Mathematics — Numbers: Division

For learners aged ~11 (Kenyan context)

These notes explain what division is, how to work with whole numbers and decimals, and how to solve everyday problems (for example sharing money in Kenyan shillings). Simple pictures and step-by-step methods are included.

Learning goals

• Understand division as sharing and as repeated subtraction (inverse of multiplication).
• Read division vocabulary: dividend, divisor, quotient, remainder.
• Use short and long division methods for whole numbers and decimals.
• Solve word problems using division (e.g., sharing KSh.).
• Know simple divisibility tests (2, 3, 5, 9, 10).

Key words

• Dividend — the number being divided (e.g. 15 in 15 ÷ 3).
• Divisor — the number we divide by (e.g. 3 in 15 ÷ 3).
• Quotient — the answer (e.g. 5 in 15 ÷ 3).
• Remainder — what is left if division is not exact (e.g. 1 in 13 ÷ 4 = 3 R 1).

What is division?

Division splits a number into equal parts. It is the opposite (inverse) of multiplication.

Example: 12 ÷ 4 = 3

We can read this as: "12 shared equally into 4 groups gives 3 in each group." Also 4 × 3 = 12.

Visual: sharing sweets

Division notation and terms (example)

15 ÷ 3 = 5

Here: dividend = 15, divisor = 3, quotient = 5.

Long division (step-by-step)

Use long division when the divisor is a 2-digit number or when dividing larger numbers.

Example: 154 ÷ 7

1. How many times does 7 go into 15? → 2 times (because 2 × 7 = 14).
2. Write 2 above the 5 (in the quotient). Subtract 14 from 15 → remainder 1. Bring down the next digit (4) → 14.
3. How many times does 7 go into 14? → 2 times. Subtract 14 → remainder 0.

So 154 ÷ 7 = 22.

Short division (mental method)

Use when the divisor is small (2–9) and numbers are friendly.

Example: 96 ÷ 3. Think: 9 ÷ 3 = 3 (write 3), then 6 ÷ 3 = 2 → answer 32.

Division with remainder

If dividend is not exactly divisible, we get a remainder.

Example: 13 ÷ 4 = 3 remainder 1 (we write 13 ÷ 4 = 3 R 1). Check: 3 × 4 + 1 = 13.

Dividing by 10, 100, 1000 (quick rule)

• Divide by 10 → move decimal point one place left. Example: 450 ÷ 10 = 45.
• Divide by 100 → move decimal point two places left. Example: 450 ÷ 100 = 4.5.
• Works the same for decimals: 4.8 ÷ 0.6 = (4.8 ÷ 0.6) → move decimals to make divisor whole: multiply both by 10 → 48 ÷ 6 = 8.

Simple divisibility tests

• By 2: last digit even (0,2,4,6,8).
• By 3: sum of digits divisible by 3. (e.g., 123 → 1+2+3=6 → yes)
• By 5: last digit 0 or 5.
• By 9: sum of digits divisible by 9.
• By 10: last digit is 0.

Division and factors

If A divides B exactly, then A is a factor of B. Example: 6 divides 24, so 6 is a factor of 24.

Real-life (Kenyan) examples

1. Share KSh 540 equally among 6 students. How much does each get?

   Work: 540 ÷ 6 = 90. Each student gets KSh 90.

2. A teacher has 48 exercise books. She puts them into packs of 5. How many full packs and how many books left?

   Work: 48 ÷ 5 = 9 remainder 3. So 9 full packs, 3 books left.

Worked example with decimals

Find 6.3 ÷ 0.7.

Method: Multiply both numbers by 10 so divisor is whole: 63 ÷ 7 = 9. So 6.3 ÷ 0.7 = 9.

Practice questions

1. 24 ÷ 6 = ?
2. 37 ÷ 4 = ? (write remainder)
3. 156 ÷ 3 = ?
4. 82 ÷ 5 = ? (write remainder)
5. 540 ÷ 9 = ?
6. 4.2 ÷ 0.6 = ?
7. Is 243 divisible by 3? (use test)
8. Share KSh 360 equally among 8 pupils. How much each?

Answers

1. 24 ÷ 6 = 4
2. 37 ÷ 4 = 9 R 1
3. 156 ÷ 3 = 52
4. 82 ÷ 5 = 16 R 2
5. 540 ÷ 9 = 60
6. 4.2 ÷ 0.6 = 7
7. Yes. 2+4+3 = 9, divisible by 3.
8. KSh 360 ÷ 8 = KSh 45

These notes follow basic Kenyan primary-level ideas for learners aged about 11. Practice many examples — division becomes faster with practice and understanding the link to multiplication.