Division: Long Division, Remainders, and Practice

Division splits a number into equal groups and tells you how many are in each group, or how many groups you can make. This page covers division vocabulary, long division step by step, remainders, checking your answer, and practice.

What are the parts of a division problem?

Division is the arithmetic operation that finds how many times one number is contained inside another (Britannica). Every division problem has four parts.

The dividend is the number being split up. The divisor is the number you divide by. The quotient is the answer, the number of equal groups. The remainder is what’s left over when the dividend doesn’t split evenly.

In 87 ÷ 5, 87 is the dividend, 5 is the divisor, and once you divide it out the quotient is 17 with a remainder of 2.

This section covers the four basic terms only. It doesn’t cover division with decimals or fractions, which use the same words but a different setup.

How do you do long division step by step?

Long division breaks a big division problem into a repeating cycle of four steps: divide, multiply, subtract, bring down.

Worked example. Divide 936 by 4.

1. Look at the first digit of the dividend, 9. Divide: 4 goes into 9 two times (2 x 4 = 8, and 3 x 4 = 12 is too big). Write 2 above the 9.
2. Multiply: 2 x 4 = 8. Write 8 under the 9.
3. Subtract: 9 − 8 = 1.
4. Bring down the next digit, 3, to make 13.
5. Divide: 4 goes into 13 three times (3 x 4 = 12). Write 3 next to the 2 in the answer.
6. Multiply: 3 x 4 = 12. Subtract: 13 − 12 = 1.
7. Bring down the last digit, 6, to make 16.
8. Divide: 4 goes into 16 exactly four times (4 x 4 = 16). Write 4 in the answer.
9. Multiply and subtract: 16 − 16 = 0. Nothing left over.

The quotient is 234, with no remainder. So 936 ÷ 4 = 234.

This section covers whole-number long division with a one-digit divisor. It doesn’t cover two-digit divisors or decimal quotients, which use the same four steps but take more rounds.

What happens when a division problem has a remainder?

A remainder is the amount left over after you’ve made as many equal groups as you can. It’s always smaller than the divisor. If it weren’t, you could make one more full group.

Worked example. Divide 87 by 5.

1. Look at the first digit of the dividend, 8. Divide: 5 goes into 8 one time (1 x 5 = 5). Write 1. Subtract: 8 − 5 = 3.
2. Bring down the 7 to make 37.
3. 5 goes into 37 seven times (7 x 5 = 35). Write 7. Subtract: 37 − 35 = 2.
4. There are no more digits to bring down, so 2 is the remainder.

87 ÷ 5 = 17 remainder 2, often written 17 r2.

This section covers whole-number remainders. It doesn’t cover writing a remainder as a fraction or decimal, which comes up once a learner is ready to divide further instead of stopping at r2.

How do you check a division answer?

You can check any division problem with multiplication, since division is the reverse of multiplication. Multiply the quotient by the divisor, then add the remainder. The result should equal the dividend.

Checking example. Check that 87 ÷ 5 = 17 r2. Multiply the quotient by the divisor: 17 x 5 = 85. Add the remainder: 85 + 2 = 87. That matches the original dividend, so the answer is correct.

This section covers checking whole-number division. It doesn’t cover checking division that involves decimals, which uses the same idea but needs matching decimal places.

Practice set

Work through these on paper, then check your answers.

1. 144 ÷ 6
2. 523 ÷ 4
3. 96 ÷ 8
4. 205 ÷ 5
5. 1000 ÷ 8
6. 37 ÷ 6

Long division is the same four-step cycle no matter how big the numbers get, so once you can divide 936 by 4, you can divide much bigger problems the same way. Division also shows up constantly in fractions, since a fraction is really a division problem written with a bar instead of a division sign, and in everyday word problems about sharing or grouping things evenly. For more topics, visit our math hub.

Sources

• Britannica. Division.