
6 × 6 = 36; 64 + 3 = 39 ( the first digits are the square of the first digit plus the carry: 3 9 _ _ _ _.
So 622 × 628 = 390616.
See the pattern?
If the first number is 221, choose 229 as the second number (same first digits, third digits add to 10).
1 × 9 = 9 (multiply the third digits) - last two digits:
_ _ _ 0 9.
The third digit from the right is 6: _ _ 6 _ _.
5 × 2 = 10 (the next digit to the left is 5 times the first digit (keep carry 1): _ 0 _ _ _ .
2 × 2 = 4; 4 + 1 = 5 ( the first digits are the square of the first digit plus the carry: 5 _ _ _ _.
So 221 × 229 = 50609.
v Multiplying two selected 3-digit numbers
(middle digit 3)
Select a 3-digit number with a middle digit of 3 (last digit not zero).
Choose a multiplier with the same first two digits, whose third digit sums to 10 with the third digit of the first 3-digit number.
The last two digits will be the product of the third digits: _ _ _ _ X X.
The third digit from the right will be 2: _ _ 2 _ _.
The next digit to the left will be 7 times the first digit of the number plus 1 (keep carry): _ _ X _ _ _.
The first digits will be the square of the first digit plus the carry: X X _ _ _ _.
As you determine the digits in the answer from right to left, repeat them to yourself at each step until you have the whole answer.
Example:
If the first number is 631, choose 639 as the second number (same first digits, third digits add to 10).
1 × 9 = 09 (multiply the third digits) - last two digits:
_ _ _ _ 0 9.
The third digit from the right is 2: _ _ 2 _ _ _.
7 × 6 = 42, 42 + 1 = 43 (the next digit to the left is 7 times the first digit plus 1 (keep carry 4): _ _ 3 _ _ _ .
6 × 6 = 36; 36 + 4 = 40 ( the first digits are the square of the first digit plus the carry: 4 0 _ _ _ _.
So 631 × 639 = 403209.
See the pattern?
If the first number is 236, choose 234 as the second number (same first digits, third digits add to 10).
6 × 4 = 24 (multiply the third digits) - last two digits: _ _ _ _ 2 4.
The third digit from the right is 2: _ _ 2 _ _ _.
7 × 2 = 14, 14 + 1 = 15 (the next digit to the left is 7 times the first digit plus 1 (keep carry 1): _ _ 5 _ _ _ .
2 × 2 = 4; 4 + 1 = 5 ( the first digits are the square of the first digit plus the carry: 0 5 _ _ _ _.
So 236 × 234 = 55224.
v Multiplying two selected 3-digit numbers
(middle digit 4)
Select a 3-digit number with a middle digit of 4 (last digit not zero).
Choose a multiplier with the same first two digits, whose third digit sums to 10 with the third digit of the first 3-digit number.
The last three digits will be 0 and the product of the third digits: _ _ _ 0 X X.
The third digit from the right will be 9 times the first digit + 2 (keep the carry): _ _ X _ _.
The first two digits will be the square of the first digit plus the carry: X X _ _ _ _.
As you determine the digits in the answer from right to left, repeat them to yourself at each step until you have the whole answer.
Example:
If the first number is 541, choose 549 as the second number (same first digits, third digits add to 10).
Last three digits: 0 and the product of the third digits: 1 × 9 = 9: _ _ 0 0 9
Next digit: 9 times the first digit + 2: 9 × 5 = 45, 45 + 2 = 47 (keep carry 4): _ _ 7 _ _ _
First two digits: square the first and carry: 5 × 5 = 25, 25 + 4 = 29: 2 9 _ _ _ _
So 541 × 549 = 297009.
See the pattern?
If the first number is 344, choose 346 as the second number (same first digits, third digits add to 10).
Last three digits: 0 and the product of the third digits: 4 × 6 = 24: _ _ 0 2 4
Next digit: 9 times the first digit + 2: 9 × 3 = 27, 27 + 2 = 29 (keep carry 2): _ _ 9 _ _ _
First two digits: square the first and carry: 3 × 3 = 9, 9 + 2 = 11: 1 1 _ _ _ _
So 344 × 346 = 119024.
v Multiplying two selected 3-digit numbers
(middle digit 5)
Select a 3-digit number with a middle digit of 5 (last digit not zero).
Choose a multiplier with the same first two digits, whose third digit sums to 10 with the third digit of the first 3-digit number.
The last three digits will be 0 and the product of the third digits: _ _ _ 0 X X.
The third digit from the right will be the first digit + 3 (keep the carry): _ _ X _ _.
The first digit will be the first digit times the next number plus the carry: X X _ _ _ _.
Repeat those digits from left to right as you get them.
Example:
If the first number is 752, choose 758 as the second number (same first digits, third digits add to 10).
Last three digits: 0 and the product of the third digits:
2 × 8 = 16: _ _ 0 1 6
Next digit: first digit + 3: 7 + 3 = 10 (keep carry 1):
_ _ 0 _ _ _
First two digits: first digit times next number plus carry: 7 × 8 = 56, 56 + 1 = 57: 5 7 _ _ _ _
So 752 × 758 = 570016.
See the pattern?
If the first number is 654, choose 656 as the second number (same first digits, third digits add to 10).
Last three digits: 0 and the product of the third digits:
4 × 6 = 24: _ _ 0 2 4
Next digit: first digit + 3: 6 + 3 = 9: _ _ 9 _ _ _
First two digits: first digit times next number:
6 × 7 = 42: 4 2 _ _ _ _
So 654 × 656 = 429024.
v Multiplying two 2-digit numbers
(difference of 1)
Choose a 2-digit number.
Select a number either 1 smaller or 1 larger.
Square the larger number (multiply it by itself).
Subtract the larger number from the product.
OR
Square the smaller number (multiply it by itself).
Add the smaller number to the product. Pick the easier one to square.
Example:
If the first number is 76, choose 75 as the second number.
75 × 75 = 5625 (square the smaller).
5625 + 75 = 5700 (add the smaller).
So 76 × 75 = 5700.
See the pattern?
If the first number is 32, choose 31 as the second number.
32 × 32 = 1024 (square the larger).
1024 - 32 = 992 (subtract the larger).
So 32 × 31 = 992.
v Multiplying two 2-digit numbers
(difference of 2)
Choose a 2-digit number.
Select a number either 2 smaller or 2 larger.
Square the average of the two numbers.
Subtract 1 from this square.
Example:
If the first number is 29, choose 31 as the second number.
The average of 29 and 31 is 30. Square 30: 30 × 30 = 900.
Subtract 1: 900 - 1 = 899.
So 29 × 31 = 899.
See the pattern?
If the first number is 76, choose 74 as the second number.
The average of 76 and 74 is 75. Square 75: 75 × 75 = 5625.
Subtract 1: 5625 - 1 = 5624.
So 76 × 74 = 5624.
Practice this shortcut (remember your methods of squaring numbers).
v Multiplying two 2-digit numbers
(difference of 3)
Choose a 2-digit number.
Select a number either 3 smaller or 3 larger.
Add 1 to the smaller number, then square.
Subtract one from the smaller number.
Add this to the square.
Example:
If the first number is 27, choose 24 as the second number.
Add 1 to the smaller number: 24 + 1 = 25.
Square this number: 25 × 25 = 625.
Subtract one from the smaller number: 24 - 1 = 23.
Add this to the square: 625 + 23 = 648.
So 27 × 24 = 648.
See the pattern?
If the first number is 34, choose 31 as the second number.
Add 1 to the smaller number: 31 + 1 = 32.
Square this number: 32 × 32 = 1024.
Subtract one from the smaller number: 31 - 1 = 30.
Add this to the square: 1024 + 30 = 1054.
So 34 × 31 = 1054.
Choose the second number that will give you the easier square, and use your square shortcuts.
v Multiplying two 2-digit numbers
(difference of 4)
Choose a 2-digit number.
Select a number either 4 smaller or 4 larger.
Find the middle number of the two (the average).
Square this middle number.
Subtract 4 from this square.
Example:
If the first number is 63, choose 67 as the second number.
The middle number (the average) is 65.
Square this middle number: 65 × 65 = 4225.
Subtract 4 from this square: 4225 - 4 = 4221.
So 63 × 67 = 4221.
See the pattern?
If the first number is 38, choose 42 as the second number.
The middle number (the average) is 40.
Square this middle number: 40 × 40 = 1600.
Subtract 4 from this square: 1600 - 4 = 1596.
So 38 × 42 = 1596.
Choose the second number that will give you the easier square, and use your square shortcuts.
v Multiplying two 2-digit numbers
(difference of 6)
Choose a 2-digit number.
Select a number either 6 smaller or 6 larger.
Find the middle number of the two (the average).
Square this middle number.
Subtract 9 from this square.
Example:
If the first number is 78, choose 72 as the second number.
The middle number (the average) is 75.
Square this middle number: 75 × 75 = 5625.
Subtract 9 from this square: 5625 - 9 = 5616.
So 78 × 72 = 5616.
See the pattern?
If the first number is 31, choose 37 as the second number.
The middle number (the average) is 34.
Square this middle number: 34 × 34 = 1156.
Subtract 9 from this square: 1156 - 9 = 1147.
So 31 × 37 = 1147.
Choose the second number that will give you the easier square, and use your square shortcuts. Practice!
v Multiplying two 2-digit numbers
(difference of 
Choose a 2-digit number.
Select a number either 8 smaller or 8 larger.
Find the middle number of the two (the average).
Square this middle number (multiply it by itself).
Subtract 16 from this square.
Example:
If the first number is 34, choose 26 as the second number (8 smaller).
The middle number (the average) is 30.
Square this middle number: 30 × 30 = 900.
Subtract 16 from this square: 900 - 16 = 884.
So 34 × 26 = 884.
See the pattern?
If the first number is 64, choose 72 as the second number (8 larger).
The middle number (the average) is 68.
Square this middle number: 68 × 68 = 4624.
Subtract 16 from this square: 4624 - 16 = 4608.
So 64 × 72 = 4608.
Choose the second number that will give you the easier square, and use your square shortcuts. Practice!
v Multiplying two 2-digit numbers
(difference of 10)
Choose a 2-digit number.
Select a number either 10 smaller or 10 larger.
Find the middle number of the two (the average).
Square this middle number (multiply it by itself).
Subtract 25 from this square.
Example:
If the first number is 36, choose 26 as the second number (10 smaller).
The middle number (the average) is 31.
Square this middle number: 31 × 31 = 961.
Subtract 25 from this square: 961 - 25 = 936
(subtract mentally in steps: think 961 - 20 - 5 = 941 - 5 = 936).
So 36 × 26 = 936.
See the pattern?
If the first number is 78, you might pick 88 as the second number (10 larger).
The middle number (the average) is 83.
Square this middle number: 83 × 83 = 6889.
Subtract 25 from this square: 6889 - 25 = 6864
(subtract mentally in steps: think 6889 - 20 - 5 = 6869 - 5 = 6864).
So 78 × 88 = 6864.
Remember to subtract in easy steps and pick your number to get an easy square. With practice you will be a whiz at getting these products.
v Multiplying a 2-digit number by 1.1
Select a 2-digit number.
Move decimal point one place left.
Add this to original number.
Example:
The 2-digit number chosen to multiply by 1.1 is 21.
Move decimal one place left: 2.1.
Add this to original number: 2.1 + 21 = 23.1.
So 1.1 × 21 = 23.1.
See the pattern?
The 2-digit number chosen to multiply by 1.1 is 73.
Move decimal on place left: 7.3.
Add this to original number: 7.3 + 73 = 80.3.
So 1.1 × 73 = 80.3.
v Multiplying a 2-digit number by 1 1/9
Select a 2-digit number.
Add a zero to the number.
Divide the result by 9.
Example:
The 2-digit number chosen to multiply by 1 1/9 is 32.
Add zero: 320
Divide by 9: 320/9 = 35 5/9
So 32 × 1 1/9 = 35 5/9.
See the pattern?
If the 2-digit number chosen to multiply by 1 1/9 is 74:
Add zero: 740
Divide by 9: 740/9 = 82 2/9
So 74 × 1 1/9 = 82 2/9.
Those using calculators may have difficulty entering 1 1/9, and their answers will be repeating decimals. Your answer will be exact.
v Multiplying a 2-digit number by 1 1/8
Multiply the number by 9.
Divide by 8.
Example:
If the 2-digit number chosen to multiply by 1 1/8 is 32:
Multiply by 9: 9 × 32 = 270 + 18 = 288
Divide by 8: 288/8 = 36
So 32 × 1 1/8 = 36.
See the pattern?
If the number to be multiplied by 1 1/8 is 71:
Multiply by 9: 9 × 71 = 639
Divide by 8: 639/8 = 79 7/8
So 71 × 1 1/8 = 79 7/8.
v Multiplying a 2-digit number by 1 1/7
Multiply the number by 8.
Divide by 7.
Example:
If the 2-digit number chosen to multiply by 1 1/7 is 32:
Multiply by 8: 8 × 32 = 240 + 16 = 256
Divide by 7: 256/7 = 36 4/7
So 1 1/7 × 32 = 36 4/6.
See the pattern?
If the number to be multiplied by 1 1/7 is 51:
Multiply by 8: 8 × 51 = 408
Divide by 7: 408/7 = 52 2/7
So 1 1/7 × 51 = 52 2/7.
v Multiplying a 2-digit number by 1 1/6
Select a 2-digit number.
Multiply by 7.
Divide the result by 6.
Example:
The 2-digit number chosen to multiply by 1 1/6 is 34.
Multiply by 7: 7 × 34 = 210 + 28 = 238
Divide by 6: 238/6 = 39 4/6
So 34 × 1 1/6 = 39 2/3.
See the pattern?
If the 2-digit number chosen to multiply by 1 1/6 is 57:
Multiply by 7: 7 × 57 = 350 + 49 = 399
Divide by 6: 399/6 = 66 3/6
So 57 × 1 1/6 = 66 1/2.
v Multiplying a 2-digit number by 1 1/5
Select a 2-digit number.
Multiply the number by 6.
Divide the product by 5.
Example:
The 2-digit number chosen to multiply by 1 1/5 is 34.
Multiply by 6: 6 × 34 = 180 + 24 = 204
Divide the product by 5: 204/5 = 40.8
So 34 × 1 1/5 = 40.8.
See the pattern?
The 2-digit number chosen to multiply by 1 1/5 is 61.
Multiply by 6: 6 × 61 = 366
Divide the product by 5: 366/5 = 73.2
So 61 × 1 1/5 = 73.2.
v Multiplying a 2-digit number by 1 2/9
Select a 2-digit number.
Multiply the number by 11 (add the digits right to left).
Divide the result by 9.
Example:
The 2-digit number chosen to multiply by 1 2/9 is 41.
Multiply by 11: 11 × 41= 451
Right digit is 1
Middle digit: 4 + 1 = 5
Left digit is 4
Divide by 9: 451/9 = 50 1/9
So 41 × 1 2/9 = 50 1/9.
See the pattern?
If the 2-digit number chosen to multiply by 1 2/9 is 62:
Multiply by 11: 11 × 62 = 682
Right digit is 2
Middle digit is 2 + 6 = 8
Left digit is 6
Divide by 9: 682/9 = 75 7/9
So 62 × 1 2/9 = 75 7/9.
Those using calculators may have difficulty entering 1 2/9, and their answers will be repeating decimals. Your answer will be exact.
v Multiplying a 2-digit number by 1 1/4
Add a zero to the number.
Divide by 8.
Example:
If the 2-digit number chosen to multiply by 1 1/4 is 37:
Add a zero: 370
Divide by 8: 370/8 = 46 1/4
So 37 × 1 1/4 = 46 1/4.
See the pattern?
If the number to be multiplied by 1 1/4 is 72:
Add a zero: 720
Divide by 8: 720/8 = 90
So 72 × 1 1/4 = 90.
v Multiplying a 2-digit number by 1 2/7
Multiply the number by 9.
