Some division patterns are given below. You may practise these. If you find any irregularity, you may send suggestions. So, now enjoy the world of division.
v Dividing a 2-digit number by 1 1/9
Select a 2-digit number.
Multiply by 9.
Move the decimal point one place to the left.
Example:
The 2-digit number chosen to divide by 1 1/9 is 24.
Multiply by 9: 9 × 24 = 180 + 36 = 216
Move the decimal point one place to the left: 21.6
So 24 divided by 1 1/9 = 21.6.
See the pattern?
The 2-digit number chosen to divide by 1 1/9 is 91.
Multiply by 9: 9 × 91 = 819
Move the decimal point one place to the left: 81.9
So 91 divided by 1 1/9 = 81.9.
v Dividing a 2-digit number by 1 1/8
Select a 2-digit number.
Multiply by 8.
Divide the result by 9.
Example:
The 2-digit number chosen to divide by 1 1/8 is 42.
Multiply by 8: 8 × 42 = 320 + 16 = 336
Divide by 9: 336/9 = 37 1/3
So 42 divided by 1 1/8 = 37 1/3.
See the pattern?
The 2-digit number chosen to divide by 1 1/8 is 71.
Multiply by 8: 8 × 71 = 568
Divide by 9: 568/9 = 63 1/9
So 71 divided by 1 1/8 = 63 1/9.
v Dividing a 2-digit number by 1 2/7
Multiply the number by 7.
Divide by 9.
Example:
If the 2-digit number chosen to divide by 1 2/7 is 32:
Multiply by 7: 7 × 32 = 210 + 14 = 224
Divide by 9: 224/9 = 24 8/9
So 32 / 1 2/7 = 24 8/9.
See the pattern?
If the number to be divided by 1 2/7 is 61:
Multiply by 7: 7 × 61 = 427
Divide by 9: 427/9 = 47 4/9
So 61 / 1 2/7 = 47 4/9.
Answers found by using a calculator will produce repeating decimals rounded by the calculator.
v Dividing a 2-digit number by 1 3/5
Select a 2-digit number.
Multiply it by 5.
Divide by 8.
Example:
The number chosen to divide by 1 3/5 is 42.
Multiply by 5: 5 × 42 = 210
Divide by 8: 210/8 = 26 1/4
So 42 divided by 1 3/5 = 26 1/4.
See the pattern?
If the number chosen to divide by 1 3/5 is 61:
Multiply by 5: 5 × 61 = 305
Divide by 8: 305/8 = 38 1/8
So 61 divided by 1 3/5 = 38 1/8.
v Dividing a 2-digit number by 1 4/5
Select a 2-digit number.
Multiply it by 5.
Divide by 9.
Example:
The number chosen to divide by 1 4/5 is 32.
Multiply by 5: 5 × 32 = 150 + 10 = 160
Divide by 9: 160/9 = 17 7/9
So 32 divided by 1 4/5 = 17 7/9.
See the pattern?
If the number chosen to divide by 1 4/5 is 61:
Multiply by 5: 5 × 61 = 305
Divide by 9: 305/9 = 33 8/9
So 61 divided by 1 4/5 = 33 8/9.
Your answers will be exact, while others who are using calculators will obtain quotients that are repeating decimals.
v Dividing a 2-digit number by 2 2/9
Select a 2-digit number.
Multiply by 9.
Divide the product by 2.
Move the decimal point one place to the left.
Example:
The 2-digit number chosen to divide by 2 2/9 is 31.
Multiply by 9: 9 × 31 = 279
Divide by 2: 279/2 = 139 1/2
Move the decimal point one place to the left: 13.9 1/2
So 31 divided by 2 2/9 = 13.9 1/2.
See the pattern?
The 2-digit number chosen to divide by 2 2/9 is 71.
Multiply by 9: 9 × 71 = 639
Divide by 2: 639/2 = 319 1/2
Move the decimal point one place to the left: 31.9 1/2
So 71 divided by 2 2/9 = 31.9 1/2.
v Dividing a 2- or 3-digit number by 2 1/2
Select a 2- or 3-digit number.
Multiply by 4 (or by 2 twice).
Move the decimal point one place to the left.
Example:
The 2-digit number chosen to divide by 2 1/2 is 86.
Multiply by 4: 4 × 80 + 4 × 6 = 320 + 24 = 344
Move the decimal point one place to the left: 34.4
So 86 divided by 2 1/2 = 34.4.
See the pattern?
The 3-digit number chosen to divide by 2 1/2 is 624.
Multiply by 2: 2 × 624 = 1248
Multiply by 2: 2 × 1248 = 2400 + 96 = 2496
Move the decimal point one place to the left: 249.6
So 624 divided by 2 1/2 = 249.6.
