The context decides what the remainder means

1 · Learn

Short division shares each place value and exchanges remaining units into the next place. For 1,257 ÷ 4, the whole-number quotient is 314 with remainder 1.

A remainder may need to be left over, written as a fraction or decimal, or rounded up for a practical purpose. If 125 people need vehicles with 4 seats each, 31 full vehicles are not enough: one more is needed.

Work through 1,257 divided by 4 from left to right. One thousand cannot fill four equal groups, so exchange it: twelve hundreds give three hundreds per group. Five tens give one ten per group with one ten left. Exchange that ten for ten ones; with seven ones there are seventeen ones. Each group gets four ones with one left. This records 314 remainder 1; check 314 times 4 plus 1 = 1,257.

2 · Worked example

For sharing 125 metres equally into four lengths, 125 ÷ 4 = 31.25 m. Unlike a vehicle count, the length can be split into a fraction of a metre.

3 · Your turn

98 pupils need tables seating four each. What is 98 ÷ 4 with a remainder, and how many tables are needed?

4 · Apply your learning

Solve two problems with the same division but different contexts. Explain why their final forms differ.