Divide the product by 7.
Example:
If the 2-digit number chosen to multiply by 1 2/7 is 31:
Multiply by 9: 9 × 31 = 279
Divide by 7: 279/7 = 39 6/7
So 1 2/7 × 31 = 39 6/7.
See the pattern?
If the number to be multiplied by 1 2/7 is 52:
Multiply by 9: 9 × 52 = 450 + 18 = 468
Divide by 7: 468/7 = 66 6/7
So 1 2/7 × 52 = 66 6/7.
Answers found by using a calculator will produce repeating decimals rounded by the calculator.
v Multiplying a 2-digit number by 1.3
Select a 2-digit number.
Multiply by 3.
Move decimal point one place left.
Add original number.
Example:
The 2-digit number chosen to multiply by 1.3 is 21.
Multiply by 3: 3 × 21 = 63.
Move decimal one place left: 6.3.
Add original number: 6.3 + 21 = 27.3
So 1.3 × 21 = 27.3.
See the pattern?
The 2-digit number chosen to multiply by 1.3 is 47.
Multiply by 3. 3 × 47 = 120 + 21 + 141.
Move decimal on place left: 14.1.
Add original number: 14.1 + 47 = 57 + 4.1 = 61.1.
So 1.3 × 47 = 61.1.
v Multiplying a 2-digit number by 1 1/3
Select a 2-digit number.
Multiply by 4.
Divide by 3.
Example:
The 2-digit number chosen to multiply by 1 1/3 is 32.
Multiply by 4: 4 × 32 = 120 + 8 = 128
Divide by 3: 128/3 = 42 2/3
So 32 × 1 1/3 = 42 2/3.
See the pattern?
If the 2-digit number chosen to multiply by 1 1/3 is 83:
Multiply by 4: 4 × 83 = 320 + 12 = 332
Divide by 3: 332/3 = 110 2/3
So 83 × 1 1/3 = 110 2/3.
Remember, if you use a calculator you will get a decimal approximation, whereas the fractional form will be exact.
v Multiplying a 2-digit number by 1 3/8
Select a 2-digit number.
Multiply by 11 (see example - add numbers from right to left).
Divide the result by 8.
Example:
The 2-digit number chosen to multiply by 1 3/8 is 62.
Multiply by 11: 11 × 62 = 682
(Add the digits left to right.
The last digit is 2.
The next digit is 2 + 6 = 8.
The first digit is 6.)
Divide by 8: 682/8 = 85 2/8
So 62 × 1 3/8 = 85 1/4.
See the pattern?
If the 2-digit number chosen to multiply by 1 3/8 is 44:
Multiply by 11: 11 × 44 = 484
(Add the digits left to right.
The last digit is 4.
The next digit is 4 + 4 = 8.
The first digit is 4.)
Divide by 8: 484/8 = 60 4/8
So 44 × 1 3/8 = 60 1/2.
To produce these products promptly, practice multiplying by 11.
v Multiplying a 2-digit number by 1 2/5
Select a 2-digit number.
Multiply the number by 7.
Divide the product by 5.
Example:
The 2-digit number chosen to multiply by 1 2/5 is 24.
Multiply by 7: 7 × 24 = 140 + 28 = 168
Divide the product by 5: 168/5 = 33 3/5
So 24 × 1 2/5 = 33 3/5.
See the pattern?
The 2-digit number chosen to multiply by 1 2/5 is 71.
Multiply by 7: 7 × 71 = 497
Divide the product by 5: 497/5 = 99 2/3
So 71 × 1 2/5 = 99 2/3.
v Multiplying a 2-digit number by 1 3/7
Add zero to the number.
Divide by 7.
Example:
If the 2-digit number chosen to multiply by 1 3/7 is 24:
Add zero: 240
Divide by 7: 240/7 = 34 2/7
So 1 3/7 × 24 = 34 2/7.
See the pattern?
If the number to be multiplied by 1 3/7 is 54:
Add zero: 540
Divide by 7: 540/7 = 77 1/7
So 1 3/7 × 54 = 77 1/7.
Practice dividing by 7 and you will give these products quickly.
v Multiplying a 2-digit number by 1 1/2
Select a 2-digit number.
Multiply by 3.
Divide by 2.
Example:
The 2-digit number chosen to multiply by 1 1/2 is 63.
Multiply by 3: 3 × 63 = 180 + 9 = 189.
Divide by 2: 189/2 = 94 1/2.
So 63 × 1 1/2 = 94 1/2.
See the pattern?
If the 2-digit number chosen to multiply by 1 1/2 is 97:
Multiply by 3: 3 × 97 = 270 + 21 = 291.
Divide by 2: 291/2 = 145 1/2.
So 97 × 1 1/2 = 145 1/2.
Remember, if you use a calculator you will get a decimal approximation, whereas the fractional form will be exact.
v Multiplying a 2-digit number by 1 4/7
Multiply the number by 11. (See procedure below.)
Divide the product by 7.
Example:
If the 2-digit number chosen to multiply by 1 4/7 is 21:
Multiply by 11:
The right digit is 1 (same as number): 1
The middle digit is the sum of the two digits of the number: 2 + 1 = 3
The left digit is the left digit of the number: 2
So 11 × 21 = 231
Divide by 7: 231/7 = 33
So 1 4/7 × 21 = 33.
See the pattern?
If the 2-digit number chosen to multiply by 1 4/7 is 52:
Multiply by 11:
The right digit is 1 (same as number): 1
The middle digit is the sum of the two digits of the number: 5 + 2 = 7
The left digit is the left digit of the number: 5 So 11 × 52 = 572
Divide by 7: 572/7 = 81 5/7
So 1 4/7 × 52 = 81 5/7.
Practice multiplying by 11 and you will be proficient in giving these products.
v Multiplying a 2-digit number by 1 3/5
Select a 2-digit number.
Multiply the number by 8.
Divide the product by 5.
Example:
The 2-digit number chosen to multiply by 1 3/5 is 21.
Multiply by 8: 8 × 21 = 168
Divide the product by 5: 168/5 = 33 3/5
So 21 × 1 3/5 = 33 3/5.
See the pattern?
The 2-digit number chosen to multiply by 1 3/5 is 62.
Multiply by 8: 8 × 62 = 480 + 16 = 496
Divide the product by 5: 496/5 = 99 1/5
So 62 × 1 3/5 = 99 1/5.
v Multiplying a 2-digit number by 1.6
Select a 2-digit number.
Multiply by 6.
Move decimal point one place left.
To this, add the original number.
Example:
The 2-digit number chosen to multiply by 1.6 is 21.
Multiply by 6: 6 × 21 = 126.
Move decimal one place left: 12.6.
To this, add the original number: 12.6 + 21 = 33.6.
So 1.6 × 21 = 33.6.
See the pattern?
The 2-digit number chosen to multiply by 1.6 is 73.
Multiply by 6: 6 × 73 = 420 + 18 = 438.
Move decimal on place left: 43.8.
To this, add the original number: 43.8 + 73 = 110 + 3.8 + 3 = 116.8
So 1.6 × 73 = 116.8.
v Multiplying a 2- or 3-digit number by 1 2/3
Select a 2-digit number.
Divide by 6 (or by 2 and 3).
Move the decimal point one place to the right, or add a zero.
Example:
The 2-digit number chosen to multiply by 1 2/3 is 78.
Divide by 2: 78/2 = 39
Divide by 3: 39/3 = 13. (39 is divisible by 3 because the sum of its digits is divisible by 3.)
Add a zero: 130.
So 78 × 1 2/3 = 130.
See the pattern?
If the 3-digit number chosen to multiply by 1 2/3 is 315:
Divide by 3: 315 / 3 = 105. (315 is divisible by 3 because the sum of its digits is divisible by 3.)
Divide by 2: 105/2 = 52.5.
Move the decimal point one place to the right: 525.
So 315 × 1 2/3 = 525.
Test the number to see if it is divisible by 3 (if the sum of the digits is divisible by 3, so is the number). If not, divide by 2 first. This should make the division easier.
v Multiplying a 2-digit number by 1 5/7
Select a 2-digit number.
Add one zero.
Add the original number twice.
Divide the result by 7.
Example:
The 2-digit number chosen to multiply by 1 5/7 is 21.
Add one zero: 210
Add the original number twice: 210 + 21 + 21 =
210 + 40 + 2 = 252
Divide by 7: 252/7 = 36
So 21 × 1 5/7 = 36.
See the pattern?
If the 2-digit number chosen to multiply by 1 5/7 is 72:
Add one zero: 720
Add the original number twice: 720 + 72 + 72 =
720 + 140 + 4 = 860 + 4 = 864
Divide by 7: 864/7 = 123 3/7
So 72 × 1 5/7 = 123 3/7.
v Multiplying a 2-digit number by 1 3/4
Multiply the number by 7.
Divide by 4.
Example:
If the number chosen to multiply by 1 3/4 is 42:
Multiply by 7: 7 × 42 = 280 + 14 = 294
Divide by 4: 294/4 = 73 2/4
So 42 × 1 3/4 = 73 1/2.
See the pattern?
If the number to be multiplied by 1 3/4 is 29:
Multiply by 7: 7 × 29 = 140 + 63 = 203
Divide by 4: 203/4 = 50 3/4
So 29 × 1 3/4 = 50 3/4.
Practice, and these products will be fast and accurate
v Multiplying a 2-digit number by 1 4/5
Select a 2-digit number.
Multiply the number by 9.
Divide the product by 5.
Example:
The 2-digit number chosen to multiply by 1 4/5 is 31.
Multiply by 9: 9 × 31 = 279
Divide the product by 5: 279/5 = 55 4/5
So 31 × 1 4/5 = 55 4/5.
See the pattern?
The 2-digit number chosen to multiply by 1 4/5 is 82.
Multiply by 9: 9 × 82 = 720 + 18 = 738
Divide the product by 5: 738/5 = 147 3/5
So 82 × 1 4/5 = 147 3/5.
v Multiplying a 2-digit number by 1 5/6
Select a 2-digit number.
Multiply by 11.
Divide the result by 6.
Example:
The 2-digit number chosen to multiply by 1 5/6 is 34.
Multiply by 11: 11 × 34 = 374
(Add the digits left to right.
The last digit is 4.
The next digit is 4 + 3 = 7.
The first digit is 3.)
Divide by 6: 374/6 = 62 2/6
So 34 × 1 5/6 = 62 1/3.
See the pattern?
If the 2-digit number chosen to multiply by 1 5/6 is 62:
Multiply by 11: 11 × 62 = 682
Divide by 6: 682/6 = 113 4/6
So 62 × 1 5/6 = 113 2/3.
To produce these products promptly, practice multiplying by 11.
v Multiplying a 2-digit number by 1.9
Select a 2-digit number.
Multiply the number by 9.
Move the decimal point one place left.
Add this to the original number.
Example:
The 2-digit number chosen to multiply by 1.9 is 21.
Multiply by 9: 9 × 21 = 189.
Move decimal one place left: 18.9.
Add original number: 18.9 + 21 = 39.9.
So 1.9 × 21 = 39.9.
See the pattern?
The 2-digit number chosen to multiply by 1.9 is 33.
Multiply by 9: 9 × 33 = 270 + 27 = 297.
Move decimal on place left: 29.7.
Add original number: 29.7 + 33 = 59.7 + 3 = 62.7.
So 1.9 × 33 = 62.7.
Alternate method: Subtract .1 of original number (move decimal one place left) from 2 times original number. Try this method, too.
With some practice you will be able to give these products using one or both of these methods.
v Multiplying a 2-digit number by 2.1
Select a 2-digit number.
Move decimal point one place left.
To this add two times the original number.
Example:
The 2-digit number chosen to multiply by 2.1 is 21.
Move decimal one place left: 2.1.
To this add two times the original number: 2.1 + 2(21) = 2.1 + 42 = 44.1.
So 2.1 × 21 = 44.1.
See the pattern?
The 2-digit number chosen to multiply by 2.1 is 63.
Move decimal on place left: 6.3.
To this add two times the original number: 6.3 + 2(63) = 6.3 + 126 = 132.3.
So 63 times 2.1 is 132.3.
v Multiplying a 2-digit number by 2 1/9
Select a 2-digit number.
Multiply by two.
Add one zero.
Subtract the original number.
Divide by nine.
Example:
The 2-digit number chosen to multiply by 2 1/9 is 24.
Multiply by 2: 2 × 24 = 48
Add one zero: 480
Subtract the original number: 480 - 24 =
480 - 20 - 4 = 460 - 4 = 456
Divide by 9: 456/9 = 50 6/9
So 24 × 2 1/9 = 50 2/3.
See the pattern?
The 2-digit number chosen to multiply by 2 1/9 is 52.
Multiply by 2: 2 × 52 = 104
Add one zero: 1040
Subtract the original number: 1040 - 52 =
1040 - 50 - 2 = 990 - 2 = 988
Divide by 9: 988/9 = 109 7/9
So 52 × 2 1/9 = 109 7/9.
Practice subtracting in two steps and this process will become an easy one.
v Multiplying a 2-digit number by 2 1/5
Select a 2-digit number.
Multiply the number by 11. Add the digits right to left.
Divide the product by 5.
Example:
The 2-digit number chosen to multiply by 2 1/5 is 43.
Multiply by 11: the last digit of the product is 3. 3 + 4 = 7 (next left digit). The product is 473.
Divide the product by 5: 473/5 = 94.6.
So 43 × 2 1/5 = 94.6.
See the pattern?
The 2-digit number chosen to multiply by 2 1/5 is 78.
Multiply by 11: the last digit of the product is 8. 8 + 7 = 15. The next digit is 5, carry 1. 7 + 1 = 8. The product is 858.
Divide the product by 5: 858/5 = 171.6.
So 78 × 2 1/5 = 171.6.
v Multiplying a 2-digit number by 2 2/9
Select a 2-digit number.
Multiply by two.
Add one zero.
Divide by nine.
Example:
The 2-digit number chosen to multiply by 2 2/9 is 31.
Multiply by 2: 2 × 31 = 62
Add one zero: 620
Divide by 9: 620/9 = 68 8/9
So 31 × 2 2/9 = 68 8/9.
See the pattern?
The 2-digit number chosen to multiply by 2 2/9 is 74.
Multiply by 2: 2 × 74 = 148
Add one zero: 1480
Divide by 9: 1480/9 = 164 4/9
So 74 × 2 2/9 = 164 4/9.
Those using calculators will have difficulty entering 2 2/9 (2.222222...) and their results may be repeating decimals. Your steps will produce exact results.
v Multiplying a 2-digit number by 2 1/4
Select a 2-digit number.
Multiply the number by 9.
Divide by 4.
Example:
The 2-digit number chosen to multiply by 2 1/4 is 51.
Multiply by 9: 9 × 51 = 450 + 9 = 459.
Divide by 4: 459/4 = 114 3/4.
So 51 × 2 1/4 = 114 3/4.
See the pattern?
The 2-digit number chosen to multiply by 2 1/3 is 28.
Multiply by 9: 9 × 28 = 180 + 72 = 252.
Divide by 4: 252/4 = 63.
So 51 × 2 1/4 = 63.
v Multiplying a 2-digit number by 2.3
Multiply the number by 3.
Move decimal one place left.
Add this to 2 times original number.
Example:
The 2-digit number chosen to multiply by 2.3 is 21.
Multiply by 3: 3 × 21 = 63.
Move decimal one place left: 6.3.
Add to 2 times original number: 6.3 + 2(21) = 6.3 + 42 = 48.3.
So 2.3 × 21 is 48.3.
See the pattern?
The 2-digit number chosen to multiply by 2.3 is 34.
Multiply by 3: 3 × 34 = 90 + 12 = 102.
Move decimal one place left: 10.2.
Add to 2 times original number: 10.2 + 2(34) = 10.2 + 68 = 78.2.