Multiply by 4 when this is easy; otherwise use two steps and multiply by 2 twice.
v Dividing a 2-digit number by 2 2/3
Select a 2-digit number.
Multiply by 3.
Divide by 8.
Example:
The 2-digit number chosen to divide by 2 2/3 is 32.
Multiply by 3: 3 × 32 = 96
Divide by 8: 96/8 = 12
So 32 divided by 2 2/3 = 12.
See the pattern?
The 2-digit number chosen to divide by 2 2/3 is 61.
Multiply by 3: 3 × 61 = 183
Divide by 8: 183/8 = 22 7/8
So 61 divided by 2 2/3 = 22 7/8.
Using this method, your answers will be exact. Those using calculators will only get approximations.
v Dividing a 2- or 3-digit number by 3 1/3
Select a 2- or 3-digit number.
Multiply by 3.
Move the decimal point one place to the left.
Example:
The 2-digit number chosen to divide by 3 1/3 is 72.
Multiply by 3: 72 × 3 = 216
Move the decimal point one place to the left: 21.6
So 72 divided by 3 1/3 = 21.6.
See the pattern?
The 2-digit number chosen to divide by 3 1/3 is 48.
Multiply by 3: 48 × 3 = 120 + 24 = 144
Move the decimal point one place to the left: 14.4
So 48 divided by 3 1/3 = 14.4.
After practicing, choose larger numbers. Insist on exact answers (you won't get an exact answer if you divide by 3.3 using a calculator). Multiply from left to right in steps and impress your friends with your mental powers.
v Dividing a 2-digit number by 3 4/7
Select a 2-digit number.
Multiply it by 7.
Multiply the product by 4.
Move the decimal point 2 places to the left.
Example:
The number chosen to divide by 3 4/7 is 21.
Multiply by 7: 7 × 21 = 147
Multiply by 4: 4 × 147 = 400 + 160 + 28 = 588
Move the decimal point 2 places to the left: 5.88
So 21 divided by 3 4/7 = 5.88.
See the pattern?
The number chosen to divide by 3 4/7 is 51.
Multiply by 7: 7 × 51 = 357
Multiply by 4: 4 × 357 = 1200 + 200 + 28 = 1428
Move the decimal point 2 places to the left: 14.28
So 51 divided by 3 4/7 = 14.28.
v Dividing a 2-digit number by 4 1/6
Select a 2-digit number.
Multiply by 6.
Multiply this product by 4.
Move the decimal point 2 places to the left.
Example:
The 2-digit number chosen to divide by 4 1/6 is 24.
Multiply by 6: 6 × 24 = 120 + 24 = 144
Multiply by 4: 4 × 144 = 400 + 160 + 16 = 576
Move the decimal point 2 places to the left: 5.76
So 24 divided by 4 1/6 = 5.76.
See the pattern?
The 2-digit number chosen to divide by 4 1/6 is 61.
Multiply by 6: 6 × 61 = 366
Multiply by 4: 4 × 366 = 1200 + 240 + 24 = 1464
Move the decimal point 2 places to the left: 14.64
So 61 divided by 4 1/6 = 14.64.
v Dividing a 2-digit number by 4 4/9
Select a 2-digit number.
Multiply by 9.
Divide the product by 4.
Move the decimal point one place to the left.
Example:
The 2-digit number chosen to divide by 4 4/9 is 31.
Multiply by 9: 9 × 31 = 279
Divide by 4: 279/4 = 69 3/4
Move the decimal point one place to the left: 6.9 3/4
So 31 divided by 4 4/9 = 6.9 3/4.
See the pattern?
The 2-digit number chosen to divide by 4 4/9 is 52.
Multiply by 9: 9 × 52 = 450 + 18 = 468
Divide by 4: 468/4 = 117
Move the decimal point one place to the left: 11.7
So 52 divided by 4 4/9 = 11.7.
v Dividing a 2-digit number by 5 5/7
Select a 2-digit number.
Multiply by 7.
Divide by 4.
Move the decimal point one place to the left.
Example:
The 2-digit number chosen to divide by 5 5/7 is 21.
Multiply by 7: 7 × 21 = 147
Divide by 4: 147/4 = 36 3/4
Move the decimal point one place to the left: 3.6 3/4
So 21 divided by 5 5/7 = 3.675.
See the pattern?
The 2-digit number chosen to divide by 5 5/7 is 52.
Multiply by 7: 7 × 52 = 350 + 14 = 364
Divide by 4: 364/4 = 91
Move the decimal point one place to the left: 9.1
So 52 divided by 5 5/7 = 9.1.
v Dividing a 2-digit number by 6 2/3
Select a 2-digit number.
