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Division

NumberDivision Hint
2All even numbers will divide exactly by two
3Add up all the digits in any number. If the total will divide exactly by 3 then the original number will divide exactly by 3
4If the last two digits of a number will divide exactly by 4 then the original number will divide exactly by 4.
5If the last digit of a number is either 0 or 5 then the entire number will divide exactly by 5
6If both of these are true
- Add up all the digits in a number and the total will divide by 3
- The original number is an even number
then the original number will divide exactly by 6
7Double the last digit of original number and subtract this from the remainig digits. If your answer will divide exactly bt 7 then the original number will divide by 7. (You may have to repeat process to decide whenther answer will divide by 7)
8If the last three digits of a number will divide exactly by 8 then the original number will divide exactly by 8.
9Add up all the digits in any number. If the total will divide exactly by 9 then the original number will divide exactly by 9
10If the last digit of a number is 0 then the number will divide exactly by 10
11Add up "every other" digit in the number. Subtract the sum of the remaining digits. If the answer will divide exactly by 11 then the original number will divide exactly by 11
12If both of these are true
- Add up all the digits in your number. If the total will divide exactly by 3
- The last 2 digits of your number will divide exactly by 4
then your number will divide exactly by 12

Multiplication

NumberMultiplication Hint
2Multiplying by two is identical to adding the number to itself.
4Double the number and double your answer. (i.e. multiply by 2 and multiply by 2 again.)
5Divide the number by 2 and then multiply by 10

Squaring Numbers

To square any number ending in ".5" --> Multiply (number - 0.5) by (number + 0.5) and add 0.25
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