So 2.3 × 34 is 78.2.
In no time you will be giving these products easily. Practice and you will become expert in these calculations.
v Multiplying a 2-digit number by 2 1/3
Select a 2-digit number.
Multiply the number by 7.
Divide by 3.
Example:
The 2-digit number chosen to multiply by 2 1/3 is 67.
Multiply by 7: 7 × 67 = 420 + 49 = 469.
Divide by 3: 469/3 = 156 1/3.
So 67 × 2 1/3 = 156 1/3.
See the pattern?
The 2-digit number chosen to multiply by 2 1/3 is 91.
Multiply by 7: 7 × 91 = 630 + 7 = 637.
Divide by 3: 637/3 = 212 1/3.
So 91 × 2 1/3 = 212 1/3.
v Multiplying a 2-digit number by 2 3/8
Select a 2-digit number.
Multiply the number by 2.
Add a zero.
Subtract the original number from this product.
Divide the result by 8.
Example:
The 2-digit number chosen to multiply by 2 3/8 is 31.
Multiply by 2: 2 × 31 = 62
Add a zero: 620
Subtract the original number from this product: 620 - 31 = 589
Divide by 8: 589/8 = 73 5/8
So 31 × 2 3/8 = 73 5/8.
See the pattern?
If the 2-digit number chosen to multiply by 2 3/8 is 54:
Multiply by 2: 2 × 54 = 108
Add a zero: 1080
Subtract the original number from this product: 1080 - 54 = 1026
Divide by 8: 1026/8 = 128 2/8
So 54 × 2 3/8 = 128 1/4.
v Multiplying a 2-digit number by 2 2/5
Select a 2-digit number.
Add a zero.
Multiply the original number by 2.
Add these two numbers.
Divide by 5.
Example:
The 2-digit number chosen to multiply by 2 2/5 is 21.
Add a zero: 210
Multiply the original number by 2: 2 × 21 = 42
Add these two numbers: 210 + 42 = 252
Divide by 5: 252/5 = 50 2/5
So 21 × 2 2/5 = 50 2/5.
See the pattern?
The 2-digit number chosen to multiply by 2 2/5 is 61.
Add a zero: 610
Multiply the original number by 2: 2 × 61 = 122
Add these two numbers: 610 + 122 = 732
Divide by 5: 732/5 = 146 2/5
So 61 × 2 2/5 = 146 2/5.
v Multiplying a 2-digit number by 2 4/9
Select a 2-digit number.
Multiply the number by 2.
Add one zero.
Add to this number its first two digits.
Divide by nine.
Example:
The 2-digit number chosen to multiply by 2 4/9 is 21.
Multiply by 2: 2 × 21 = 42
Add one zero: 420
Add to this number its first two digits: 420 + 42 = 462
Divide by 9: 462/9 = 51 3/9
So 21 × 2 4/9 = 51 3/9.
See the pattern?
The 2-digit number chosen to multiply by 2 4/9 is 38.
Multiply by 2: 2 × 38 = 76
Add one zero: 760
Add to this number its first two digits: 760 + 76 = 760 + 70 + 6 = 830 + 6 = 836
Divide by 9: 836/9 = 92 8/9
So 38 × 2 4/9 = 92 8/9.
v Multiplying a 2- or 3-digit number by 2 1/2
Select a 2- or 3-digit number.
Divide by 4 (or by 2 twice).
Move the decimal point one place to the right, or add a zero.
Example:
If the 2-digit number chosen to multiply by 2 1/2
is 98
Divide by 2: 98/2 = 49
Divide by 2: 49/2 = 24.5.
Move the decimal point one place to the right: 245
So 98 × 2 1/2 = 245.
See the pattern?
If the 3-digit number chosen to multiply by 2 1/2
is 123
Divide by 2: 123/2 = 61.5
Divide by 2: 61.5/2 = 30.75.
Move the decimal point one place to the right: 307.5
So 123 × 2 1/2 = 307.5.
If the 3-digit number chosen to multiply by 2 1/2
is 488
Divide by 4: 488/4 = 122
Divide by 2: 61.5/2 = 30.75.
Move the decimal point one place to the right (add a zero): 1220.
So 488 × 2 1/2 = 1220.
Divide by 4 when it is easy (the number is divisible by 4 if its last two digits are divisible by 4), or divide by 2 twice. This method should become an easy one.
v Multiplying a 2-digit number by 2 4/7
Multiply the number by 2.
Add a zero.
Subtract the original number twice.
Divide by 7.
Example:
If the 2-digit number chosen to multiply by 2 4/7 is 21:
Multiply by 2: 2 × 21 = 42
Add a zero: 420
Subtract the original number twice:
420 - 21 - 21 = 420 - 40 - 2 = 380 - 2 = 378
Divide by 7: 378/7 = 54
So 21 × 2 4/7 = 54.
See the pattern?
If the 2-digit number chosen to multiply by 2 4/7 is 52:
Multiply by 2: 2 × 52 = 104
Add a zero: 1040
Subtract the original number twice:
1040 - 52 - 52 = 1040 - 100 - 4 = 940 - 4 = 936
Divide by 7: 936/7 = 133 5/7
So 52 × 2 4/7 = 133 5/7.
v Multiplying a 2-digit number by 2.6
Multiply the number by 6.
Move decimal one place left.
Add this to 2 times original number.
Example:
The 2-digit number chosen to multiply by 2.6 is 21.
Multiply by 6: 6 × 21 = 126.
Move decimal one place left: 12.6.
Add to 2 times original number: 12.6 + 2(21) = 12.6 + 42 = 54.6.
So 2.6 × 21 is 54.6.
See the pattern?
The 2-digit number chosen to multiply by 2.6 is 37.
Multiply by 6: 6 × 37 = 180 + 42 = 222.
Move decimal one place left: 22.2.
Add to 2 times original number: 22.2 + 2(37) = 22.2 + 60 + 14 = 82.2 + 14 = 96.2.
So 2.6 × 37 is 96.2.
Multiply and add left to right and you will be able to give these answers quickly and accurately.
v Multiplying a 2-digit number by 2.9
Move decimal one place left.
Subtract this from 3 times original number.
Example:
The 2-digit number chosen to multiply by 2.9 is 21.
Move decimal one place left: 2.1.
Subtract this from 3 times original number: 3(21) - 2.1 = 63 - 2.1 = 61 - 0.1 = 60.9.
So 2.9 × 21 is 60.9.
See the pattern?
The 2-digit number chosen to multiply by 2.9 is 47.
Move decimal one place left: 4.7.
Subtract this from 3 times original number: 3(47) - 4.7 = 120 + 21 - 4.7 = 141 - 4.7 = 137 - 0.7 = 136.3.
So 2.9 × 73 is 136.3.
Multiply, add, and subtract left to right in easily managed increments and you will be able to give these answers with ease.
v Multiplying a 2-digit number by 3.1
Select a 2-digit number.
Move decimal point one place left.
To this add three times the original number.
Example:
The 2-digit number chosen to multiply by 3.1 is 21.
Move decimal one place left: 2.1.
To this add three times the original number: 2.1 + 3(21) = 2.1 + 63 = 65.1.
So 3.1 × 21 = 65.1.
See the pattern?
The 2-digit number chosen to multiply by 3.1 is 83.
Move decimal on place left: 8.3.
To this add three times the original number: 8.3 + 3(83) = 8.3 + 3(83) = 8.3 + (240 + 9) = 8.3 + 249 = 257 + 0.3 = 257.3
So 83 times 3.1 is 257.3.
v Multiplying a 2-digit number by 3.2
Divide number by 5.
Add this to 3 times original number.
Example:
The 2-digit number chosen to multiply by 3.2 is 21.
Divide by 5: 21/5 = 4.2.
Add to 3 times original number: 4.2 + 3(21) = 4.2 + 63 = 67.2.
So 3.2 × 21 is 67.2.
See the pattern?
The 2-digit number chosen to multiply by 3.2 is 62.
Divide by 5: 4 62/5 = 12.4.
Add to 3 times original number: 12.4 + 3(62) = 12.4 + 180 + 6 = 18.4 + 180 = 190 + 8.4 = 198.4
So 3.2 × 62 is 198.4.
Add left to right in easily handled increments and you will be giving these answers with ease using mental math.
v Multiplying a 2-digit number by 3.4
Multiply the number by 4.
Move decimal one place left.
Add this to 3 times original number.
Example:
The 2-digit number chosen to multiply by 3.4 is 21.
Multiply by 4: 4 × 21 = 84.
Move decimal one place left: 8.4.
Add to 3 times original number: 8.4 + 3(21) = 8.4 + 63 = 71.4.
So 3.4 × 21 is 71.4.
See the pattern?
The 2-digit number chosen to multiply by 3.4 is 73.
Multiply by 4: 4 × 73 = 280 + 12 = 292.
Move decimal one place left: 29.2.
Add to 3 times original number: 29.2 + 3(73) = 29.2 + 210 + 9 = 239.2 + 9 = 248.2
So 3.4 × 73 is 248.2.
Ease this process by adding from left to right in small manageable increments. Then you will be producing these answers quickly.
v Multiplying a 2-digit number by 3.6
Multiply the number by 6.
Move decimal one place left.
Add this to 3 times original number.
Example:
The 2-digit number chosen to multiply by 3.6 is 21.
Multiply by 6: 6 × 21 = 126.
Move decimal one place left: 12.6.
Add to 3 times original number: 12.6 + 3(21) = 12.6 + 63 = 72.6 + 3 = 75.6.
So 3.6 × 21 is 75.6.
See the pattern?
The 2-digit number chosen to multiply by 3.6 is 63.
Multiply by 6: 6 × 63 = 360 + 18 = 378.
Move decimal one place left: 37.8.
Add to 3 times original number: 37.8 + 3(63) = 37.8 + 180 + 9 = 46.8 + 180 =220 + 6.8 = 226.8.
So 3.6 × 63 is 226.8.
Remember to multiply and add left to right in small increments.
Multiplying a 2-digit number by 3 4/7
Add two zeros to the number.
Divide by 4.
Divide by 7.
Example:
If the 2-digit number chosen to multiply by 3 4/7 is 24:
Add two zeros: 2400
Divide by 4: 2400/4 = 600
Divide by 7: 600/7 = 85 5/7
So 3 4/7 × 24 = 85 5/7.
See the pattern?
If the 2-digit number chosen to multiply by 3 4/7 is 62:
Add two zeros: 6200
Divide by 4: 6200/4 = 1550
Divide by 7: 1550/7 = 221 3/7
So 3 4/7 × 62 = 221 3/7.
People using calculators will have a problem entering 3 4/7 as the multiplier, and their answers will be long decimals. Your answers will be exact.
v Multiplying a 2-digit number by 4.1
Select a 2-digit number.
Move decimal point one place to the left.
Add this to 4 times original number.
Example:
The 2-digit number chosen to multiply by 4.1 is 21.
Move decimal one place to the left: 2.1.
Add to 4 times original number: 2.1 + 4(21) = 2.1 + 84 = 86.1.
So 4.1 × 21 is 86.1.
See the pattern?
The 2-digit number chosen to multiply by 4.1 is 53.
Move decimal one place to the left: 5.3.
Add to 4 times original number: 5.3 + 4(53) = 5.3 + 200 + 12 = 200 + 17.3 = 217.3.
So 4.1 × 53 is 217.3.
Practice multiplying left to right and these computations will come easily and accurately.
v Multiplying a 2-digit number by 4.3
Multiply the number by 3.
Move decimal one place left.
Add this to 4 times original number.
Example:
The 2-digit number chosen to multiply by 4.3 is 21.
Multiply by 3: 3 × 21 = 63.
Move decimal one place left: 6.3.
Add to 4 times original number: 6.3 + 4(21) = 6.3 + 84 = 90.3.
So 4.3 × 21 is 90.3.
See the pattern?
The 2-digit number chosen to multiply by 4.3 is 62.
Multiply by 3: 3 × 62 = 186.
Move decimal one place left: 18.6.
Add to 4 times original number: 18.6 + 4(62) = 18.6 + 240 + 8 = 18.6 + 248 = 258 + 8.6 = 266.6
So 4.3 × 62 is 266.6.
Remember to multiply and add left to right and these problems will become easy. In not time you will be giving these answers quickly using mental math.
v Multiplying a 2-digit number by 4.6
Multiply the number by 6.
Move decimal point one place to the left.
Add to 4 times the original number.
Example:
The first number to multiply by 4.6 is 21.
Multiply by 6: 6 × 21 = 126.
Move decimal point one place to the left: 12.6.
Add this to 4 times the original number: 12.6 + 4(21) = 12.6 + 84 = 96 + .6 = 96.6.
So 4.6 × 21 = 96.6.
See the pattern?
The second number to multiply by 4.6 is 73.
Multiply by 6: 6 × 73 = 420 + 18 = 438.
Move decimal one place to the left: 43.8.
Add this to 4 times the original number: 43.8 + 4(73) = 43.8 + 280 + 12 = 55.8 + 280 = 330 + 5.8 = 335.8.
So 4.6 × 73 is 335.8.
Multiply and add left to right and you will be able to do these computations using mental math.
v Multiplying a 2-digit number by 4.7
Select a 2-digit number.
Multiply the number by seven.
Move the decimal point one place to the left.
To this add four times the original number.
Example:
The 2-digit number chosen to multiply by 4.7 is 21.
Multiply by 7: 7 × 21 = 147.
Move decimal point one place left: 14.7.
Add this to four times the original number: 14.7 + 4(21) = 14.7 + 84 = 94 + 4.7 = 98.7.
So 4.7 × 21 = 98.7.
See the pattern?
The 2-digit number chosen to multiply by 4.7 is 62.
Multiply by 7: 7 × 62 = 420 + 14 = 434.
Move decimal point one place left: 43.4.
To this add two times the original number: 43.4 + 4(62) = 43.4 + 240 + 8 = 51.4 + 240 = 291.4.
So 4.7 × 62 = 291.4.
Keep on adding and multiplying left to right and these answers will come quickly and accurately.
v Multiplying a 2-digit number by 4 3/4
Multiply the number by 2.
Add a zero.
Subtract the original number.
Divide by 4.
Example:
If the number chosen to multiply by 4 3/4 is 48:
Multiply by 2: 2 × 48 = 96
Add a zero: 960
Subtract the original number: 960 - 48 = 912
Divide by 4: 912/4 = 228
So 48 × 4 3/4 = 228.
See the pattern?
If the number chosen to multiply by 4 3/4 is 59:
Multiply by 2: 2 × 59 = 118
Add a zero: 1180
Subtract the original number: 1180 - 59 = 1121
Divide by 4: 1121/4 = 280 1/4
So 59 × 4 3/4 = 280 1/4.
v Multiplying a 2-digit number by 5.1
Select a 2-digit number.
Move decimal point one place to the left.
Add this to 5 times original number.
Example:
The 2-digit number chosen to multiply by 5.1 is 21.
Move decimal one place to the left: 2.1.
Add to 5 times original number: 2.1 + 5(21) = 2.1 + 105 = 107.1.
So 5.1 × 21 is 107.1.
See the pattern?
The 2-digit number chosen to multiply by 5.1 is 38.
Move decimal one place to the left: 3.8.
Add to 5 times original number: 3.8 + 5(38) = 3.8 + 150 + 40 = 43.8 + 150 = 193.8
So 5.1 × 38 is 193.8.
Keep practicing adding left to right in easily handled increments.
v Multiplying a 2-digit number by 5.2
Select a 2-digit number.
Multiply the number by 2.
Move decimal point one place to the left.
Add this to 5 times original number.
Example:
The 2-digit number chosen to multiply by 5.2 is 21.
Multiply the number by 2: 2 × 21 = 42.
Move decimal one place to the left: 4.2.
Add to 5 times original number: 4.2 + 5(21) = 4.2 + 105 = 109.2.
