Division Shortcuts - PowerPoint PPT Presentation

Title: Division Shortcuts


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Cheat codes for solving division problems without
the use of a calculator

• Division Shortcuts

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If the last digit is even, the number is
divisible by 2.
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2,245,432 is even therefore is divisible by 2
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If the sum of the digits is divisible by 3, the
number is also.
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For example 12,123 (121239) 9 is divisible
by 3, therefore 12,123 is too!
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If the last two digits form a number divisible by
4, the number is also.
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For example 358,912 ends in 12 which is
divisible by 4, thus so is 358,912
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If the last digit is a 5 or a 0, the number is
divisible by 5.
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If the number is divisible by both 3 and 2, it
is also divisible by 6.
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Take the last digit, double it, and subtract it
from the rest of the number if the answer is
divisible by 7 (including 0), then the number
is also.
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Is 854 divisible by 7?Number A 85Number B
4Number A (2 Number B) 85 - 2 4 7777
is most certainly divisible by 7, therefore 854
is also divisible by 7
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If the last three digits form a number
divisible by 8, then so is the whole number.
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Example 6,008 - The last 3 digits are divisible
by one, therefore, so is 6,008.
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If the sum of the digits is divisible by 9, the
number is also.
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• Example 357 (Double the 7 to get 14. Subtract 14
  from 35 to get 21 which is divisible by 7 and we
  can now say that 357 is divisible by 7.

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For example 43,785 (4378527) 27 is
divisible by 9, therefore 43,785 is too!
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If the number ends in 0, it is divisible by 10.
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Alternately add and subtract the digits from left
to right. If the result (including 0) is
divisible by 11, the number is also.
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Example to see whether 365,167,484 is divisible
by 11, start by subtracting 3-65-16-74-84
0 therefore 365,167,484 is divisible by 11.
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If the number is divisible by both 3 and 4, it
is also divisible by 12.
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If the sum of the digits in the odd places
subtracted by the sum of the digits in the even
places is divisible by 13
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13- Delete the last digit from the number, then
subtract 9 times the deleted digit from the
remaining number. If what is left is divisible by
13, then so is the original number.
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For example 16,313,349 1631334 -81
1631253 163125 27 163098 16309 72
16237 1623 63 1560 156 0 156 13 12
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25 - if the number formed by the last 2 digits
is divisible by 25 or both are zeros 25, 50, 75,
00
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125- if the last three digits are divisible by
125 or all are zeros example 125, 250, 375,
500, 625, 750, 875, 1,000
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To divide by 10 or a power of 10, move the
decimal to the left or right Example 2,340 10
234 ( 1 place left) 234 100 2.34
234 0.01 23,400 2.34
0.1 23.4
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To divide by 5- multiply by 2 and divide by 10.
If a zero can be removed, divide first. Example
240 5 24 x 2 48 1,200 5 120 x 2 240
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• If the last digit is not a zero, multiply first,
  then move the decimal one place to the left.
• Example 23 5
• 23 x 2 10 4.6
• 124 5 124 x 2 10 24.8

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• To divide by 25- multiply by 4 and divided by
  100. Use the same procedure as before for removal
  of zeros or placement of the decimal.

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• 600 25 6 x 4 24
• 2,300 25 23 x 4 92
• 212 25 212 x 4 100 8.48

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• To divide by 125 multiply by 8 and divide by
  1,000.
• Example
• 7,000 125 7 x 8 56
• 12,000 125 12 x 8 96
• 2,011 125 2,011 x 8 1,000 16. 088

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• List the numbers by which each of the following
  is divisible. Test for 2, 3, 4, 5, 6, 7, 8, 9,
  10, 11, 12, 13, 25, and 125.

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• 576
• 2,3,4,6,8,9,
• 435
• 3, 5
• 132,132
• 2,3,4,6,7,11,12,13
• 225
• 3,5,9,25