Division With Remainders

Division with Remainders

When dividing whole numbers, sometimes the divisor does not fit evenly into the dividend. In that case, the answer has two parts: a quotient and a remainder.

1) Find the largest whole-number quotient

Ask: how many times does the divisor fit into the dividend without going over?

• Multiply the divisor by a nearby whole number.
• Choose the largest product that is less than or equal to the dividend.

2) Subtract to find the remainder

Take the product you found and subtract it from the dividend.

• The result is the remainder.
• The remainder must be smaller than the divisor.

3) Write the answer clearly

Use the form:

• quotient r remainder

Example: if 17 is divided by 5, then 5 fits into 17 three times because 5 × 3 = 15. The remainder is 17 − 15 = 2, so the result is 3 r 2.

4) Check your work

Use this test:

• divisor × quotient + remainder = dividend

For the example: 5 × 3 + 2 = 17, so the answer is correct.

Tips

• The remainder should never be equal to or larger than the divisor.
• If there is no leftover, the remainder is 0.