Division Tips and Tricks
Draw a Picture
If you're just starting out with division, drawing a picture may help you to understand division problems better. First, draw the same number of boxes as the number for the divisor. Then move from box to box adding in a dot that represents 1 out of the total dividend. The number that you have in each box is the answer.
In the picture below we are trying to solve 20 ÷ 4 = ?. We have drawn 4 boxes. We start putting in the 20 dots one box at a time. We end up with 5 dots in each box. The answer is 5.
Check Your Answer by Multiplying
If you know how to multiply well, then you can use this to check your answers. Just take the quotient, or answer, and multiply it by the divisor. You should get the dividend.
Division by Subtraction
Another way to do division is to keep subtracting the the divisor from the dividend until you get to the answer. Here is an example:
532 ÷ 97 = ?
Once you've reached a point where subtracting by 97 gives you an answer that is less than 97, then you are done. Just count up the number of times you subtracted 97, that's your answer. The number that was left over from the last subtraction is your remainder.
Divide by Three Trick
This is a fun trick. If the sum of the digits in a number can be divided by three, then the number can as well.
1) The number 12. The digits 1+2=3 and 12 ÷ 3 = 4.
2) The number 1707. The digits 1+7+0+7=15, which is divisible by 3. It turns out that 1707 ÷ 3 = 569.
3) The number 25533708 = 2+5+5+3+3+7+0+8 = 33, which ÷ 3 = 11. It turns out that 25533708 ÷ 3 = 8511236.
More Divide by Number Tricks
- Divide by 1 - Anytime you divide by 1, the answer is the same as the dividend.
- Divide by 2 - If the last digit in the number is even, then the entire number is divisible by 2. Remember that divide by 2 is the same as cutting something in half.
- Divide by 4 - If the last two digits divide by 4, then the entire number is divisible by 4. For example, we know that 14237732 can be divided evenly by 4 because 32 ÷ 4 = 8.
- Divide by 5 - If the number ends in a 5 or a 0, it is divisible by 5.
- Divide by 6 - If the rules for divide by 2 and divide by 3 above are true, then the number is divisible by 6.
- Divide by 9 - Similar to the divide by 3 rule, if the sum of all the digits is divisible by 9, then the entire number is divisible by 9. For example, we know that 18332145 is divisible by 9 because 1+8+3+3+2+1+4+5 = 27 and 27 ÷ 9 = 3.
- Divide by 10 - If the number ends in a 0, then it is divisible by 10.
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