So 5.2 × 21 is 109.2.
See the pattern?
The 2-digit number chosen to multiply by 5.2 is 72.
Multiply the number by 2: 2 × 72 = 144.
Move decimal one place to the left: 14.4.
Add to 5 times original number: 14.4 + 5(72) = 14.4 + 350 + 10 = 24.4 + 350 = 374.4.
So 5.2 × 72 is 374.4.
Remember to multiply and add left to right and these answers will come easily.
v Multiplying a 2-digit number by 5.3
Multiply the number by 3.
Move decimal one place left.
Add this to 5 times original number.
Example:
The 2-digit number chosen to multiply by 5.3 is 21.
Multiply by 3: 3 × 21 = 63.
Move decimal one place left: 6.3.
Add to 5 times original number: 6.3 + 5(21) = 6.3 + 105 = 111.3.
So 5.3 × 21 is 111.3.
See the pattern?
The 2-digit number chosen to multiply by 5.3 is 73.
Multiply by 3: 3 × 73 = 210 + 9 = 219.
Move decimal one place left: 21.9.
Add to 5 times original number: 21.9 + 5(73) = 21.9 + 350 + 15 = 365 + 21.9 = 386.9.
So 5.3 × 73 is 386.9.
Remember to multiply and add left to right in small, easy-to-handle increments.
v Multiplying a 2-digit number by 5.6
Multiply the number by 6.
Move decimal point one place to the left.
Add to 5 times the original number.
Example:
The first number to multiply by 5.6 is 21.
Multiply by 6: 6 × 21 = 126.
Move decimal point one place to the left: 12.6.
Add this to 5 times the original number: 12.6 + 5(21) = 12.6 + 100 + 5 = 17.6 + 100 = 117.6.
So 5.6 × 21 = 117.6.
See the pattern?
The second number to multiply by 5.6 is 35.
Multiply by 6: 6 × 35 = 180 + 30 = 210.
Move decimal one place to the left: 21.0.
Add this to 5 times the original number: 21 + 5(35) = 21 + 150 + 25 = 46 + 150 = 196.
So 5.6 × 35 is 196.
With these steps you will be able give correct answers using mental math. And beat the friend using a calculator.
v Multiplying a 2-digit number by 5.7
Multiply the number by 7.
Move decimal point one place to the left.
Add to 5 times the original number.
Example:
The first number to multiply by 5.7 is 21.
Multiply by 7: 7 × 21 = 147.
Move decimal point one place to the left: 14.7.
Add to 5 times the original number: 14.7 + 5(21) = 14.7 + 100 + 5 = 114.7 + 5 = 119.7.
So 5.7 × 21 = 119.7.
See the pattern?
The second number to multiply by 5.7 is 46.
Multiply by 7: 7 × 46 = 280 + 42 = 322.
Move decimal one place to the left: 32.2
Add to 5 times the original number: 32.2 + 5(46) = 32.2 + 200 + 30 = 62.2 + 200 = 262.2.
So 5.7 × 61 = 262.2.
Multiplying and adding left to right is the key to producing these answers using mental math.
v Multiplying a 2-digit number by 5 4/7
Multiply the number by 4.
Add a zero.
Subtract the original number.
Divide by 7.
Example:
If the 2-digit number chosen to multiply by 5 4/7 is 21:
Multiply by 4: 4 × 21 = 84
Add a zero: 840
Subtract the original number:
840 - 21 = 840 - 20 - 1 = 820 - 1 = 819
Divide by 7: 819/7 = 117
So 21 × 5 4/7 = 117.
See the pattern?
If the 2-digit number chosen to multiply by 5 4/7 is 72:
Multiply by 4: 4 × 72 = 288
Add a zero: 2880
Subtract the original number:
2880 - 72 = 2808
Divide by 7: 2808/7 = 401 1/7
So 72 × 5 4/7 = 401 1/7.
v Multiplying a 2-digit number by 6.1
Select a 2-digit number.
Move decimal point one place to the left.
Add this to 6 times original number.
Example:
The 2-digit number chosen to multiply by 6.1 is 21.
Move decimal one place to the left: 2.1.
Add to 6 times original number: 2.1 + 6(21) = 2.1 + 120 + 6 = 128.1.
So 6.1 × 21 is 128.1.
See the pattern?
The 2-digit number chosen to multiply by 6.1 is 91.
Move decimal one place to the left: 9.1.
Add to 6 times original number: 9.1 + 6(91) = 9.1 + 540 + 6 = 15.1 + 540 = 555.1.
So 6.1 × 91 is 555.1.
Using this short procedure you will be able to give these products quickly.
v Multiplying a 2-digit number by 6.4
Select a 2-digit number.
Multiply number by 4.
Move decimal point one place to the left.
Add this to 6 times original number.
Example:
The 2-digit number chosen to multiply by 6.4 is 21.
Multiply number by 4: 4 × 21 = 84.
Move decimal one place to the left: 8.4.
Add to original number: 8.4 + 6(21) = 8.4 + 126 = 134.4.
So 6.4 × 21 is 134.4.
See the pattern?
The 2-digit number chosen to multiply by 6.4 is 72.
Multiply number by 4: 4 × 72 = 280 + 8 = 288.
Move decimal one place to the left: 28.8.
Add seven times original number: 28.8 + 6(72) = 28.8 + 420 + 12 = 40.8 + 420 = 460.8.
So 6.4 × 72 is 460.8.
Multiply and add left to right and you will be able to give these answers quickly.
v Multiplying a 2-digit number by 6.6
Multiply the number by 6.
Move decimal point one place to the left.
Add to 6 times the original number.
Example:
The first number to multiply by 6.6 is 21.
Multiply by 6: 6 × 21 = 126.
Move decimal point one place to the left: 12.6.
Add this to 6 times the original number: 12.6 + 6(21) = 12.6 + 126 = 136 + 2.6 = 138.6.
So 6.6 × 21 = 138.6.
See the pattern?
The second number to multiply by 6.6 is 36.
Multiply by 6: 6 × 36 = 180 + 36 = 216.
Move decimal one place to the left: 21.6.
Add this to 6 times the original number: 21.6 + 6(36) = 21.6 + 180 + 36 = 57.6 + 180 = 230 + 7.6 = 237.6.
So 6.6 × 36 is 237.6.
Multiply and add left to right and these products will be easy as you follow the three steps.
v Multiplying a 2-digit number by 7.1
Select a 2-digit number.
Move decimal point one place to the left.
Add this to 7 times original number.
Example:
The 2-digit number chosen to multiply by 7.1 is 21.
Move decimal one place to the left: 2.1.
Add to 7 times original number: 2.1 + 7(21) = 2.1 + 147 = 149.1.
So 7.1 × 21 is 149.1.
See the pattern?
The 2-digit number chosen to multiply by 7.1 is 53.
Move decimal one place to the left: 5.3.
Add to 7 times original number: 5.3 + 7(53) = 5.3 + 350 + 21 =5.3 + 371 = 376.3.
So 7.1 × 53 is 376.3.
Remember to multiply and add left to right.
v Multiplying a 2-digit number by 7.3
Multiply the number by 3.
Move decimal point one place left.
Add this to 7 times original number.
Example:
The 2-digit number chosen to multiply by 7.3 is 21.
Multiply by 3: 3 × 21 = 63.
Move decimal one place left: 6.3.
Add to 7 times original number: 6.3 + 7(21)= 6.3 + 140 + 7 = 140 + 13.3 = 153.3.
So 7.3 × 21 is 153.3.
See the pattern?
The 2-digit number chosen to multiply by 7.3 is 46.
Multiply by 3: 3 × 46 = 120 + 18 = 138.
Move decimal one place left: 13.8.
Add to 7 times original number: 13.8 + 7(46) = 13.8 + 280 + 42 = 293.8 + 40 + 2 = 333.8 + 2 = 335.8.
So 7.3 × 46 is 335.8.
With some practice you will be producing these products quickly and accurately.
v Multiplying a 2-digit number by 7.4
Select a 2-digit number.
Multiply number by 4.
Move decimal point one place to the left.
Add this to 7 times original number.
Example:
The 2-digit number chosen to multiply by 7.4 is 21.
Multiply number by 4: 4 × 21 = 84.
Move decimal one place to the left: 8.4.
Add to original number: 8.4 + 7(21) = 8.4 + 140 + 7 = 8.4 + 147 = 155.4.
So 7.4 × 21 is 155.4.
See the pattern?
The 2-digit number chosen to multiply by 7.4 is 46.
Multiply number by 4: 4 × 46 = 160 + 24 = 184.
Move decimal one place to the left: 18.4.
Add seven times original number: 18.4 + 7(46) = 18.4 + 280 + 42 = 60.4 + 280 = 340 + 0.4 = 340.4.
So 7.4 × 46 is 340.4.
Remember to add and multiply left to right in small increments easy to handle and you will be giving these products easily.
v Multiplying a 2-digit number by 7.6
Select a 2-digit number.
Multiply number by 6.
Move decimal point one place to the left.
Add this to 7 times original number.
Example:
The 2-digit number chosen to multiply by 7.6 is 21.
Multiply number by 6: 6 × 21 = 126.
Move decimal one place to the left: 12.6.
Add to original number: 12.6 + 7(21) = 12.6 + 147 = 157 + 2.6 = 159.6
So 7.6 × 21 is 159.6.
See the pattern?
The 2-digit number chosen to multiply by 7.6 is 43.
Multiply number by 6: 6 × 43 = 240 + 18 = 258.
Move decimal one place to the left: 25.8.
Add seven times original number: 25.8 + 7(43) = 25.8 + 280 + 21 = 46.8 + 280 = 320 + 6.8 = 326.8
So 7.6 × 43 is 326.8.
Remember to add left to right in easy increments and this procedure will become easy for you.
v Multiplying a 2-digit number by 7.7
Select a 2-digit number.
Multiply the number by 7.
Move decimal point one place to the left.
Add this to 7 times original number (first step answer).
Example:
The 2-digit number chosen to multiply by 7.7 is 21.
Multiply number by 7: 7 × 21 = 147.
Move decimal one place to the left: 14.7.
Add this to 7 times original number (first step answer): 14.7+ 147 = 157 + 4.7 = 161.7.
So 7.7 × 21 is 161.7.
See the pattern?
The 2-digit number chosen to multiply by 7.7 is 82.
Multiply number by 7: 7 × 82 = 560 + 14 = 574.
Move decimal one place to the left: 57.4.
Add this to seven times original number (first step answer): 57.4 + 574 = 627.4 + 7.4 = 631.4.
So 7.7 × 82 is 631.4.
Think left to right when multiplying and adding and these answers should become easy.
v Multiplying a 2-digit number by 8.1
Select a 2-digit number.
Move decimal point one place to the left.
Add this to 8 times original number.
Example:
The 2-digit number chosen to multiply by 8.1 is 21.
Move decimal one place to the left: 2.1.
Add to 8 times original number: 2.1 + 8(21) = 2.1 + 160 + 8 = 170.1.
So 8.1 × 21 is 170.1.
See the pattern?
The 2-digit number chosen to multiply by 8.1 is 62.
Move decimal one place to the left: 6.2.
Add to 8 times original number: 6.2 + 8(62) = 6.2 + 480 + 16 = 480 + 22.6 = 500 + 2.2 = 502.2.
So 8.1 × 62 is 502.2.
Multiply and add left to right in small (easy to handle) increments and you will be giving these products quickly and accurately.
v Multiplying a 2-digit number by 8.3
Multiply the number by 3.
Move decimal one place left.
Add this to 8 times original number.
Example:
The 2-digit number chosen to multiply by 8.3 is 21.
Multiply by 3: 3 × 21 = 63.
Move decimal one place left: 6.3.
Add to 8 times original number: 6.3 + 8(21) = 6.3 + 168 = 174.3.
So 8.3 × 21 is 174.3.
See the pattern?
The 2-digit number chosen to multiply by 8.3 is 54.
Multiply by 3: 3 × 54 = 150 + 12 = 162.
Move decimal one place left: 16.2.
Add to 8 times original number: 16.2 + 8(54) = 16.2 + 400 + 32 = 48.2 + 400 = 448.2.
So 8.3 × 54 is 448.2.
Remember to multiply and add left to right in small increments and you will be giving these products with ease.
v Multiplying a 2-digit number by 8.6
Select a 2-digit number.
Multiply by 6.
Move decimal point one place to the left.
To this add eight times original number.
Example:
The 2-digit number chosen to multiply by 8.6 is 21.
Multiply number by 6: 6 × 21 = 126.
Move decimal one place to the left: 12.6.
To this add eight times the original number: 12.6 + 8(21) = 12.6 + 168 = 178 + 2.6 = 180.6.
So 8.6 × 21 is 180.6.
See the pattern?
The 2-digit number chosen to multiply by 8.6 is 52.
Multiply number by 6: 6 × 52 = 300 + 12 = 312.
Move decimal one place to the left: 31.2.
To this add eight times the original number: 31.2 + 8(52) = 31.2 + 400 + 16 = 47.2 + 400 = 447.2.
So 8.6 × 43 is 447.2.
Remember to add and multiple left to right in manageable parts and you will be able to give these answers quickly and accurately.
v Multiplying a 2-digit number by 9.3
Multiply the number by 3.
Move decimal point one place left.
Add this to nine times the original number.
Example:
The 2-digit number chosen to multiply by 9.3 is 21.
Multiply by 3: 3 × 21 = 63.
Move decimal one place left: 6.3.
Add this to nine times the original number: 6.3 + 9(21) = 6.3 + 189 = 195 + .3 = 195.3.
So 9.3 × 21 is 195.3.
See the pattern?
The 2-digit number chosen to multiply by 9.3 is 61.
Multiply by 3: 3 × 61 = 183.
Move decimal one place left: 18.3.
Add this to 9 times original number: 18.3 + 9(61) = 18.3 + 549 = 559 + 8.3 = 567 + .3 = 567.3.
So 9.3 × 61 is 567.3.
Remember to add left to right in small, easy-to-handle increments, and this procedure will be an easy one.
v Multiplying a 2-digit number by 9.4
Multiply the number by 4.
Move decimal point one place left.
Add this to nine times the original number.
Example:
The 2-digit number chosen to multiply by 9.4 is 21.
Multiply by 4: 4 × 21 = 84.
Move decimal one place left: 8.4.
Add this to nine times the original number: 8.4 + 9(21) = 8.4 + 189 = 197.4.
So 9.4 × 21 is 197.4.
See the pattern?
The 2-digit number chosen to multiply by 9.4 is 52.
Multiply by 4: 4 × 52 = 208.
Move decimal one place left: 20.8.
Add this to 9 times original number: 20.8 + 9(52) = 20.8 + 450 + 18 = 38.8 + 450 = 488.8.
So 9.4 × 52 is 488.8.
v Multiplying a 2-digit number by 9 1/2
Select a 2-digit number.
Multiply the number by 2.
Add one zero.
Subtract the original number.
Divide by 2.
Example:
The 2-digit number chosen to multiply by 9 1/2 is 21.
Multiply by 2: 2 × 21 = 42
Add one zero: 420
Subtract the original number twice: 420 - 21 = 399
Divide by 2: 399/2 = 199.5
So 21 × 9 1/2 = 199.5.
See the pattern?
The 2-digit number chosen to multiply by 9 1/2 is 73.
Multiply by 2: 2 × 73 = 146
Add one zero: 1460
Subtract the original number twice: 1460 - 73 = 1400 - 13 = 1387
Divide by 2: 1387/2 = 693.5
So 73 × 9 1/2 = 693.5.
v Multiplying a 2-digit number by 9.6
Multiply the number by 6.
Move decimal point one place left.
Add this to nine times the original number.
Example:
The 2-digit number chosen to multiply by 9.6 is 21.
Multiply by 6: 6 × 21 = 126.
Move decimal one place left: 12.6.
