Long Division

Study Sheet

Long Division

Quotients and remainders

Sharing What Is Left

Concept
The Big Idea

Divide as far as you can in whole groups. Whatever cannot be shared is the remainder, and it is always smaller than the divisor.

Tip
The check

Always: divisor×quotient+remainder=the original number\text{divisor} \times \text{quotient} + \text{remainder} = \text{the original number}. If that fails, something went wrong.

Example
Finding 47÷547 \div 5

5×9=455 \times 9 = 45, and 47−45=247 - 45 = 2. So the quotient is 99 remainder 22. Check: 5×9+2=475 \times 9 + 2 = 47.

In Plain Terms & More Examples

Concept
In plain terms

Share into equal groups as far as you can; whatever is left over is the remainder, and it is always smaller than the number you divided by.

Example
Finding 58÷658 \div 6

6×9=546 \times 9 = 54, and 58−54=458 - 54 = 4. So 99 remainder 44. Check: 6×9+4=586 \times 9 + 4 = 58.

Example
Finding 73÷873 \div 8

8×9=728 \times 9 = 72, and 73−72=173 - 72 = 1. So 99 remainder 11. Check: 8×9+1=738 \times 9 + 1 = 73.