Multiply by 15.
Move the decimal point two places to the left.
Example:
The 2-digit number chosen to divide by 6 2/3 is 21.
Multiply by 15: 15(21) = 210 + 105 = 310 + 5 = 315.
Move the decimal point two places to the left: 3.15.
So 21 divided by 6 2/3 = 3.15.
See the pattern?
The 2-digit number chosen to divide by 6 2/3 is 86.
Multiply by 15: 15(86) = 860 + 400 + 30 = 1260 + 30 = 1290.
Move the decimal point two places to the left: 12.9.
So 86 divided by 6 2/3 = 12.9.
v Dividing a 2-digit number by 7 1/2
Select a 2-digit number.
Multiply it by 4 (or by 2 twice).
Divide by 3.
Move the decimal point 1 place to the left.
Example:
The 2-digit number chosen to divide by 7 1/2
is 42.
Multiply by 4: 42 × 4 = 168
Divide by 3: 168/3 = 56
Move the decimal point 1 place to the left: 5.6
So 42 divided by 7 1/2 = 5.6.
See the pattern?
The 2-digit number chosen to divide by 7 1/2
is 93.
Multiply by 4: 93 × 4 = 360 + 12 = 372
Divide by 3: 372/3 = 124
Move the decimal point 1 place to the left: 12.4
So 93 divided by 7 1/2 = 12.4.
Practice and you will soon be cranking out these quotients with speed and accuracy
v Dividing a 2-digit number by 8 1/3
Select a 2-digit number.
Multiply by 6.
Divide by 5.
Move the decimal point one place to the left.
Example:
The 2-digit number chosen to divide by 8 1/3 is 21.
Multiply by 6: 6 × 21 = 126
Divide by 5: 126/5 = 25.2
Move the decimal point one place to the left: 2.52
So 21 divided by 8 1/3 = 2.52.
See the pattern?
The 2-digit number chosen to divide by 8 1/3 is 51.
Multiply by 6: 6 × 51 = 306
Divide by 5: 306/5 = 61.2
Move the decimal point one place to the left: 6.12
So 51 divided by 8 1/3 = 6.12.
v Dividing a 2-digit number by 12 1/2
Select a 2-digit number.
Multiply it by 8 (or by 2 three times).
Move the decimal point 2 places to the left.
Example:
The 2-digit number chosen to divide by 12 1/2
is 78.
Multiply by 2 three times:
2 × 78 = 156
2 × 156 = 312
2 × 312 = 624
Move the decimal point 2 places to the left: 6.24
So 78 divided by 12 1/2 = 6.24.
See the pattern?
If the 2-digit number chosen to divide by 12 1/2
is 91:
Double three times: 182, 364, 728.
Move the decimal point 2 places to the left: 7.28
So 91 divided by 12 1/2 = 7.28.
Practice doubling numbers and this should become a fast calculation for you.
v Dividing a 2-digit number by 15
Select a 2-digit number.
Multiply it by 2.
Divide the result by 3.
Move the decimal point 1 place to the left.
Example:
The 2-digit number chosen to divide by 15 is 68.
Multiply by 2: 2 × 68 = 120 + 16 = 136
Divide the result by 3: 136/3 = 45 1/3
Move the decimal point 1 place to the left: 4.5 1/3
So 68 divided by 15 = 4.5 1/3.
See the pattern?
The 2-digit number chosen to divide by 15 is 96.
Multiply by 2: 2 × 96 = 180 + 12 = 192
Divide the result by 3: 192/3 = 64
Move the decimal point 1 place to the left: 6.4
So 96/15 = 6.4.
With this method you will be able to divide numbers by 15 with two quick calculations - one multiplication and one division.
v Dividing a 2- or 3-digit number by 25
Select a 2-digit number. (Choose larger numbers when you feel sure about the method.)
Multiply by 4 (or by 2 twice).
Move the decimal point two places to the left.
Example:
The 2-digit number chosen to divide by 25 is 38.
Multiply by 4: 4 × 38 = 4 × 30 = 120 + 32 = 152.
Move the decimal point 2 places to the left: 1.52
So 38 divided by 25 = 1.52.
See the pattern?
The 3-digit number chosen to divide by 25 is 641.
Multiply by 2 twice:
2 × 64 = 1282.
2 × 1282 = 2400 + 164 = 2564.
Move the decimal point 2 places to the left: 25.64.
So 641 divided by 25 = 25.64.