Add this to nine times the original number: 12.6 + 189 = 2.6 + 199 = 201.6.
So 9.6 × 21 is 201.6.
See the pattern?
The 2-digit number chosen to multiply by 9.6 is 63.
Multiply by 6: 6 × 63 = 360 + 18 = 378.
Move decimal one place left: 37.8.
Add this to 9 times original number: 37.8 + 9(63) = 37.8 + 540 + 27 = 567 + 37.8 = 597 + 7.8 = 604 + 0.8 = 604.8.
So 9.6 × 63 is 604.8.
Remember to multiply and add left to right in easily handled increments. Then you be giving these product with ease.
v Multiplying a 2-digit number by 9.7
Select a 2-digit number.
Multiply by 3.
Move decimal point one place left.
Subtract this from ten times the original number.
Example:
The 2-digit number chosen to multiply by 9.7 is 21.
Multiply by 3: 3 × 21 = 63
Move decimal one place left: 6.3
Subtract this from ten times the original number: 210 - 6.3 = 204 - 0.3 = 203.7
So 9.7 × 21 is 203.7.
See the pattern?
The 2-digit number chosen to multiply by 9.7 is 37.
Multiply by 3: 3 × 37 = 90 + 21 = 111
Move decimal one place left: 11.1
Subtract this from ten times original number: 370 - 11.1 = 360 - 1.1 = 359 - .1 = 358.9
So 9.7 × 37 is 358.9.
Practice subtracting left to right in small increments and you will be giving these answers quickly.
v Multiplying a 2-digit number by 10.4
Multiply the number by 4.
Move decimal one place left.
Add this to 10 times original number.
Example:
The 2-digit number chosen to multiply by 10.4 is 21.
Multiply by 4: 4 × 21 = 84.
Move decimal one place left: 8.4.
Add to 10 times original number: 8.4 + 10(21) = 8.4 + 210 = 218.4.
So 10.4 × 21 is 218.4.
See the pattern?
The 2-digit number chosen to multiply by 10.4 is 82.
Multiply by 4: 4 × 82 = 320 + 8 = 328.
Move decimal one place left: 32.8.
Add to 10 times original number: 32.8 + 10(82) = 32.8 + 820 = 852.8.
So 10.4 × 82 is 852.8.
Add left to right. use these three steps, and you will be giving these products with ease.
Multiplying a 2-digit number by 10.7
Multiply the number by 7.
Move decimal one place left.
Add this to 10 times original number.
Example:
The 2-digit number chosen to multiply by 10.7 is 21.
Multiply by 7: 7 × 21 = 147.
Move decimal one place left: 14.7.
Add to 10 times original number: 14.7 + 10(21) = 14.7 + 210 = 220 + 4.7 = 224.7.
So 10.7 × 21 is 224.7.
See the pattern?
The 2-digit number chosen to multiply by 10.7 is 38.
Multiply by 7: 7 × 38 = 210 + 56 = 266.
Move decimal one place left: 26.6.
Add to 10 times original number: 26.6 + 10(38) = 26.6 + 380 = 400 + 6.6 = 406.6.
So 10.7 × 38 is 406.6.
v Multiplying a 2-digit number by 15
Select a 2-digit number.
Add a zero to it.
Divide it by 2.
Add the number obtained by dividing by 2 to the last number.
Example:
The 2-digit number chosen to multiply by 15 is 62.
Add a zero: 620.
Find half (divide by 2): 620/2 = 310.
Add: 620 + 310 = 930.
So 62 × 15 = 930.
See the pattern?
If the number to be multiplied by 15 is 36:
Add a zero: 360.
Find half (divide by 2): 360/2 = 180.
Add: 360 + 180 = 540.
So 36 × 15 = 540.
v Multiplying a 2-digit number by 18
Select a 2-digit number.
Multiply it by 2.
Add one zero.
Subtract the number obtained by multiplying by 2 from the last number.
Example:
The 2-digit number chosen to multiply by 18 is 28.
28 × 2 = 56 (multiply by 2).
Add one zero: 560.
Subtract: 560 - 56 = 504.
So 18 × 28 = 504.
See the pattern?
If the number to be multiplied by 18 is 46:
2 × 46 = 92 (multiply by 2).
(Think (40 × 2) + (6 × 2) = 80 + 12 = 92)
Add one zero: 920.
Subtract: 920 - 92 = 828
(Subtract in easy increments:
920 - 100 = 820, 820 + 8 = 828)
So 46 × 18 = 828.
Practice this procedure, especially selecting the easiest ways to subtract.
v Multiplying a 2-digit number by 21
Select a 2-digit number.
Multiply the number by 2.
Add one zero.
Add the original number.
Example:
The 2-digit number chosen to multiply by 21 is 23.
Multiply by 2: 2 × 23 = 46.
Add one zero: 460.
Add the original number: 460 + 23 = 483.
So 21 × 23 = 483.
See the pattern?
The 2-digit number chosen to multiply by 21 is 74.
Multiply by 2: 2 × 74 = 148.
Add one zero: 1480.
Add the original number: 1480 + 74 =
1480 + 70 + 4 = 1550 + 4 = 1554.
So 21 × 74 = 1554.
v Multiplying a 2-digit number by 22
Select a 2-digit number.
Multiply it by 2.
The last digit will be the same. _ _ _ X
Add the digits right to left.
Example:
The 2-digit number chosen to multiply by 22 is 78.
78 × 2 = 156 (multiply by 2).
Last digit is 6. _ _ _ 6
Add digits right to left. 6 + 5 = 11 _ _ 1 _
5 + 1 + 1 (carry) = 7 _ 7 _ _
The first digit is the same. 1 _ _ _
So 22 × 78 = 1716.
See the pattern?
The 2-digit number chosen to multiply by 22 is 34.
34 × 2 = 68 (multiply by 2).
Last digit is 8. _ _ 8
Add digits right to left. 8 + 6 = 14 _ 4 _
First digit + carry: 6 + 1 = 7 7 _ _
So 22 × 34 = 748.
Practice getting products by adding digits right to left. Then you will be able to multiply by 22 in your head with ease.
v Multiplying a 2-digit number by 23
Select a 2-digit number.
Add two zeros to number.
Divide by 4.
From this subtract original number twice.
Example:
First pick is 21.
Add two zeros: 2100.
Divide by 4: 2100/4 = 525.
Subtract original number twice: 525 - 21 - 21 = 504 - 21 = 484 - 1 = 483.
So 23 × 21 = 483.
See the pattern?
Next option is 72.
Add two zeros: 7200.
Divide by 4: 7200/4 = 1800.
Subtract original number twice: 1800 - 72 - 72 = 1800 - 144 = 1700 - 44 = 1656.
So 23 × 72 = 1656.
Practice subtracting left to right in easily handled increments and you will be giving these answers with ease.
v Multiplying a 2-digit number by 24
Select a 2-digit number.
Add two zeros to the number.
Divide it by 4.
From this, subtract the original number.
Example:
The 2-digit number chosen to multiply by 24 is 21.
Add two zeros: 2100.
Divide by 4: 2100/4 = 525.
Subtract the original number: 525 - 21 = 504.
So 21 × 24 = 504.
See the pattern?
If the number to be multiplied by 24 is 82:
Add two zeros: 8200.
Divide by 4: 8200/4 = 2050.
Subtract the original number: 2050 - 82 = 2000 - 32 = 1970 - 2 = 1968.
So 82 × 24 = 1968.
Multiplying a 2- or 3-digit number by 25
Select a 2- or 3-digit number. (Choose larger numbers when you feel sure about the method.)
Divide by 4 (or by 2 twice).
Add 2 zeros (or move the decimal point 2 places to the right).
Example:
The 2-digit number chosen to multiply by 25 is 78.
Divide by 2 twice: 78/2 = 39, 39/2 = 19.5
Move the decimal point 2 places to the right: 1950
So 78 × 25 = 1950.
See the pattern?
The 3-digit number chosen to multiply by 25 is 258.
Divide by 2 twice: 258/2 = 129, 129/2 = 64.5
Move the decimal point 2 places to the right: 6450
So 258 × 25 = 6450
v Multiplying a 2-digit number by 26
Select a 2-digit number.
Add two zeros to the number.
Divide it by 4.
Add this to the original number.
Example:
The 2-digit number chosen to multiply by 26 is 21.
Add two zeros: 2100.
Divide by 4: 2100/4 = 525.
Add this to the original number: 525 + 21 = 546.
So 21 × 26 = 546.
See the pattern?
If the number to be multiplied by 26 is 72:
Add two zeros: 7200.
Divide by 4: 7200/4 = 1800.
Add this to the original number: 72 + 1800 = 1872.
So 72 × 26 = 1872.
Use the three easy steps and you will be giving these products using mental math.
v Multiplying a 2-digit number by 27
Select a 2-digit number.
Multiply it by 3.
Add one zero.
Subtract the number obtained by multiplying by 3 from the last number.
Example:
The 2-digit number chosen to multiply by 27 is 42.
3 × 42 = 120 + 6 = 126 (multiply by 3).
Subtract left to right in steps:
1260 - 100 - 20 - 6 = 1160 - 20 - 6 = 1140 - 6 = 1134
or 1260 - 130 + 4 - 1130 + 4 = 1134.
So 42 × 27 = 1134.
See the pattern?
If the number to be multiplied by 27 is 63:
3 × 63 = 189 (multiply by 3).
Add one zero: 1890.
Subtract: 1890 - 189 = 1701
(Subtract left to right in steps:
1890 - 189 = 1890 - 100 - 80 - 9 = 1790 - 80 - 9 = 1710 - 9 = 1701
or 1890 - 190 + 1 = 1700 + 1 = 1701.
So 63 × 27 = 1701.
v Multiplying a 2-digit number by 28
Select a 2-digit number.
Multiply it by 3.
Add one zero.
Subtract the original number twice.
Example:
The 2-digit number chosen to multiply by 28 is 21.
Multiply by 3: 3 × 21 = 63
Add one zero: 630
Subtract the original number twice: 630 - 21 - 21 =
630 - 42 = 590 - 2 = 588
So 28 × 21 = 588.
See the pattern?
If the 2-digit number chosen to multiply by 28 is 67.
Multiply by 3: 3 × 67 = 180 + 21 = 201
Add one zero: 2010
Subtract the original number twice: 2010 - 67 - 67 =
2010 - 134 = 2000 - 124 = 1900 - 24 = 1876
So 28 × 67 = 1876.
Practice subtracting left to right in easy increments and you will give these products with ease.
v Multiplying a 2-digit number by 29
Multiply by 3.
Add one zero.
From this, subtract the original number.
Example:
The 2-digit number chosen to multiply by 29 is 21.
Multiply by 3: 3 × 21 = 63
Add one zero: 630
Subtract original number:
630 - 21 = 610 - 1 = 609
So 21 × 29 = 609.
See the pattern?
The 2-digit number chosen to multiply by 29 is 81.
Multiply by 3: 3 × 81 = 243
Add one zero: 2430
Subtract the original number:
2430 - 81 = 2350 - 1 = 2349
So 81 × 29 = 2349.
v Multiplying a 2-digit number by 30 œ
Divide the number by 2.
Add this to 30 times the original number.
Example:
The 2-digit number chosen to multiply by 30 œ is 21.
Divide by 2: 21/2 = 10 œ.
Add this to 30 times the original number: 10 œ + 30(21) = 10 œ + 630 = 640 œ.
So 21 × 30 œ = 640 œ.
See the pattern?
The 2-digit number chosen to multiply by 30 œ is 52.
Divide by 2: 52/2 = 26.
Add to 30 times 52: 26 + 30(52) = 26 + 1500 + 60 = 86 + 1500 = 1586.
So 52 × 30 œ = 1586.
Remember to add left to right. Then these products will come easily.
v Multiplying a 2-digit number by 31
Select a 2-digit number.
Multiply it by 3.
Add one zero.
Add the original number.
Example:
The 2-digit number chosen to multiply by 31 is 21.
Multiply by 3: 3 × 21 = 63.
Add one zero: 630.
Add original number: 630 + 21 = 651.
So 31 × 21 = 651.
See the pattern?
The 2-digit number chosen to multiply by 31 is 46.
Multiply by 3: 3 × 46 = 120 + 18 = 138.
Add one zero: 1380.
Add original number. 1380 + 46 = 1420 + 6 = 1426.
So 31 × 46 = 1426.
Challenge a friend and BEAT THE CALCULATOR
v Multiplying a 2-digit number by 32
Select a 2-digit number.
Multiply it by 3.
Add one zero.
To this, add the original number twice.
Example:
The 2-digit number chosen to multiply by 32 is 21.
Multiply by 3: 3 × 21 = 63.
Add one zero: 630.
To this, add the original number twice: 630 + 21 + 21 = 630 + 42 = 672.
So 32 × 21 = 672.
See the pattern?
The 2-digit number chosen to multiply by 32 is 81.
Multiply by 3: 3 × 81 = 243.
Add one zero: 2430.
To this, add the original number twice: 2430 + 81 + 81 = 2430 + 162 = 2530 + 62 = 2592.
So 32 × 81 is 2592.
With these three steps you will be giving these answers with ease. Remember to multiply and add from left to right.
v Multiplying a 2-digit number by 33
Select a 2-digit number.
Multiply it by 3.
Add the digits from right to left
(see examples, below).
Example:
The 2-digit number chosen to multiply by 33 is 38.
Multiply by 3: 3 × 38 = 90 + 24 = 114
The last digit is 4: _ _ _ 4.
Add right to left. 4 + 1 = 5: _ _ 5 _
1 + 1 = 2: _ 2 _ _
First digit is 1: 1 _ _ _
So 33 × 38 = 1254.
See the pattern?
If the number to be multiplied by 33 is 82:
Multiply by 3: 3 × 82 = 246
The last digit is 6: _ _ _ 6.
Add right to left. 6 + 4 = 10: _ _ 0 _
4 + 2 + 1 (carry) = 7: _ 7 _ _
First digit is 2: 2 _ _ _
So 33 × 82 = 2706.
v Multiplying a 2-digit number by 34
Select a 2-digit number.
Multiply it by 11 (add the digits from right to left).
Multiply by 3.
Add the original number.
Example:
The 2-digit number chosen to multiply by 34 is 21.
Multiply by 11: 11 × 21 =
- the last digit is 1
- the next digit is 1+2 = 3
- the first digit is 2: 231
Multiply by 3: 3 × 231 = 693
Add the original number: 693 + 21 = 714
So 34 × 21 = 714.
See the pattern?
The 2-digit number chosen to multiply by 34 is 52.
Multiply by 11: 11 × 52 =
- the last digit is 2
- the next digit is 2+5 = 7
- the first digit is 5: 572
Multiply by 3: 3 × 572 = 1500 + 210 + 6 =
1710 + 6 = 1716
Add the original number: 1716 + 52 = 1768
So 34 × 52 = 1768.
v Multiplying a 2-digit number by 35
Select a 2-digit number.
Multiply it by 7.
Divide by 2.
Add a zero.
Example:
The 2-digit number chosen to multiply by 35 is 28.
7 × 28 = 140 + 56 = 196.
Divide by 2: 196/2 = 98.
Add one zero: 980.
So 35 × 28 = 980.
See the pattern?
The 2-digit number chosen to multiply by 35 is 68.
7 × 68 = 420 + 56 = 476.
Divide by 2: 476/2 = 238.
Add one zero: 2380.
So 35 × 68 = 2380.
Practice and you will be able to give these products easily and accurately
v Multiplying a 2-digit number by 36
Select a 2-digit number.
Multiply it by 4.
Add one zero.
Subtract the number obtained by multiplying by 4 from the last number.
Example:
The 2-digit number chosen to multiply by 36 is 52.
4 × 52 = 208 (multiply by 4).
Add one zero: 2080.
2080 - 208 = 1872
(Subtract left to right in steps:
2080 - 200 - 8 = 1880 - 8 = 1872)
So 52 × 36 = 1872.
