Long division: learn and practice

Who this lesson is for

This long division lesson is for grade 4. Students divide one place at a time and stop when the remainder is smaller than the divisor. The grade 4 hub links here, and this page does not have a second copy under another grade.

Four steps, one place at a time

Long division breaks a larger division into place-value steps. The number being divided is the dividend. The number you divide by is the divisor. The answer is the quotient. Sometimes a whole number of groups does not use up the dividend, and the amount left is the remainder. The remainder must be smaller than the divisor. If it is not, the quotient digit is too small and you can make another group.

Why the remainder has to be smaller

Suppose you are sharing 14 stickers among 4 friends and you say each friend gets 2, with 6 left. Those 6 stickers can still make another full share, because 6 is bigger than 4. The remainder is not finished. Each friend can get 3 stickers, and 2 stickers are left. 2 is smaller than 4, so you stop. The sentence that checks the whole problem is dividend = divisor × quotient + remainder. Here 4 × 3 + 2 = 14. If that sentence fails, a step was wrong.

Worked example 1: 84 divided by 4

Divide 84 by 4. Look at the tens first. 8 tens ÷ 4 = 2 tens, so write 2 above the 8. Multiply 2 × 4 = 8, and subtract 8 − 8 = 0. Bring down the 4 ones. Now 4 ÷ 4 = 1, so write 1 above the 4. Multiply 1 × 4 = 4, and subtract 4 − 4 = 0. The remainder is 0. The quotient is 21. Check: 4 × 21 = 84. There is nothing left over, so the division is exact.

Worked example 2: 75 divided by 3

Divide 75 by 3. 7 tens ÷ 3 = 2 tens, with something left, because 3 × 2 = 6 and 7 − 6 = 1 ten. Write 2 above the 7. Bring down the 5 ones beside the leftover ten to make 15. 15 ÷ 3 = 5, so write 5 above the 5. Multiply 5 × 3 = 15, and subtract 15 − 15 = 0. The quotient is 25 and the remainder is 0. Check: 3 × 25 = 75. The first digit was not 7, because 3 does not go into 7 a whole 3 times without going past it. 3 × 3 = 9, and 9 is more than 7.

Worked example 3: 58 divided by 5

Divide 58 by 5. 5 goes into 5 one time, so write 1 above the tens digit. 1 × 5 = 5, and 5 − 5 = 0. Bring down the 8. 5 goes into 8 one time, because 5 × 1 = 5 and 5 × 2 = 10, which is too big. Write 1 above the ones digit. Subtract 8 − 5 = 3. No digit is left to bring down, and 3 is smaller than 5, so the remainder is 3. The quotient is 11 remainder 3. Check: 5 × 11 + 3 = 55 + 3 = 58. You can also say 11 groups of 5, with 3 left that do not make another group.

A check you can do every time

After the last subtraction, read the quotient from the top and the remainder from the bottom. Rebuild the dividend with divisor × quotient + remainder. The product should match the starting number, and the remainder should be smaller than the divisor. Then practice the same steps on the board.

Common questions about long division

What does a remainder of 0 mean?

The divisor goes into the dividend an exact number of times. Nothing is left over. The check is divisor times quotient, with nothing added.

Can the remainder be equal to the divisor?

No. If the remainder equals the divisor, you can make one more group. Increase the last quotient digit by 1 and the new remainder is 0.

Where do I start if the first digit is too small?

If the divisor does not fit into the first digit, take the first two digits as the first piece. The first quotient digit then sits above the second digit of the dividend.