Mathematics • Year 7 • Unit 1 • Lesson 9
Multiplying and Dividing Fractions
Build the rules: multiply straight across (top × top, bottom × bottom). Divide? Keep, change, flip — keep the first fraction, change ÷ to ×, flip the second.
1. I do — fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. Calculate 3/4 × 8/9 in simplest form.
Step 1 — Cross-cancel before multiplying (optional but smart).
Top-left 3 and bottom-right 9 share factor 3: 3 ÷ 3 = 1, 9 ÷ 3 = 3.
Top-right 8 and bottom-left 4 share factor 4: 8 ÷ 4 = 2, 4 ÷ 4 = 1.
Reason: cancelling diagonally before multiplying keeps numbers small and avoids simplifying later.
Step 2 — Multiply straight across with the simplified numbers.
1/1 × 2/3 = (1 × 2)/(1 × 3) = 2/3
Reason: when multiplying fractions you don't need a common denominator — just multiply tops together and bottoms together.
Step 3 — Check by multiplying without cancelling.
3/4 × 8/9 = 24/36. Simplify: HCF(24, 36) = 12. 24 ÷ 12 = 2, 36 ÷ 12 = 3. = 2/3 ✓.
Answer: 2/3.
2. We do — fill in the missing steps
Same structure as Section 1, but for division. Fill in each blank line. 4 marks
Problem. Calculate 5/6 ÷ 5/12 in simplest form.
Step 1 — Keep the first fraction, change ÷ to ×, flip the second fraction:
5/6 ÷ 5/12 becomes _____ / _____ × _____ / _____
Step 2 — Cross-cancel:
5 (top-left) and _____ (bottom-right) share factor _____, giving _____ and _____.
6 (bottom-left) and 12 (top-right) share factor _____, giving _____ and _____.
Step 3 — Multiply straight across with the simplified numbers:
_____ / _____ × _____ / _____ = _____ / _____
Step 4 — Final answer (simplify if needed): _____.
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation, the middle two are standard, and the last two are extension.
Foundation — single step
3.1 1/2 × 1/3 = ? 1 mark
3.2 2/3 × 3/4 = ? (Simplify your answer.) 1 mark
3.3 1/2 ÷ 1/4 = ? (Keep, change, flip — then multiply.) 1 mark
3.4 3/4 × 8 = ? (Write 8 as 8/1 first.) 1 mark
Standard — combine two ideas
3.5 4/9 × 3/8. Cross-cancel before multiplying. 2 marks
3.6 3/5 ÷ 9/10. Keep, change, flip, then cross-cancel. 2 marks
Extension — push your thinking
3.7 2 1/2 × 1 1/3. Convert both to improper fractions first, then multiply. Write the final answer as a mixed number. 3 marks
3.8 2 1/4 ÷ 1 1/2. Convert both to improper fractions, then keep-change-flip and multiply. Write the final answer as a mixed number. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (5/6 ÷ 5/12)
Step 1: becomes 5/6 × 12/5.
Step 2: 5 (top-left) and 5 (bottom-right) share factor 5, giving 1 and 1. 6 (bottom-left) and 12 (top-right) share factor 6, giving 1 and 2.
Step 3: 1/1 × 2/1 = 2/1.
Step 4: 2.
3.1 — 1/2 × 1/3
(1 × 1)/(2 × 3) = 1/6.
3.2 — 2/3 × 3/4
Cross-cancel 3 and 3 (share 3): 1 and 1. Then 2/1 × 1/4 = 2/4 = 1/2. (Or compute 6/12 then simplify.)
3.3 — 1/2 ÷ 1/4
Keep, change, flip: 1/2 × 4/1. = 4/2 = 2. (Sense check: how many 1/4's fit in 1/2? Two.)
3.4 — 3/4 × 8
Write 8 = 8/1. Then 3/4 × 8/1 = 24/4 = 6. (Or: 3/4 of 8 = 6.)
3.5 — 4/9 × 3/8
Cross-cancel: 4 and 8 share 4 (→ 1 and 2). 9 and 3 share 3 (→ 3 and 1). Result: 1/3 × 1/2 = 1/6.
3.6 — 3/5 ÷ 9/10
Keep, change, flip: 3/5 × 10/9. Cross-cancel: 3 and 9 share 3 (→ 1 and 3). 5 and 10 share 5 (→ 1 and 2). Result: 1/1 × 2/3 = 2/3.
3.7 — 2 1/2 × 1 1/3
Convert: 2 1/2 = 5/2, 1 1/3 = 4/3. Multiply: 5/2 × 4/3. Cross-cancel: 4 and 2 share 2 (→ 2 and 1). So 5/1 × 2/3 = 10/3 = 3 1/3.
3.8 — 2 1/4 ÷ 1 1/2
Convert: 2 1/4 = 9/4, 1 1/2 = 3/2. Keep, change, flip: 9/4 × 2/3. Cross-cancel: 9 and 3 share 3 (→ 3 and 1). 4 and 2 share 2 (→ 2 and 1). Result: 3/2 × 1/1 = 3/2 = 1 1/2.