See the pattern?
If the number to be multiplied by 36 is 86:
4 × 86 = 344 (multiply by 4):
(Think 4 × 86 = (4 × 80) + (4 × 6) = 320 + 24 = 344.)
Add one zero: 3440.
3440 - 344 = 3096
(Subtract left to right in steps:
3440 - 300 - 40 - 4= 3140 - 40 - 4 = 3100 - 4 = 3096)
So 86 × 36 = 3096.
Mastering the subtraction from left to right will enable you to produce these products of 36 and 2-digit numbers quickly and accurately.
v Multiplying a 2-digit number by 37
Select a 2-digit number.
Multiply it by 4.
Add one zero.
Subtract 3 times original number.
Example:
The 2-digit number chosen to multiply by 37 is 21.
Multiply by 4: 4 × 21 = 84.
Add one zero: 840.
Subtract 3 times original number: 840 - 3(21) = 840 - 63 = 800 - 23 = 777
So 37 × 21 is 777.
See the pattern?
If the number to be multiplied by 36 is 52:
Multiply by 4: 4 × 52 = 208.
Add one zero: 2080.
Subtract 3 times original number: 2080 - 3(52) = 2080 - 156 = 1980 - 56 = 1930 - 6 = 1924
So 37 × 52 is 1924.
Practice subtracting left to right in manageable increments and you will give these answers with ease.
v Multiplying a 2-digit number by 38
Select a 2-digit number.
Multiply by 4.
Add one zero.
Subtract the original number twice.
Example:
The 2-digit number chosen to multiply by 38 is 21.
Multiply by 4: 4 × 21 = 84.
Add one zero: 840.
Subtract the original number twice:
840 - 42 = 800 - 2 = 798.
So 21 × 38 = 798.
See the pattern?
The 2-digit number chosen to multiply by 38 is 62.
Multiply by 4: 4 × 62 = 240 + 8 = 248.
Add one zero: 2480.
Subtract the original number twice:
2480 - 124 = 2380 - 24 = 2360 - 4 = 2356.
So 62 × 38 = 2356.
Remember to multiply and subtract left to right and these answers will come easily.
v Multiplying a 2-digit number by 39
Select a 2-digit number.
Multiply by 4.
Add one zero.
Subtract the original number.
Example:
The 2-digit number chosen to multiply by 39 is 21.
Multiply by 4: 4 × 21 = 84.
Add one zero: 840.
Subtract the original number:
840 - 21 = 819.
So 21 × 39 = 819.
See the pattern?
The 2-digit number chosen to multiply by 39 is 71.
Multiply by 4: 4 × 71 = 284.
Add one zero: 2840.
Subtract the original number:
2840 - 71 = 2800 - 31 = 2769.
So 71 × 39 = 2769.
v Multiplying a 2-digit number by 42
Select a 2-digit number.
Multiply the number by four.
Add one zero.
To this add two times the original number.
Example:
The 2-digit number chosen to multiply by 42 is 21.
Multiply by 4: 4 × 21 = 84.
Add one zero: 840.
To this add two times the original number: 840 + 2(21) = 840 + 42 = 882.
So 42 × 21 is 882.
See the pattern?
The 2-digit number chosen to multiply by 42 is 81.
Multiply by 4: 4 × 81 = 324.
Add one zero: 3240.
To this add two times the original number: 3240 + 81 + 81 = 3240 + 160 + 2 = 3400 + 2 = 3402.
So 42 × 81 is 3402.
v Multiplying a 2-digit number by 43
Select a 2-digit number.
Multiply the number by four.
Add one zero.
To this add three times the original number.
Example:
The 2-digit number chosen to multiply by 43 is 21.
Multiply by 4: 4 × 21 = 84.
Add one zero: 840.
To this add three times the original number: 840 + 3(21) = 840 + 63 = 900 + 3 = 903.
So 43 × 21 is 903.
See the pattern?
The 2-digit number chosen to multiply by 43 is 52.
Multiply by 4: 4 × 52 = 200 + 8 = 208.
Add one zero: 2080.
To this add three times the original number: 2080 + 3(52) = 2080 + 150 + 6 = 2180 + 50 + 6 = 2230 + 6 = 2236.
So 43 × 52 is 2236.
Remember to add and multiply left to right in manageable increments, and you will be able to give these products using mental math.
v Multiplying a 2-digit number by 44
Select a 2-digit number.
Multiply it by 4.
Add the digits from right to left.
Example:
The 2-digit number chosen to multiply by 44 is 36.
4 × 36 = 120 + 24 = 144.
The last digit is 4: _ _ _ 4
Add the digits in 144 right to left:
4 + 4 = 8 _ _ 8 _
4 + 1 = 5: _ 5 _ _
First digit is 1: 1 _ _ _
So 44 × 36 = 1584.
See the pattern?
The 2-digit number chosen to multiply by 44 is 69.
4 × 69 = 240 + 36 = 276.
The last digit is 6: _ _ _ 6
Add the digits in 276 right to left:
6 + 7 = 13 _ _ 3 _
7 + 2 + 1 (carry) = 10: _ 0 _ _
First digit + 1 (carry) = 2 + 1 = 3: 3 _ _ _
So 44 × 69 = 3036.
v Multiplying a 2-digit number by 45
Select a 2-digit number.
Multiply it by 5.
Add a zero.
Find the difference between these two numbers
Example:
The 2-digit number chosen to multiply by 45 is 54.
5 × 54 = 270.
Add one zero: 2700.
Subtract: 2700 - 270 = 2430
(subtract left to right: 2700 - 200 - 709 = 2500 - 70 = 2430)
So 54 × 45 = 2430.
See the pattern?
If the number to be multiplied by 45 is 27:
5 × 27 = 135
Think 5 × 27 = (5 × 20) + (5 × 7) = 100 + 35 = 135.
Add one zero: 1350.
Subtract: 1350 - 135 = 1215
(subtract left to right: 1350 - 100 - 30 - 5 =
1250 - 30 - 5 = 1220 - 5 = 1215)
So 27 × 45 = 1215.
Practice - especially the subtraction - and you will become adept at finding these products.
v Multiplying a 2-digit number by 46
Select a 2-digit number.
Multiply it by 5.
Add one zero.
From this, subtract four times the original number.
Example:
The 2-digit number chosen to multiply by 46 is 21.
Multiply by 5: 5 × 21 = 105.
Add one zero: 1050.
From this subtract four times the original number: 1050 - 4(21) = 1050 - 84 = 1000 - 34 = 1070 -4 = 966.
So 21 × 46 = 966.
See the pattern?
If the number to be multiplied by 46 is 52:
Multiply by 5: 5 × 52 = 250 + 10 = 260.
Add one zero: 2600.
From this subtract four times the original number: 2600 - 4(52) = 2600 - (200 + = 2600 - 208 = 2400 - 8 = 2392.
So 52 × 46 = 2392.
Remember to multiply and add from left to right in small, manageable increments.
v Multiplying a 2-digit number by 47
Select a 2-digit number.
Multiply it by 5.
Add one zero.
Subtract 3 times the original number.
Example:
The 2-digit number chosen to multiply by 47 is 21.
Multiply by 5: 5 × 21 = 105.
Subtract 3 times the original number:
1050 - 63 = 1000 - 16 = 987.
So 21 × 47 = 987.
See the pattern?
If the number to be multiplied by 47 is 52:
Multiply by 5: 5 × 52 = 250 + 10 = 260
Add one zero: 2600.
Subtract 3 times the original number:
2600 - 156 = 2500 - 56 = 2444.
So 52 × 47 = 2444.
v Multiplying a 2-digit number by 48
Select a 2-digit number.
Multiply by 5.
Add one zero.
From this, subtract the original number twice.
Example:
The 2-digit number chosen to multiply by 48 is 21.
Multiply by 5: 5 × 21 = 100 + 5 = 105.
Add one zero: 1050.
Subtract the original number twice:
1050 - 2(21) = 1050 - 42 = 1010 - 2 = 1008.
So 21 × 48 = 1008.
See the pattern?
The 2-digit number chosen to multiply by 48 is 51.
Multiply by 5: 4 × 51 = 250 + 5 = 255.
Add one zero: 2550.
Subtract the original number twice:
2550 - 2(51) = 2550 - 102 = 2450 - 2 = 2448.
So 51 × 48 = 2448.
Remember to multiply and subtract from left to right in small and easily handled increments. Then giving these products will come easily.
v Multiplying a 2-digit number by 49 (method 1)
Select a 2-digit number.
Multiply by 5.
Add one zero.
Subtract the original number.
Example:
The 2-digit number chosen to multiply by 49 is 21.
Multiply by 5: 5 × 21 = 105
Add one zero: 1050
Subtract the original number:
1050 - 21 = 1030 - 1 = 1029
So 21 × 49 = 1029.
See the pattern?
The 2-digit number chosen to multiply by 49 is 71.
Multiply by 5: 5 × 71 = 355
Add one zero: 3550
Subtract the original number:
3550 - 71 = 3500 - 21 = 3479
So 71 × 49 = 3479.
v Multiplying a 2-digit number by 49 (method 2)
Select a 2-digit number.
Add two zeros.
Divide by 2.
Subtract original number.
Example:
The 2-digit number chosen to multiply by 49 is 21.
Add two zeros: 2100.
Divide by 2: 2100/2 = 1050.
Subtract original number: 1050 - 21 = 1030 - 1 = 1029.
So 21 × 49 = 1029.
Use the method that is easier for you to use mental math. You will soon be able to get these answers with ease.
v Multiplying a 2-digit number by 51
Select a 2-digit number.
Multiply it by 5.
Add one zero.
Add the original number.
Example:
The 2-digit number chosen to multiply by 51 is 21.
Multiply by 5: 5 × 21 = 105.
Add one zero: 1050.
Add the original number: 1050 + 21 = 1071.
So 51 × 21 = 1071.
See the pattern?
The 2-digit number chosen to multiply by 51 is 61.
Multiply by 5: 5 × 61 = 305.
Add one zero: 3050.
Add the original number: 3050 + 61 = 3100 + 11 = 3111.
So 51 × 61 = 3111.
v Multiplying a 2-digit number by 52
Select a 2-digit number.
Multiply it by 5.
Add one zero.
Add the original number twice.
Example:
The 2-digit number chosen to multiply by 52 is 21.
Multiply by 5: 5 × 21 = 105
Add one zero: 1050
Add the original number twice: 1050 + 21 + 21 =
1050 + 42 = 1092
So 52 × 21 = 1092.
See the pattern?
The 2-digit number chosen to multiply by 52 is 71.
Multiply by 5: 5 × 71 = 355
Add one zero: 3550
Add the original number:
3550 + 71 + 71 = 3550 + 142 =
3550 + 140 + 2 = 3690 + 2 = 3692
So 52 × 71 = 3692.
v Multiplying a 2-digit number by 53
Select a 2-digit number.
Multiply it by 5.
Add one zero.
To this add three times the original number.
Example:
The 2-digit number chosen to multiply by 53 is 21.
Multiply by 5: 5 × 21 = 105.
Add one zero: 1050.
To this add three times the original number: 1050 + 3(21) = 1050 + 63 = 1110 + 3 = 1113.
So 53 × 21 = 1113.
See the pattern?
The 2-digit number chosen to multiply by 53 is 34.
Multiply by 5: 5 × 34 = 150 + 20 =170.
Add one zero: 1700.
To this add three times the original number: 1700 + 3(34) = 1700 + 90 + 12 = 1790 + 12 = 1802.
So 53 × 34 = 1802.
Multiplying left to right will enable you to give these answers quickly and accurately.
v Multiplying a 2-digit number by 54
Select a 2-digit number.
Add one zero to the number.
Subtract the original number.
Multiply this by 6.
Example:
The 2-digit number chosen to multiply by 54 is 21.
Add one zero: 210.
Subtract original number: 210 - 21 = 190 - 1 = 189.
Multiply this by 6: 6 × 189 = 6(190 - 1) = 600 + 540 - 6 = 1140 - 6 = 1134.
So 54 × 21 = 1134.
See the pattern?
The 2-digit number chosen to multiply by 54 is 34.
Add one zero: 340.
Subtract original number: 340 - 34 = 306.
Multiply this by 6: 6 × 306 = 1800 + 36 = 1836.
So 54 × 34 = 1836.
Multiply and add left to right and you will be producing these products pronto.
v Multiplying a 2-digit number by 55 (method 1)
Select a 2-digit number.
Multiply it by 50. (An easy way to do this is to take half of it (divide by 2), then add two zeros.)
Add 1/10 (one-tenth) of the product. (Take off the last zero of the product and add this number to the product.)
Example:
The 2-digit number chosen to multiply by 55 is 28.
50 × 28 = 1400 (half of 28 is 14; add 2 zeros).
1400 + 140 = 1540 (add 1/10 of the product - take off last zero).
So 28 × 55 = 1540.
See the pattern?
If the number to be multiplied by 55 is 62:
50 × 62 = 3100 (half of 62 is 31; add 2 zeros).
3100 + 310 = 3410 (add 1/10 of the product - take off last zero).
So 62 × 55 = 3410.
v Multiplying a 2-digit number by 55 (method 2)
Select a 2-digit number.
Multiply it by 5.
Add the digits from right to left.
Example:
The 2-digit number chosen to multiply by 55 is 42.
Multiply by 5: 5 × 42 = 200 + 10 = 210
The last digit is 0: _ _ _ 0
Add right to left: 0 + 1 = 1 _ _ 1 _
1 + 2 = 3: _ 3 _ _
The first digit is the same: 2 _ _ _
So 55 × 42 = 2310.
See the pattern?
If the 2-digit number chosen to multiply by 55 is 86:
Multiply by 5: 5 × 86 = 400 + 30 = 430
The last digit is 0: _ _ _ 0
Add right to left: 0 + 3 = 3 _ _ 3 _
3 + 4 = 7: _ 7 _ _
The first digit is the same: 4 _ _ _
So 55 × 86 = 4730.
v Multiplying a 2-digit number by 56
Select a 2-digit number.
Multiply number by 6.
Add one zero.
Subtract four times the original number.
Example:
The 2-digit number chosen to multiply by 56 is 21.
Multiply number by 6: 6 × 21 = 126.
Add one zero: 1260.
Subtract four times the original number: 1260 - 4(21) = 1260 - 84 = 1200 - 24 = 1180 - 4 = 1176.
So 56 × 21 is 1176.
See the pattern?
The 2-digit number chosen to multiply by 56 is 46.
Multiply number by 6: 6 × 46 = 276.
Add one zero: 2760.
Subtract four times original number: 2760 - 4(46) = 2760 - 160 - 24 = 2600 - 24 = 2580 - 4 = 2576.
So 56 × 46 is 2576.
v Multiplying a 2-digit number by 57
Select a 2-digit number.
Multiply number by 6.
Add one zero.
Subtract three times the original number.
Example:
The 2-digit number chosen to multiply by 57 is 21.
Multiply number by 6: 6 × 21 = 126.
Add one zero: 1260
Subtract three times the original number: 1260 - 3(21) = 1260 - 63 = 1200 - 3 = 1197.
So 57 × 21 is 1197.
See the pattern?
The 2-digit number chosen to multiply by 57 is 52.
Multiply number by 6: 6 × 52 = 312.
Add one zero: 3120
Subtract three times original number: 3120 - 3(52) = 3120 - 156 = 3020 - 56 = 3000 - 36 = 2964.
So 57 × 52 is 2964.
Practice subtracting left to right in easy increments and this process will become an easy one.
v Multiplying a 2-digit number by 58
Select a 2-digit number.
Multiply it by 6.
Add one zero.
Subtract the original number twice.
Example:
The 2-digit number chosen to multiply by 58 is 21.
Multiply by 6: 6 × 21 = 126.
Add one zero: 1260.
