Division

What is division?

Division splits a total into equal parts. It answers two kinds of questions:

1. Sharing: 18 cookies shared equally among 3 friends. How many each? → 6
2. Grouping: 18 cookies put into bags of 3. How many bags? → 6

Both are written 18 ÷ 3 = 6.

Division and multiplication

Division is the inverse of multiplication: it undoes it.

• 3 × 6 = 18 → 18 ÷ 3 = 6 and 18 ÷ 6 = 3

So to divide, ask: "What times the divisor gives the dividend?" For 18 ÷ 3, think 3 × ? = 18. The answer is 6.

Ways to divide

Share out: deal 18 counters one at a time into 3 piles. Each pile gets 6.

Make groups: make groups of 3 from 18 counters. You make 6 groups.

Repeated subtraction: 18 − 3 − 3 − 3 − 3 − 3 − 3 = 0. You subtracted 3 six times.

Arrays: 18 dots in 3 rows makes 6 columns.

Skip count: count by 3s to 18: 3, 6, 9, 12, 15, 18. That’s 6 counts.

Division rules to remember

Why not divide by zero? Because no number times 0 gives 5.

Order matters

Unlike multiplication, you can’t swap the numbers. 12 ÷ 3 = 4, but 3 ÷ 12 is a fraction (one quarter).

Word clues

"Share equally", "each", "split", "per", "how many groups" and "how many in each" often mean divide.

Worked examples

Example 1: 18 ÷ 3 = ?

3 × 6 = 18, so 6.

Example 2: 24 students make teams of 4. How many teams?

24 ÷ 4 = 6 teams.

Example 3: 35 stickers shared among 5 friends. How many each?

35 ÷ 5 = 7 stickers.

Common mistakes

• Dividing the smaller number by the bigger one by mistake.
• Mixing up sharing and grouping: both give the same quotient, but the meaning of the answer changes (number per group or number of groups).
• Forgetting to check with multiplication.

Try it yourself

1. 28 ÷ 7 =
2. 45 ÷ 9 =
3. 0 ÷ 8 =
4. 56 apples go into bags of 8. How many bags?
5. Write the multiplication fact that checks 42 ÷ 6 = 7.

Answers: 1) 4 2) 5 3) 0 4) 7 5) 6 × 7 = 42

Quick recap

• Division means sharing equally or grouping.
• Dividend ÷ divisor = quotient.
• Use the related multiplication fact: division is its inverse.