Mathematics — Numbers: Division

What is Division?

Division is a way of sharing or grouping objects into equal parts. It is the opposite (inverse) of multiplication. If 4 × 5 = 20, then 20 ÷ 5 = 4 and 20 ÷ 4 = 5.

Words we use

• Dividend — the number being divided (e.g., 20 in 20 ÷ 4).
• Divisor — the number we divide by (e.g., 4 in 20 ÷ 4).
• Quotient — the answer (e.g., 5 in 20 ÷ 4 = 5).
• Remainder — what is left if the number does not divide exactly (example below).

Two ways to think about division

1. Sharing — Share 12 sweets equally among 3 children. Each child gets 4 sweets. So 12 ÷ 3 = 4.
2. Grouping — Put objects into groups of a certain size. How many groups of 4 are there in 12? Answer: 3 groups.

Visual example — sharing 12 sweets among 3 children

Basic division facts (use times table to help)

Memorise these to work faster:

Division with remainder

Sometimes a number does not divide exactly. Example: 17 sweets shared among 5 children.

17 ÷ 5 = 3 remainder 2 (because 5 × 3 = 15 and 17 − 15 = 2).

You can also write remainder as a fraction: 17 ÷ 5 = 3 2/5.

Short division (bus-stop method) — step by step

Use when the divisor is a one-digit number. Example: 156 ÷ 3.

1. How many times does 3 go into 1? 0 times → write 0 above 1 but we group with next digit.
2. How many times does 3 go into 15? 5 times because 3×5 = 15. Write 5 above the 5. Subtract 15 − 15 = 0.
3. Bring down the next digit 6. How many times does 3 go into 6? 2 times. Write 2 above the 6.

Answer: 156 ÷ 3 = 52.

Long division (when divisor has two or more digits) — short example

Example: 474 ÷ 14.

1. See how many times 14 goes into 47. It goes 3 times (3×14 = 42). Put 3 above. Subtract 47 − 42 = 5.
2. Bring down the next digit 4 → 54. How many times does 14 go into 54? 3 times (3×14 = 42). Subtract 54 − 42 = 12.
3. No more digits. Remainder = 12. So 474 ÷ 14 = 33 r 12, or 33 12/14 → simplify 12/14 = 6/7 → 33 6/7.

Practice examples (try these)

1. 28 ÷ 7 = ?
2. 45 ÷ 9 = ?
3. 93 ÷ 3 = ?
4. 130 ÷ 5 = ?
5. 205 ÷ 4 = ? (give quotient and remainder)

Answers

1. 28 ÷ 7 = 4
2. 45 ÷ 9 = 5
3. 93 ÷ 3 = 31
4. 130 ÷ 5 = 26
5. 205 ÷ 4 = 51 remainder 1 (because 4×51 = 204, 205 − 204 = 1)

Word problem — Kenyan context

A farmer has 120 kg of maize. He packs it into bags of 25 kg each. How many full bags can he make and how much maize is left?

120 ÷ 25 = 4 remainder 20. He makes 4 full bags and has 20 kg left.

Tips for learning division

• Learn multiplication tables up to 10 × 10 — they help with division.
• Use sharing with real objects (stones, sweets, beans) to understand the idea.
• Write down steps clearly when doing bus-stop or long division.
• Check your answer by multiplying divisor × quotient and adding remainder (if any). This should equal the dividend.

Prepared for class learners (age ~10). Use the examples and practise with small objects at home or in class.