Practice multiplying left to right or by 2 twice and you will be able to do these computations quickly and accurately.
v Dividing a 2- or 3-digit number by 35
Select a 2-digit number. (Choose larger numbers when you feel sure about the method.)
Multiply by 2.
Divide the resulting number by 7.
Move the decimal point 1 place to the left.
Example:
If the number chosen to divide by 35 is 61:
Multiply by 2: 2 × 61 = 122.
Divide by 7: 122/7 = 17 3/7
Move the decimal point 1 place to the left: 1.7 3/7
So 61 divided by 35 = 1.7 3/7.
See the pattern?
If the number chosen to divide by 35 is 44:
Multiply by 2: 2 × 44 = 88
Divide by 7: 88/7 = 12 4/7
Move the decimal point 1 place to the left: 1.2 4/7
So 44 divided by 35 = 1.2 4/7.
Division done by calculator will give repeating decimals (unless the original number is a multiple of 7), truncated by the limits of the display. The exact answer must be expressed as a mixed number.
v Dividing a 2-digit number by 45
Select a 2-digit number.
Divide by 5.
Divide the resulting number by 9.
Example:
If the number chosen to divide by 45 is 32:
Divide by 5: 32/5 = 6.4
Divide the result by 9: 6.4/9 = .71 1/9
So 32 divided by 45 = .71 1/9.
See the pattern?
If the number chosen to divide by 45 is 61:
Divide by 5: 61/5 = 12.2
Divide the result by 9: 12.2/9 = 1.35 5/9
So 61 divided by 45 = 1.35 5/9.
v Dividing a 2- or 3-digit number by 75
Select a 2-digit number. (Choose larger numbers when you feel sure about the method.)
Multiply by 4 (or by 2 twice).
Move the decimal point two places to the left.
Divide by 3 (express remainder as a fraction).
Example:
The 2-digit number chosen to divide by 75 is 82.
Multiply by 4: 4 × 82 = 328.
Move the decimal point 2 places to the left: 3.28
Divide by 3: 3.28/3 = 1.09 1/3
So 82 divided by 75 = 1.09 1/3.
See the pattern?
The 3-digit number chosen to divide by 75 is 631.
Multiply by 4 (multiply left to right):
4 × 631 = 2400 + 120 + 4 = 2520 + 4 = 2524.
Move the decimal point 2 places to the left: 25.24.
Divide by 3: 25.24/3 = 8.41 1/3
So 631 divided by 75 = 8.41 1/3.
Practice multiplying left to right so you can do it mentally. You will be able to divide numbers by 75 quickly and accurately.
v Dividing a 2-digit number by 375
Select a 2-digit number.
Multiply by 8.
Divide the product by 3 (express remainder as a fraction).
Move the decimal point three places to the left.
Example:
The number chosen to divide by 375 is 32.
Multiply by 8: 8 × 32 = 240 + 16 = 256
Divide by 3: 256/3 = 85.3 1/3
Move the decimal point 3 places to the left: .0853 1/3
So 32 divided by 375 = .0853 1/3.
See the pattern?
The number chosen to divide by 375 is 61.
Multiply by 8: 8 × 61 = 480 + 8 = 488
Divide by 3: 488/3 = 162 2/3
Move the decimal point 3 places to the left: .162 2/3
So 61 divided by 375 = .162 2/3.
v Dividing a 2-digit number by 625
Select a 2-digit number.
Multiply by 8.
Divide the product by 5.
Move the decimal point 3 places to the left.
Example:
The 2-digit number chosen to divide by 625 is 65.
Multiply by 8: 8 × 65 = 480 + 40 = 520
Divide by 5: 520/5 = 104
Move the decimal point 3 places to the left: .104
So 65 divided by 625 = .104.
See the pattern?
The 2-digit number chosen to divide by 625 is 32.
Multiply by 8: 8 × 32 = 240 + 16 = 256
Divide by 5: 256/5 = 51.2
Move the decimal point 3 places to the left: .0512
So 32 divided by 625 = .0512.
v Dividing a 2-digit number by 875
Select a 2-digit number.
Multiply it by 8.
Divide by 7.
Move the decimal point 3 places to the left.
Example:
The 2-digit number chosen to divide by 875
is 31.
Multiply by 8: 31 × 8 = 248
Divide by 7: 248/7 = 35 3/7
Move the decimal point 3 places to the left: .035 3/7
So 31 divided by 875 = .035 3/7.
See the pattern?
The 2-digit number chosen to divide by 875
is 63.
Multiply by 8: 8 × 63 = 480 + 24 =
480 + 20 + 4 = 500 + 4 = 504
Divide by 7: 504/7 = 72
Move the decimal point 3 places to the left: .072
So 63 divided by 875 = .072.
