Division with remainders (age 10+)
Divide numbers up to 4 digits by a two-digit divisor using formal written long division, interpreting remainders as whole numbers, fractions, or by rounding as appropriate
What a learner can do afterwards
- Compute 4,752 ÷ 13 using long division and express the remainder as a fraction
- Decide whether to round up or down a division remainder in a real-life context (e.g. buses needed)
- Explain each step of the long division algorithm for a 4-digit ÷ 2-digit calculation
1 · Read
You already know how to multiply big numbers using the column method. Long division works the other way: it splits a big number into equal groups, like sharing stickers fairly or working out how many coaches a trip needs. The steps are always the same: divide, multiply, subtract, bring down. You repeat those steps until there are no more digits left to bring down. The remainder must stay smaller than the divisor. A leftover can be written as remainder over divisor.
Work out 1,848 ÷ 24. Look at the first three digits: 184. Divide: 24 goes into 184 seven times, since 7 × 24 = 168. Multiply: write 168 under the 184. Subtract: 184 − 168 = 16. Bring down: bring down the last digit, 8, to make 168. Divide again: 24 goes into 168 exactly 7 times, with nothing left over. The answer is 77.
A school is taking 130 pupils on a trip. Each coach holds 40 pupils. 130 ÷ 40 = 3 remainder 10. Three coaches only seat 120 pupils, so the 10 pupils left over still need a seat. The school has to book 4 coaches, even though the last one will not be full. If you count only full boxes, the leftover does not make another full one.
Look at what the remainder means before deciding what to do with it. If it is people, buses, or boxes that still need to fit somewhere, round up. If it can stay a leftover, write it as a fraction instead. Always check that your remainder is smaller than the divisor.
Divide, multiply, subtract, bring down, repeat, then decide whether the remainder becomes a fraction or gets rounded away depending on real life.
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2 · Watch
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Where it sits
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.