Subtract the original number twice: 1260 - 42 = 1240 - 2 = 1218.
So 58 × 21 = 1218.
See the pattern?
If the 2-digit number chosen to multiply by 58 is 54.
Multiply by 6: 6 × 54 = 300 + 24 = 324.
Add one zero: 3240.
Subtract the original number twice: 3240 - 54 - 54 =
3240 - 108 = 3140 - 8 = 3132.
So 58 × 54 = 3132.
Practice subtracting left to right in easy increments and you will give these products with ease.
v Multiplying a 2-digit number by 59
Select a 2-digit number.
Multiply it by 6.
Add one zero.
Subtract the original number.
Example:
The 2-digit number chosen to multiply by 59 is 21.
Multiply by 6: 6 × 21 = 126
Add one zero: 1260
Subtract the original number: 1260 - 21 = 1240 - 1 = 1239
So 59 × 21 = 1218.
See the pattern?
If the 2-digit number chosen to multiply by 59 is 53.
Multiply by 6: 6 × 53 = 318
Add one zero: 3180
Subtract the original number: 3180 - 53 = 3130 - 3 = 3127
So 59 × 53 = 3127.
Practice subtracting left to right in easy increments and you will give these products with ease.
v Multiplying a 2-digit number by 61
Select a 2-digit number.
Multiply it by 6.
Add one zero.
Add the original number.
Example:
The 2-digit number chosen to multiply by 61 is 21.
Multiply by 6: 6 × 21 = 126.
Add one zero: 1260.
Add the original number: 1260 + 21 = 1281.
So 61 × 21 = 1281.
See the pattern?
The 2-digit number chosen to multiply by 61 is 54.
Multiply by 6: 6 × 54 = 300 + 24 = 324.
Add one zero: 3240.
Add the original number:
3240 + 54 = 3290 + 4 = 3294.
So 61 × 54 = 3294.
v Multiplying a 2-digit number by 62
Select a 2-digit number.
Multiply it by 6.
Add one zero.
Add twice the original number to this.
Example:
The 2-digit number chosen to multiply by 62 is 21.
Multiply by 6: 6 × 21 = 126.
Add one zero: 1260.
Add twice the original number to this:
1260 + 21 + 21 = 1302.
So 62 × 21 = 1302.
See the pattern?
The 2-digit number chosen to multiply by 62 is 72.
Multiply by 6: 6 × 72 = 420 + 12 = 432.
Add one zero: 4320.
Add twice the original number to this:
4320 + 144 = 4420 + 44 = 4464.
So 62 × 72 = 4464.
Multiply and add left to rights in small increments and you will be able to give these products with ease.
Multiplying a 2-digit number by 63
Select a 2-digit number .
Multiply it by 63:
Multiply the 2-digit number by 7, add one zero, and
subtract the smaller number from the larger.
Example:
The 2-digit number chosen to multiply by 63 is 28.
7 × 28 = 196
Add one zero: 1960
Subtract: 1960 - 196 = 1764 (subtract left to right:
1960 - 100 - 90 - 6 = 1860 - 90 - 6 = 1770 - 6 = 1764)
So 28 × 63 = 1764.
See the pattern?
The 2-digit number chosen to multiply by 63 is 83.
7 × 83 = 581 (think (7x80) + (7x3) = 560 + 21 = 581)
Add one zero: 5810
Subtract: 5810 - 581 = 5229 (subtract left to right:
5810 - 500 - 80 - 1 = 5310 - 80 - 1 = 5230 - 1 = 5229)
So 83 × 63 = 5229.
v Multiplying a 2-digit number by 64
Select a 2-digit number.
Multiply it by 11.
Multiply this product by 6.
From this, subtract twice the original number.
Example:
The 2-digit number chosen to multiply by 64 is 21.
Multiply it by 11: 11 × 21 = 231.
Multiply this product by 6: 6 × 231 = 1200 + 186 = 1386.
From this, subtract twice the original number: 1386 - 2(21) = 1386 - 42 = 1346 - 2 = 1344.
So 64 × 21 = 1344.
See the pattern?
The 2-digit number chosen to multiply by 64 is 52.
Multiply it by 11: 11 × 52 = 572.
Multiply this product by 6: 6 × 572 = 3000 + 420 + 12 = 3420 + 12 = 3432.
From this, subtract twice the original number: 3432 - 2(52) = 3432 - 104 = 3332 - 4 = 3328.
So 64 × 52 = 3328.
Practice multiplying by 11. Remember to multiply and add from left to right
v Multiplying a 2-digit number by 65
Select a 2-digit number.
Multiply it by 11 (add digits right to left).
Multiply by 6.
Subtract the original number.
Example:
The 2-digit number chosen to multiply by 65 is 21.
Multiply by 11: right digit is 1, 1+2 = 3,
left digit is 2: 231
Multiply by 6: 6 × 231 = 1200 + 186 = 1386
Subtract the original number: 1386 - 21 = 1365
So 65 × 21 = 1365.
See the pattern?
The 2-digit number chosen to multiply by 65 is 52.
Multiply by 11: right digit is 2, 2+5 = 7,
left digit is 5: 572
Multiply by 6: 6 × 572 = 3000 + 420 + 12 = 3432
Subtract the original number: 3432 - 52 = 3380
So 65 × 52 = 3380.
Practice multiplying by 11 (sum digits right to left) and subtracting left to right and you will be able to give these products easily and accurately.
v Multiplying a 2-digit number by 66
Select a 2-digit number.
Multiply it by 6.
Add the digits from right to left
(see examples, below).
Example:
The 2-digit number chosen to multiply by 66 is 54.
Multiply by 6: 6 × 54 = 300 + 24 = 324
The last digit is 4: _ _ _ 4
Add right to left. 4 + 2 = 6: _ _ 6 _
2 + 3 = 5: _ 5 _ _
First digit is 3: 3 _ _ _
So 66 × 54 = 3564.
See the pattern?
If the number to be multiplied by 66 is 92:
Multiply by 6: 6 × 92 = 540 + 12 = 552
The last digit is 2: _ _ _ 2
Add right to left. 2 + 5 = 7: _ _ 7 _
5 + 5 = 10 (carry 1) : _ 0 _ _
First digit + carry: 5 + 1 = 6: 6 _ _ _
So 66 × 92 = 6072.
v Multiplying a 2-digit number by 67
Select a 2-digit number.
Multiply it by 7.
Add one zero.
From this, subtract three times the original number.
Example:
The 2-digit number chosen to multiply by 67 is 21.
Multiply by 7: 7 × 21 = 147.
Add one zero: 1470.
From this, subtract three times the original number: 1470 - 3(21) = 1470 - 63 = 1407.
So 67 × 21 = 1407.
See the pattern?
The 2-digit number chosen to multiply by 67 is 52.
Multiply by 7: 7 × 52 = 350 + 14 = 364.
Add one zero: 3640.
From this, subtract three times the original number: 3640 - 3(52) = 3640 - 156 = 3540 - 56 =3500 - 16 = 3484.
So 67 × 52 = 3484.
Practice multiplying and adding left to right in small increments.
v Multiplying a 2-digit number by 68
Select a 2-digit number.
Multiply it by 7.
Add one zero.
From this, subtract the original number twice.
Example:
The 2-digit number chosen to multiply by 68 is 21.
Multiply by 7: 7 × 21 = 147.
Add one zero: 1470.
Subtract the original number twice: 1470 - 2(21) = 1470 - 42 = 1430 - 2 = 1428.
So 68 × 21 = 1428.
See the pattern?
If the 2-digit number chosen to multiply by 68 is 64.
Multiply by 7: 7 × 64 = 420 + 28 = 448.
Add one zero: 4480.
Subtract the original number twice: 4480 - 2(64) = 4480 - 128 = 4380 - 28 = 4360 - 8 = 4352.
So 68 × 64 = 4352.
Remember to multiply and subtract left to right in small increments.
v Multiplying a 2-digit number by 69
Select a 2-digit number.
Multiply by 7.
Add one zero.
Subtract the original number.
Example:
The 2-digit number chosen to multiply by 69 is 21.
Multiply by 7: 7 × 21 = 147
Add one zero: 1470
Subtract the original number:
1470 - 21 = 1450 - 1 = 1449
So 21 × 69 = 1449.
See the pattern?
The 2-digit number chosen to multiply by 69 is 53.
Multiply by 7: 7 × 53 = 350 + 21 = 371
Add one zero: 3710
Subtract the original number:
3710 - 53 = 3660 - 3 = 3657
So 53 × 69 = 3657.
v Multiplying a 2-digit number by 70 1/2
Select a 2-digit number.
Divide the number by 2.
Add this to 70 times original number.
Example:
The 2-digit number chosen to multiply by 70 1/2 is 21.
Divide by 2: 21/2 = 10 1/2
Add 70 times original number: 10 1/2 + 70(21) = 10 1/2 + 1400 + 70 = 80 1/2 + 1400 = 1480 1/2
So 70 1/2 × 21 is 1480 1/2.
See the pattern?
The 2-digit number chosen to multiply by 70 1/2 is 72.
Divide by 2: 72/2 = 36
Add to 70 times original number. 36 + 70(72) = 36 + 4900 + 140 = 5040 + 36 = 5076
So 70 1/2 × 72 is 5076.
v Multiplying a 2-digit number by 71
Select a 2-digit number.
Multiply it by 7.
Add one zero.
Add the original number.
Example:
The 2-digit number chosen to multiply by 71 is 21.
Multiply by 7: 7 × 21 = 147.
Add one zero: 1470.
Add the original number: 1470 + 21 = 1491.
So 71 × 21 = 1491.
See the pattern?
The 2-digit number chosen to multiply by 71 is 72.
Multiply by 7: 7 × 72 = 490 + 14 = 500 + 4 = 504.
Add one zero: 5040.
Add the original number: 5040+72 = 5110+2 = 5112.
So 71 × 72 = 5112.
Remember to multiply and add left to right and you will be able to produce these answers quickly.
v Multiplying a 2-digit number by 72
Select a 2-digit number.
Multiply it by 8.
Add one zero.
Subtract the first number from the second.
Example:
The 2-digit number chosen to multiply by 72 is 54.
Multiply by 8: 54 × 8 = 432
(Think: (8 × 50) + (8 × 4) = 400 + 32 = 432)
Add one zero: 4320
Subtract: 4320 - 432 = 3888 (Subtract left to right:
4320 - 400 - 30 - 2 = 3920 - 30 - 2 = 3890 - 2 = 3888)
So 54 × 72 = 3888.
See the pattern?
The 2-digit number chosen to multiply by 72 is 21.
Multiply by 8: 21 × 8 = 168
Add one zero: 1680
Subtract: 1680 - 168 = 1512 (Subtract left to right:
1680 - 100 - 60 - 8 = 1580 - 60 - 8 = 1520 - 8 = 1512)
So 21 × 72 = 1512.
Practice, practice, practice and you will become perfect in your multiplication by 72.
v Multiplying a 2-digit number by 73
Select a 2-digit number.
Multiply number by 7.
Add one zero.
Add original number three times.
Example:
First number picked is 21.
Multiply by 7. 7x21=147
Add one zero. 1470
Add original number three times. 1470 + 63 = 1530 + 3 = 1533
So 73 × 21 is 1533.
See the pattern?
Next number selected is 52.
Multiply by 7. 7 × 52 = 350 + 14 = 364
Add one zero. 3640
Add original number three times. 3640 + 3(52) = 3640 + 156 = 3740 + 56 = 3796
So 73 × 52 is 3796.
Practice, practice, practice and you will become perfect in your multiplication by 73.
v Multiplying a 2- or 3-digit number by 75
Select a 2- or 3-digit number.
Multiply it by 3.
Add two zeros.
Divide by 4.
Example:
The 2-digit number chosen to multiply by 75 is 62.
Multiply by 3: 3 × 62 = 186
Add two zeros: 18600
Divide by 4 (or by 2 twice): 18600/2 = 9300, 9300/2
= 4650
So 75 × 62 = 4650.
See the pattern?
The 3-digit number chosen to multiply by 75 is 136.
Multiply by 3: 3 × 136 = 390 + 18 = 408
Add two zeros: 40800
Divide by 4 (or by 2 twice): 40800/2 = 20400, 20400/2
= 10200
So 75 × 136 = 10200.
Practice and you will be able to give these products quickly. Multiply from left to right for simpler mental math, and divide by 2 twice if division by 4 is not easy
v Multiplying a 2-digit number by 77
Select a 2-digit number.
Multiply it by 7.
Add the digits from right to left
(see examples, below).
Example:
The 2-digit number chosen to multiply by 77 is 42.
Multiply by 7: 7 × 42 = 280 + 14 = 294
The last digit is the same: _ _ _ 4
Add right to left. 4 + 9 = 13: _ _ 3 _
9 + 2 + 1(carry) = 12: _ 2 _ _
First digit + carry: 2 + 1 = 3: 3 _ _ _
So 77 × 42 = 3234.
See the pattern?
If the number to be multiplied by 77 is 84:
Multiply by 7: 7 × 84 = 560 + 28 = 588
The last digit is the same: _ _ _ 8
Add right to left. 8 + 8 = 16: _ _ 6 _
8 + 5 + 1(carry) = 14: _ 4 _ _
First digit + carry: 5 + 1 = 6: 6 _ _ _
So 77 × 84 = 6468.
v Multiplying a 2-digit number by 78
Select a 2-digit number.
Multiply the number by 8.
Add one zero.
From this, subtract the original number twice.
Example:
The 2-digit number chosen to multiply by 78 is 21.
Multiply by 8: 8 × 21 = 160 + 8 = 168.
Add one zero: 1680.
Subtract the original number twice: 1680 - 21 - 21 = 1680 - 42 = 1640 - 2 = 1638.
So 78 × 21 = 1638.
See the pattern?
If the 2-digit number chosen to multiply by 78 is 52.
Multiply by 8: 8 × 52 = 400 + 16 = 416.
Add one zero: 4160.
Subtract the original number twice: 4160 - 52 - 52 = 4160 - 104 = 4060 - 4 = 4056.
So 78 × 52 is 4056.
Multiply and subtract from left to right and these answers will come easily. And correctly.
v Multiplying a 2-digit number by 79
Select a 2-digit number.
Multiply it by 8.
Add one zero.
Subtract that number from the original number.
Example:
The 2-digit number chosen to multiply by 79 is 21.
Multiply by 8: 8 × 21 = 168.
Add one zero: 1680.
Subtract that from the original number: 1680 - 21 = 1660 - 1 = 1659.
So 79 × 21 = 1659.
See the pattern?
The 2-digit number chosen to multiply by 79 is 52.
Multiply by 8: 8 × 52 = 416.
Add one zero: 4160.
Subtract that from the original number: 4160 - 52 = 4108.
So 79 × 52 = 4108.
You will be supplying these answers quickly using these steps. With a little practice you will be speedy and accurate.
v Multiplying a 2-digit number by 80 1/2
Select a 2-digit number.
Divide the number by 2.
Add this to 80 times original number.
Example:
The 2-digit number chosen to multiply by 80 1/2 is 21.
Divide by 2: 21/2 = 10 1/2.
Add 80 times original number: 10 1/2 + 80(21) = 10 1/2 + 1600 + 80 = 1600 + 90 1/2 = 1690 1/2.
So 80 1/2 × 21 is 1690 1/2.
See the pattern?
The 2-digit number chosen to multiply by 80 1/2 is 82.
Divide by 2: 82/2 = 41.
Add to 80 times original number: 41 + 80(82) = 41 + 6400 + 160 = 6400 + 201 = 6601.
So 80 1/2 × 82 is 6601.
Remember to multiply and add left to right and you will be able to give these answers accurately.
v Multiplying a 2-digit number by 81
Select a 2-digit number.
Multiply it by 9.
Add one zero.
Subtract the first number from the second.
Example:
The 2-digit number chosen to multiply by 81 is 31.
