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.