Long division repeats four steps: divide, multiply, subtract, bring down. First write some multiples of the divisor to help. Find how many times the divisor fits into the first part of the number, write that digit above, multiply and subtract. Bring down the next digit beside what is left and repeat. If the divisor doesn't fit, write 0. What is left at the end is the remainder.
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Equal groups
3 × 4 = 12
12 ÷ 3 = 4
The same picture shows multiplication and division. Each group must have the same number.
Words to know
- divisor
- the number you divide by
- multiple
- the result of multiplying a number by a whole number
- bring down
- move the next digit down beside what is left
Worked examples
672 ÷ 21 = ?
- 1.67 ÷ 21 = 3 (63), and 67 − 63 = 4.
- 2.Bring down 2 to make 42. 42 ÷ 21 = 2.
= 32
6384 ÷ 21 = ?
- 1.63 ÷ 21 = 3, nothing left. Bring down 8: 8 ÷ 21 won't go, write 0.
- 2.Bring down 4 to make 84. 84 ÷ 21 = 4.
= 304
7000 ÷ 23 = ? Give the answer with its remainder.
- 1.70 ÷ 23 = 3 r 1. Bring down 0 to make 10: won't go, write 0.
- 2.Bring down 0 to make 100: 100 ÷ 23 = 4 r 8.
= 304 r 8
For parents
Method: Long division
What to say: How many times does it fit? What is left? Which digit comes down next?
Common mistakes:
- After subtracting, forgets to keep what is left and bring down the next digit beside it.
- Leaves out a zero in the answer when the brought-down number is smaller than the divisor.
- Divides by the rounded divisor used for estimating (20 instead of 21) and never corrects the estimate.
- Finds the first digit of the answer and stops instead of bringing down the remaining digits.
- Works out the quotient and leaves off the remainder.
- Underestimates a digit of the answer and accepts a remainder that is bigger than the divisor.