Multiply by 9: 9 × 31 = 279
Add one zero: 2790
Subtract: 2790 - 279 = 2511
(Think: 2790 - 200 - 70 - 9 = 2590 - 70 - 9 = 2520 - 9 = 2511)
So 31 × 81 = 2511.
See the pattern?
The 2-digit number chosen to multiply by 81 is 68.
Multiply by 9: 9 × 68 = 612
(Think: 9 × 6 + 9 × 8 = 540 + 72 = 612)
Add one zero: 6120
Subtract: 6120 - 612 = 5508
(Think: 6120 - 600 - 10 - 2 = 5520 - 10 - 2 = 5510 - 2 = 5508)
So 68 × 81 = 5508.
Practice subtracting mentally by doing it in steps from left to right. With that skill you will be able to multiply by 81 quickly.
v Multiplying a 2-digit number by 82
Select a 2-digit number.
Multiply number by 8.
Add one zero.
Add two times the original number.
Example:
The 2-digit number chosen to multiply by 82 is 21.
Multiply by 8: 8 × 21 = 168.
Add one zero: 1680.
Add two times the original number: 1680 + 2(21) = 1680 + 40 + 2 = 1720 + 2 = 1722.
So 82 × 21 = 1722.
See the pattern?
Next selection is 52.
Multiply by 8: 8 × 52 = 400 + 16 = 416.
Add one zero: 4160.
Add two times the original number: 4160 + 2(52) = 4160 + 100 + 4 = 4260 + 4 = 4264.
So 82 × 52 is 4264.
With a little practice you will be giving these products with ease. And correctly, too.
v Multiplying a 2-digit number by 83
Select a 2-digit number.
Multiply it by 8.
Add one zero.
To this add three times the original number.
Example:
The 2-digit number chosen to multiply by 83 is 21.
Multiply by 8: 8 × 21 = 160 + 8 = 168.
Add one zero: 1680.
To this add three times the original number: 1680 + 3(21) = 1680 + 63 = 1700 + 43 = 1743.
So 83 × 21 = 1743.
See the pattern?
The 2-digit number chosen to multiply by 83 is 52.
Multiply by 8: 8 × 52 = 424.
Add one zero: 4240.
To this add three times the original number: 4240 + 3(52) = 4240 + 156 = 4340 + 56 = 4396.
So 83 × 52 = 4396.
Multiply left to right. Add left to right in small manageable increments and you will giving these products quickly.
v Multiplying a 2-digit number by 84
Select a 2-digit number.
Multiply it by 8.
Add one zero.
Add to this four times original number.
Example:
The 2-digit number chosen to multiply by 84 is 21.
Multiply by 8: 8 × 21 = 168.
Add one zero: 1680.
Add to 4 times original number: 1680 + 4(21) = 1680 + 84 = 1760 + 4 = 1764.
So 84 × 21 = 1764.
See the pattern?
Next selection is 52.
Multiply by 8: 8 × 52 = 400 + 16 = 416.
Add one zero: 4160.
Add to 4 times original number: 4160 + 4(52) = 4160 + 208 = 4360 + 8 = 4368.
So 84 × 52 is 4368.
v Multiplying a 2-digit number by 87
Select a 2-digit number.
Multiply it by 9.
Add one zero.
Subtract three times the original number.
Example:
The 2-digit number chosen to multiply by 87 is 21.
Multiply by 9: 9 × 21 = 189.
Add one zero: 1890.
Subtract three times the original number: 1890 - 3(21) = 1890 - 60 - 3 = 1830 - 3 = 1827.
So 87 × 21 = 1827.
See the pattern?
Next selection is 52.
Multiply by 9: 9 × 52 = 450 + 18 = 468.
Add one zero: 4680.
Subtract three times the original number: 4680 - 3(52) = 4680 - 150 - 6 = 4530 - 6 = 4524.
So 87 × 52 is 4524.
Review subtracting and multiplying left to right and these answers should come easily.
v Multiplying a 2-digit number by 88
Select a 2-digit number.
Multiply it by 8.
Add the digits from right to left.
Example:
The 2-digit number chosen to multiply by 88 is 43.
Multiply by 8:
8 × 43 = 320 + 24 = 344.
The last digit is the same: _ _ _ 4
Add the digits in 344 right to left:
4 + 4 = 8 _ _ 8 _
3 + 4 = 7: _ 7 _ _
First digit is the same: 3 _ _ _
So 88 × 43 = 3874.
See the pattern?
The 2-digit number chosen to multiply by 88 is 82.
Multiply by 8:
8 × 82 = 640 + 16 = 656.
The last digit is the same: _ _ _ 6
Add the digits in 656 right to left:
6 + 5 = 11 _ _ 1 _
5 + 6 + 1 (carry) = 12: _ 2 _ _
First digit + 1 (carry) = 6 + 1 = 7: 7 _ _ _
So 88 × 82 = 7216.
v Multiplying a 2-digit number by 90 1/2
Select a 2-digit number.
Divide the number by 2.
Add this to 90 times original number.
Example:
The 2-digit number chosen to multiply by 90 1/2 is 21.
Divide by 2: 21/2 = 10 1/2.
Add 90 times original number: 10 1/2 + 90(21) = 10 1/2 + 1800 + 90 = 100 1/2 + 1800 = 1900 1/2.
So 90 1/2 × 21 is 1900 1/2.
See the pattern?
The 2-digit number chosen to multiply by 90 1/2 is 81.
Divide by 2: 81/2 = 40 1/2.
Add to 90 times original number: 40 1/2 + 90(81) = 40 1/2 + 7200 + 90 = 130 1/2 + 7200 = 7330 1/2.
So 90 1/2 × 81 is 7330 1/2.
Practice some more examples as you multiply and add left to right.
v Multiplying a 2-digit number by 91
Select a 2-digit number.
Multiply it by 9.
Add one zero.
To this, add the original number.
Example:
The 2-digit number chosen to multiply by 91 is 21.
Multiply by 9: 9 × 21 = 189.
Add one zero: 1890.
Add this to the original number: 1890 + 21 = 1910 + 1 = 1911.
So 91 × 21 = 1911.
See the pattern?
The 2-digit number chosen to multiply by 91 is 52.
Multiply by 9: 9 × 52 = 450 + 18 = 468.
Add one zero: 4680.
Add this to the original number: 4680 + 52 = 4730 + 2 = 4732.
So 91 × 52 = 4732.
Multiplying and adding left to right should make easy steps to the correct products
v Multiplying a 2-digit number by 92
Select a 2-digit number.
Multiply it by 9.
Add one zero.
To this, add two times the original number.
Example:
The 2-digit number chosen to multiply by 92 is 21.
Multiply by 9: 9 × 21 = 180 + 9 = 189.
Add one zero: 1890.
To this, add two times the original number: 1890 + 42 = 1930 + 2 = 1932.
So 92 × 21 = 1932.
See the pattern?
The 2-digit number chosen to multiply by 92 is 52.
Multiply by 9: 9 × 52 = 450 + 18 = 460 + 8 = 468.
Add one zero: 4680.
To this, add two times the original number: 4680 + 104 = 4780 + 4 = 4784.
So 92 × 52 = 4784.
Remember to multiply left to right and add in easily handled increments and you will become agile in producing these products.
v Multiplying a 2-digit number by 93
Select a 2-digit number.
Multiply it by 9.
Add one zero.
To this, add three times the original number.
Example:
The 2-digit number chosen to multiply by 93 is 21.
Multiply by 9: 9 × 21 = 180 + 9 = 189.
Add one zero: 1890.
To this, add three times the original number: 1890 + 21 + 21 + 21 = 1890 + 63 = 1950 + 3 = 1953.
So 93 × 21 = 1953.
See the pattern?
The 2-digit number chosen to multiply by 93 is 51.
Multiply by 9: 9 × 51 = 459.
Add one zero: 4590.
To this, add three times the original number: 4590 + 51 + 51 + 51 = 4590 + 153 = 4690 + 53 = 4743.
So 93 × 51 = 4743.
Remember to add left to right. These products will be easily found with some practice.
v Multiplying a 2-digit number by 94
Select a 2-digit number.
Multiply it by 9.
Add one zero.
To this, add four times the original number.
Example:
The 2-digit number chosen to multiply by 94 is 21.
Multiply by 9: 9 × 21 = 180 + 9 = 189.
Add one zero: 1890.
To this, add four times the original number: 1890 + 4(21) = 1890 + 84 = 1974.
So 94 × 21 = 1974.
See the pattern?
The 2-digit number chosen to multiply by 94 is 52.
Multiply by 9: 9 × 52 = 450 + 18 = 468.
Add one zero: 4680.
To this, add four times the original number: 4680 + 4(52) = 4680 + 208 = 4888.
So 94 × 52 = 4888.
Multiply and add left to right and these products should be done easily using mental math.
v Multiplying a 2-digit number by 99
Select a 2-digit number.
Add two zeros to the number.
Subtract the original number from the second number.
Example:
The 2-digit number chosen to multiply by 99 is 79.
Add two zeros: 7900.
Subtract the 2-digit number:
7900 - 79 = 7900 - 80 + 1 = 7820 + 1 = 7821.
So 79 × 99 = 7821.
See the pattern?
The 2-digit number chosen to multiply by 99 is 42.
Add two zeros: 4200.
Subtract the 2-digit number:
4200 - 42 = 4200 - 40 - 2 = 4160 - 2 = 4158.
So 42 × 99 = 4158
v Multiplying a 3-digit number by 99
Select a 3-digit number.
Subtract the 1st digit plus 1 from the number.
X X X _ _
Subtract the last two digits of the number from 100.
_ _ _ X X
Example:
The 3-digit number chosen to multiply by 99 is 274.
Subtract the 1st digit + 1 from the number:
274 - 3 = 271 : 2 7 1 _ _
Subtract the last two digits from 100:
100 - 74 = 26: _ _ _ 2 6.
So 274 × 99 = 27126.
See the pattern?
The 3-digit number chosen to multiply by 99 is 924.
Subtract the 1st digit + 1 from the number:
924 - 10 = 914 : 9 1 4 _ _
Subtract the last two digits from 100:
100 - 24 = 76: _ _ _ 7 6.
So 924 × 99 = 91476.
v Multiplying a 2-digit number by 101
Select a 2-digit number .
Write it twice!
Examples:
47 × 101 = 4747.
38 × 101 = 3838.
96 × 101 = 9696.
v Multiplying a 3-digit number by 101
Select a 3-digit number .
The sum of the first and third digits will be the middle digit: _ _ X _ _.
The first two digits plus the carry will be the first digits: X X _ _ _.
The last two digits of the number will be the last digits: _ _ _ X X.
Example:
The number chosen is 318.
3 + 8 = 11 (sum of first and third digits):
_ _ 1 _ _ (keep carry, 1)
31 + 1 = 32 (first two digits plus carry):
3 2 _ _ _.
The last two digits are the same:
_ _ _ 1 8.
So 318 × 101 = 32118.
See the pattern?
If the number chosen is 728:
7 + 8 = 15 (sum of first and third digits):
_ _ 5 _ _ (keep carry, 1)
72 + 1 = 73 (first two digits plus carry):
7 3 _ _ _.
The last two digits are the same:
_ _ _ 2 8.
So 728 × 101 = 73528.
v Multiplying a repeating 1's number by the same number of 9's
Choose a repeating 1's number (111, etc.)
Multiply it by the same number of 9's (999, etc.)
The product is made up of:
one fewer 1 than repeating 1's in the original number
one zero
one fewer 8 than repeating 1's in the original number
a final 9.
Example:
If the first number is 111:
Multiply by 999. The product is:
one fewer 1 than originally: 11
one zero: 0 one fewer 8 than repeating 1's in the original number: 88
a final 9: 9
So 111 × 999 = 110889.
See the pattern?
If the first number is 11111:
Multiply by 99999. The product is 1111088889.
So 11111 × 99999 = 1111088889.
v Multiplying a repeating 2's number by the same number of 5's
Choose a repeating 2's number (222, etc.) with a maximum of 9 digits
Multiply it by the same number of 5's (555, etc.)
The product is a sequence beginning with 1 up to the number of repeating 2's, then back down to 0.
Example:
If the first number is 222:
Multiply by 555.
The product is 123210.
See the pattern?
If the first number is 22222:
Multiply by 55555.
The product is 1234543210.
This pattern is easily seen. To make it less obvious add a step after the multiplying, such as 'add 22', and change this number when you wish. It may disguise the pattern.
v Multiplying a repeating 3's number by the same number of 6's
Choose a repeating 3's number (333, etc.)
Multiply it by the same number of 6's (666, etc.)
The product is:
One fewer 2 than there were digits in the original number.
One 1.
One fewer 7 than digits in original number.
One 8.
Example:
If the first number is 333:
Multiply by 666.
The product is:
One fewer 2 than digits in original number: 22
One 1: 221
One fewer 7 than digits in original number: 22177
One 8: 221778
So 333 × 666 is 221778.
See the pattern?
If the first number is 33333:
Multiply by 66666.
The product is:
One fewer 2 than digits in original number: 2222
One 1: 22221
One fewer 7 than digits in original number: 222217777
One 8: 2222177778
So 33333 × 66666 is 2222177778.
v Multiplying a repeating 4's number by 15
Choose a repeating 4's number (4444, etc.)
Multiply it by 15
The product is:
- the first digits are 6's -- the same number as the repeating 4's in the original number
- the last digit is 0
Example:
If the first number is 44444:
The product is:
- the first digits are 6's -- the same number as the repeating 4's in the original number: 66666.
- the last digit is 0: 0.
So 15 × 44444 = 666660.
See the pattern?
Next pick is 444444444:
The product is:
- the first digits are 6's -- the same number as the repeating 4's in the original number: 666666666.
- the last digit is 0: 0.
So 15 × 444444444 = 6666666660.
With this easy rule you will be giving these products at once.
v Multiplying a repeating 5's number by 28
Choose a repeating 5's number (555, etc.)
Multiply it by 28
The product is:
- the first two digits are 15
- the next digits are repeating 2's (two fewer than repeating 2's in the original number)
- the last two digits are 40
Example:
The number chosen to multiply by 28 is 55555.
Multiply by 28. The product is:
- the first two digits are 15
- the next digits are repeating 2's (two fewer than repeating 2's in the original number): 555.
- the last two digits are 40: 40.
So 28 × 55555 is 1555540.
See the pattern?
The number chosen to multiply by 28 is 555555555.
Multiply by 28. The product is:
- the first two digits are 15: 15.
- the next digits are repeating 2's (two fewer than repeating 2's in the original number): 5555555.
- the last two digits are 40: 40.
So 28 × 555555555 is 15555555540.
v Multiplying a repeating 6's number by the same number of 9's
Choose a repeating 6's number (666, etc.)
Multiply it by the same number of 9's (999, etc.)
The product is made up of:
one fewer 6 than repeating 6's in the original number
one 5
one fewer 3 than repeating 6's in the original number
one 4.
Example:
If the first number is 666:
Multiply by 999. The product is:
one fewer 6 than originally: 66
one 5: 5
one fewer 3 than originally: 33
one 4.
So 666 × 999 = 665334.
See the pattern?
If the first number is 66666:
Multiply by 99999. The product is:
one fewer 6 than originally: 6666
one 5: 5
one fewer 3 than originally: 3333
one 4.
So 66666 × 99999 = 6666533334.
v Multiplying a repeating 7's number by the same number of 9's
Choose a repeating 7's number (777, etc.)
Multiply it by the same number of 9's (999, etc.)
The product is made up of: one fewer 7 than there are digits in the number
one six
the same number of 2's as in the first step
one three.
Example:
If the first number is 777:
Multiply by 999. The product is: 776223
So 777 × 999 = 776223.
See the pattern?
If the first number is 77777:
Multiply by 99999. The product is 7777622223
So 77777 × 99999 = 7777622223
