Division: Sharing and Grouping

What you will learn

• Divide by sharing equally and by grouping.
• Use multiplication facts to divide.
• Find remainders when sharing does not come out even.

Before you start: you should know multiplication as equal groups. See Multiplication: Equal Groups and Arrays.

The idea

Division is about splitting a total into equal parts. It is written with the symbol $\div$. For example, $12 \div 3 = 4$ is read “twelve divided by three is four”.

There are two ways to think about the same sum.

Sharing

You know how many shares, and you find how many are in each share. $12$ sweets shared between $3$ children: deal them out one at a time to each child.

Grouping

You know the size of each group, and you find how many groups. $12$ sweets put in bags of $3$: how many bags?

Both give the same answer, $4$, because $12 \div 3 = 4$ either way.

Division is the opposite of multiplication

Division undoes multiplication. If $3 \times 4 = 12$, then $12 \div 3 = 4$ and $12 \div 4 = 3$. So to divide, ask “what times the divisor makes the total?”

Remainders

Sometimes the total does not split exactly. $17$ biscuits shared between $5$ people: each person gets $3$ and there are $2$ left over. The leftover is called the remainder.

The remainder is always smaller than the number you divide by. If it were as big, you could make another share.

Worked examples

Example 1: Using a times table

Work out $56 \div 8$.

1. Ask: what times $8$ is $56$?
2. $8 \times 7 = 56$.

Answer: $7$.

Example 2: Grouping

A coach seats $4$ children on each row. How many rows are needed for $26$ children?

1. $26 \div 4$: $4 \times 6 = 24$, which leaves $2$ children.
2. Those $2$ need a row too.

Answer: $7$ rows ($6$ full rows and one row with $2$).

Example 3: Quotient and remainder

Work out $29 \div 6$.

1. $6 \times 4 = 24$ and $6 \times 5 = 30$.
2. $30$ is more than $29$, so use $4$.
3. $29 - 24 = 5$.

Answer: $4$ remainder $5$.

You cannot divide by zero. Sharing among nobody makes no sense, so $5 \div 0$ has no answer.

Why it matters

Dividing is how we share bills, split work and work out how many packs we need. It is also the inverse of multiplication, which makes it the tool for checking times tables and later for fractions, where a fraction bar means division.