✖️ Fractions: Mixed Operations
Cambridge Lower Secondary Stage 7 · Unit 7
Multiply Fractions
23
× 34
= 612
= 12
Divide = Multiply by Reciprocal
34
÷ 38
= 34
× 83
= 2
Mixed Numbers → Improper First
213
× 112
= 73
× 32
= 72
= 312
Watch fractions in action!
What you'll master:
- Multiply fractions: multiply tops, multiply bottoms, simplify
- Divide fractions: flip the second fraction, then multiply
- Multiply and divide mixed numbers (convert first!)
- Multi-step problems with fractions
- Order of operations with fractions
- Find a fraction of a quantity
📖 Learn: Fractions — Mixed Operations
Part 1: Multiplying Fractions
To multiply two fractions: multiply the numerators and multiply the denominators, then simplify.
ab
× cd
= a × cb × d
Example: 25 × 34 = 620 = 310
💡 Cross-cancel tip: You can simplify diagonally before multiplying. E.g. 25 × 56 → cancel the 5s and 2&6 → 13.
Part 2: Dividing Fractions — "Flip and Multiply"
To divide by a fraction: keep the first fraction, change ÷ to ×, flip the second fraction (use its reciprocal).
KCF: Keep · Change · Flip
34 ÷ 38 → 34 × 83 = 2412 = 2
56 ÷ 13 → 56 × 31 = 156 = 52 = 212
Part 3: Mixed Numbers
Before multiplying or dividing mixed numbers, convert them to improper fractions first.
Converting mixed → improper: multiply the whole number by the denominator, add the numerator.
235 → (2 × 5) + 35 = 135
Multiply: 112 × 223 = 32 × 83 = 246 = 4
Divide: 312 ÷ 134 = 72 ÷ 74 = 72 × 47 = 2814 = 2
Part 4: Multi-step & Order of Operations
Apply BODMAS/BIDMAS with fractions — brackets first, then multiply/divide, then add/subtract.
Evaluate: (12 + 14) × 23
Step 1 — Brackets: 12 + 14 = 24 + 14 = 34
Step 2 — Multiply: 34 × 23 = 612 = 12
Part 5: Fraction of a Quantity
"of" means multiply. To find a fraction of a quantity: multiply the quantity by the fraction.
34 of 40 = 34 × 40 = 1204 = 30
25 of 35 kg = 25 × 35 = 705 = 14 kg
💡 Shortcut: divide by the denominator first, then multiply by the numerator.
💡 Worked Examples
Example 1: Multiplying Fractions
Calculate 49 × 38
Step 1 — Cross-cancel: 4 and 8 share a factor of 4 → 4÷49 × 38÷4 = 19 × 32
Step 2 — Cross-cancel again: 3 and 9 share factor 3 → 13 × 12
Step 3 — Multiply: = 1 × 13 × 2 = 16
Answer: 1/6
Example 2: Dividing Fractions
Calculate 710 ÷ 75
Step 1 — KCF: Keep 710 · Change ÷ to × · Flip → 57
Step 2: 710 × 57 = 3570
Step 3 — Simplify: 3570 = 12
Answer: 1/2
Example 3: Mixed Number Multiplication
Calculate 214 × 123
Step 1 — Convert: 214 = 94 and 123 = 53
Step 2 — Multiply: 94 × 53 = 4512
Step 3 — Simplify & convert back: 4512 = 154 = 334
Answer: 3 3/4
Example 4: Multi-step Problem
A ribbon is 56 m long. It is cut into pieces each 112 m long. How many pieces are there?
Step 1 — Recognise: We need 56 ÷ 112
Step 2 — KCF: 56 × 121 = 606 = 10
Answer: 10 pieces
🎨 Area Model Fraction Multiplier
Use the sliders to set two fractions. The shaded region shows their product!
Try these combinations:
Step-by-Step Division Solver
Watch KCF (Keep · Change · Flip) in action for: 35 ÷ 610
Keep: 35 — the first fraction stays exactly the same. ✏️ Write: 35 ___
Change: ÷ becomes × — flip the operation sign. ✏️ Write: 35 × ___
Flip: 610 becomes 106 — reciprocal! ✏️ Write: 35 × 106
Solve: 35 × 106 = 3030 = 1 🎉
✏️ Exercise 1: Multiplying Fractions
Type your answer as a fraction (e.g. 3/4) or whole number. Simplify fully!
✏️ Exercise 2: Dividing Fractions
Remember: Keep · Change · Flip! Type answer as a/b or whole number.
✏️ Exercise 3: Mixed Number Operations
Convert to improper fractions first! Answer as mixed number (e.g. 2 3/4) or improper fraction.
✏️ Exercise 4: Word Problems
Read each problem carefully. Show your working in your book, then type the answer.
🍪 Interactive: Cookie Recipe Scaler
This recipe makes 12 cookies. Use the buttons to scale it!
Making: 12 cookies
| Ingredient | For 12 cookies | For 12 cookies |
|---|
All amounts shown as simplified fractions or mixed numbers.
✏️ Exercise 5: Fraction of a Quantity
Find the fraction of each quantity. Include units where needed.
📝 Practice: 20 Curriculum Questions
Work out each answer in your book, then click to reveal. Cambridge Lower Secondary aligned.
🏆 Challenge Problems
Multi-step contextual problems — stretch your thinking!