Division
Dividing by partitioning
One efficient way to divide is to partition the number by place value and divide each part. To work out 84 ÷ 4, split 84 into 80 and 4: 80 ÷ 4 = 20, 4 ÷ 4 = 1, and 20 + 1 = 21. Partitioning turns a hard division into a few easy ones using known facts, then adds the results. Dividing is the reverse of multiplying, so the same facts that build the multiplication tables also answer division questions quickly.
Division with a remainder
Not every division comes out evenly, and what is left over is the remainder. 17 ÷ 5 gives 3, because five groups of 3 is 15, with 2 left over, written as 3 remainder 2. Arranging 17 objects into groups of 5 makes this clear: three full groups form, and two objects remain that cannot fill a fourth group. The remainder is always smaller than the number being divided by, because if it were as large, another whole group could be made. Recognising and recording the remainder is the first step; deciding what to do with it comes next.
Interpreting the remainder
What a remainder means depends on the problem, so it must be interpreted in context. If 23 children travel in cars holding 4 each, five cars carry 20 and 3 children are still waiting, so a sixth car is needed: the answer rounds up. If 23 lollies are shared equally among 4 children, each child gets 5 and 3 are left over, so the answer is 5 with some remaining: it rounds down. The same calculation, 23 ÷ 4, gives different sensible answers depending on what the numbers stand for. Reading the question carefully decides whether to round up, round down, or share the remainder out.
Whole number, decimal or fraction
A remainder can also be written as part of an exact answer, as a decimal or a fraction. 17 ÷ 5 is 3 remainder 2, and that 2 left over, shared into 5, is 2/5, so the exact answer is 3 2/5, or 3.4 as a decimal. Which form to use depends on the context: a remainder suits whole objects, a decimal suits money or measurement, and a fraction suits an exact share. The whole-number remainder, the decimal and the fraction are three ways of writing the same result, and moving between them shows a full understanding of the division.
Solving division problems
Division solves many everyday problems: sharing a quantity equally, splitting into groups of a fixed size, or finding a rate. The steps are the same each time: decide that division is needed, choose an efficient strategy or a calculator, carry it out, and then interpret any remainder in the context of the problem. Checking the answer against an estimate guards against mistakes, since a division answer should be close to a rounded one. Setting the problem out clearly, with the numbers and the operation, helps avoid slips and makes the remainder easy to handle.
Dividing with confidence
Dividing larger numbers confidently means putting these steps together: divide by partitioning or with a calculator, find any remainder, and then express the result in the form the problem needs, as a whole-number remainder, a decimal or a fraction, rounding up or down where the context calls for it. The link between division and multiplication, and a quick estimate to check, keep the work reliable. With these habits a child can solve division problems of many kinds, ready for the modelling and the larger calculations of later years.