✖️ Multiplying Fractions
Cambridge Lower Secondary · Grade 7 · Fractions & Decimals
Fraction × Fraction
34 ×
25 =
620 =
310
Top × Top, Bottom × Bottom
Cross-Cancelling
49 ×
38 =
13 ×
12 =
16
Simplify diagonally before multiplying
Mixed Numbers
112 ×
223 →
32 ×
83 =
4
Convert to improper fractions first!
Watch the multiplication come alive! 🍭
Top × Top = 6 | Bottom × Bottom = 15 | Simplify: 6/15 = 2/5
What you'll learn:
- Fraction × fraction: multiply tops, multiply bottoms
- Cross-cancelling to keep numbers manageable
- Fraction × whole number
- Multiplying mixed numbers (convert to improper first)
- Fraction of a quantity (e.g. ¾ of 120)
- Multi-step fraction multiplication problems
- Area of rectangles with fractional dimensions
📖 Learn: Multiplying Fractions
Part 1: Fraction × Fraction
To multiply two fractions: multiply the numerators and multiply the denominators.
📌 Rule: ab × cd = a × cb × d
Example: 23 × 45 = 2 × 43 × 5 = 815
Example: 12 × 14 = 18 (half of a quarter is an eighth!)
💡 Always simplify your answer. Find the HCF of the numerator and denominator and divide both by it.
Part 2: Cross-Cancelling
Before multiplying, look for common factors diagonally across the × sign. Cancel them out first to keep numbers small.
Example: 49 × 38
4 and 8 share a factor of 4: 4÷4=1, 8÷4=2 → 19 × 32
9 and 3 share a factor of 3: 9÷3=3, 3÷3=1 → 13 × 12
Answer: 16 (much easier than 12/72!)
💡 Cross-cancel numerator of first with denominator of second, OR numerator of second with denominator of first.
Part 3: Fraction × Whole Number
Write the whole number as a fraction over 1, then multiply as normal.
📌 Rule: ab × n = ab × n1 = a × nb
Example: 34 × 8 = 3 × 84 = 244 = 6
Example: 25 × 15 = 2 × 155 = 305 = 6
💡 Shortcut: divide the whole number by the denominator first, then multiply by the numerator. 15 ÷ 5 = 3, then 3 × 2 = 6.
Part 4: Multiplying Mixed Numbers
Always convert mixed numbers to improper fractions first, then multiply.
📌 Convert: abc = ac + bc
Example: 112 × 223
Convert: 112 = 32 and 223 = 83
Multiply: 32 × 83 = 246 = 4
⚠️ Never multiply mixed numbers by multiplying whole parts and fraction parts separately — it gives the wrong answer!
Part 5: Fraction of a Quantity
"Of" in maths means multiply.
📌 34 of 120 = 34 × 120 = 3 × 1204 = 3604 = 90
Shortcut: 120 ÷ 4 = 30, then 30 × 3 = 90
Example: 25 of £60 → 60 ÷ 5 = 12, 12 × 2 = £24
💡 Method: ÷ denominator first, then × numerator. Always works!
💡 Worked Examples
Example 1: Simple Fraction × Fraction
Calculate 35 × 47
Step 1: Multiply numerators: 3 × 4 = 12
Step 2: Multiply denominators: 5 × 7 = 35
Step 3: Simplify: HCF(12, 35) = 1, so already in simplest form
Answer: 1235
Example 2: Using Cross-Cancelling
Calculate 56 × 910
Step 1: Look for cross-factors. 5 and 10: HCF = 5. Divide: 5÷5=1, 10÷5=2
Step 2: 6 and 9: HCF = 3. Divide: 6÷3=2, 9÷3=3
Step 3: Now multiply: 12 × 32 = 34
Answer: 34
Without cross-cancelling: 45/60 → then simplify. Cross-cancelling avoids big numbers!
Example 3: Mixed Numbers
Calculate 213 × 145
Step 1: Convert: 213 = 73 (3×2+1=7)
Step 2: Convert: 145 = 95 (5×1+4=9)
Step 3: Cross-cancel: 7 and 5 — no common factors. 3 and 9: HCF=3, so 3→1, 9→3
Step 4: 71 × 35 = 215 = 415
Answer: 415
Example 4: Area with Fractional Dimensions
A rectangle is 212 cm long and 45 cm wide. Find its area.
Step 1: Area = length × width
Step 2: Convert 212 = 52
Step 3: 52 × 45 — cross-cancel: 5 and 5 → 1; 2 and 4 → 1 and 2
Step 4: 11 × 21 = 2 cm²
Answer: 2 cm²
📐 Area of rectangle = length × width. Works exactly the same with fractions!
🎨 Area Model Visualizer
Adjust the sliders to see why fraction multiplication works. The shaded overlap is the product!
2/3 × 3/4 = 6/12 = 1/2
Pink = first fraction columns · Green = second fraction rows · Purple overlap = product
🎯 Cross-Cancel Spotlight
Click the two numbers that share a common factor (one from each fraction) to cross-cancel them!
🍰 Recipe Multiplier
You're making a cake but only want a fraction of the recipe. Adjust the scale and see the ingredients update!
Scale factor:
Original recipe makes 12 cupcakes
✏️ Exercise 1: Fraction × Fraction
Give answers as simplified fractions (e.g. 3/5) or whole numbers.
✏️ Exercise 2: With Cross-Cancelling
Use cross-cancelling to simplify before multiplying. Give simplified answers.
✏️ Exercise 3: Fraction × Whole Number
Give answers as simplified fractions or whole numbers.
✏️ Exercise 4: Mixed Numbers
Convert to improper fractions first. Give answers as mixed numbers or fractions (e.g. 2/3 or 1 1/2 written as 3/2).
🍰 Exercise 5: Fraction of a Quantity & Word Problems
Give numerical answers (include units where asked).
📝 Practice: 20 Questions
Mixed topics — all types of fraction multiplication.
🏆 Challenge: 8 Hard Questions
Multi-step, area problems, and tricky mixed numbers. Show you're a fraction master!