Practice Maths

L25 — Multiplying Fractions

Key Terms

multiply fractions
Multiply the numerators together and the denominators together, then simplify.
cross-simplify (cancel)
Divide a numerator and a denominator by a common factor before multiplying, to keep numbers smaller.
simplest form
A fraction where the numerator and denominator share no common factors other than 1.
"of" means multiply
In maths, "of" always means ×. So 23 of 12 = 23 × 12 = 8.

The Rule

Multiply numerators together; multiply denominators together; then simplify.

23 × 34 = 612 = 12

Worked Example

A recipe needs 34 cup of flour. If you make 23 of the recipe, how much flour do you need?

Step 1 — Set up: 23 × 34

Step 2 — Multiply: 2 × 33 × 4 = 612

Step 3 — Simplify: 612 = 12 cup

Cross-Simplify First: Before multiplying, look for common factors between any numerator and any denominator (including diagonally). Dividing them out first keeps the numbers small and your answer is already in simplest form.

Why Multiplying Fractions Is Easier Than Adding Them

When you add fractions, you need a common denominator — which can be tricky. Multiplying fractions is actually simpler: you just multiply across the top and across the bottom. No common denominator needed!

The rule is: ab × cd = a × cb × d

  • 23 × 35 = 615 = 25 (simplified)
  • 12 × 47 = 414 = 27 (simplified)
  • 34 × 29 = 636 = 16 (simplified)

Cancelling (Cross-Simplifying) Before Multiplying

Before multiplying, look for common factors between a numerator and a denominator — even diagonally! Dividing them out first makes the numbers smaller and your final answer will already be in simplest form.

Example: 34 × 89

  • 3 (top-left) and 9 (bottom-right) share a factor of 3: cancel to give 1 and 3.
  • 4 (bottom-left) and 8 (top-right) share a factor of 4: cancel to give 1 and 2.
  • Multiply: 1 × 21 × 3 = 23
This is much easier than doing 34 × 89 = 2436 and then trying to simplify a large fraction!

Multiplying a Fraction by a Whole Number

Write the whole number as a fraction with denominator 1, then multiply as usual:

  • 35 × 4 = 35 × 41 = 125 = 225
  • 23 × 6 = 123 = 4
  • 38 × 2 = 68 = 34

A shortcut: “of” in maths means multiply. So “23 of 12” = 23 × 12 = 243 = 8.

Real-Life Meaning of Fraction Multiplication

Multiplying fractions answers questions like “What is a fraction of a fraction?” For example: “I ate 34 of a pizza. My friend ate 23 of what I left. What fraction of the whole pizza did my friend eat?”

  • I left 14 of the pizza. Friend ate 23 of 14 = 23 × 14 = 212 = 16 of the whole pizza.
Always simplify your final answer. If the result is an improper fraction (numerator bigger than denominator), convert it to a mixed number. For example, 74 = 134.

  1. Calculate

    1. 12 × 13
    2. 23 × 34
    3. 35 × 23
    4. 47 × 78

  2. Multiply by a whole number

    1. 3 × 25
    2. 4 × 38
    3. 5 × 29
    4. 6 × 15
    5. 2 × 56
    6. 9 × 23

  3. Cancel before multiplying

    1. 45 × 58
    2. 34 × 89
    3. 67 × 712
    4. 910 × 56

  4. Ribbon Problem

    A piece of ribbon is 34 m long. Emma cuts off 23 of it. How long is the piece she cuts off?

  5. Water Tank

    A tank holds 56 of a litre when full. If it is 34 full, how much water is in the tank?

  6. Calculate and simplify

    1. 56 × 310
    2. 78 × 421
    3. 59 × 310

  7. Marble Jar

    A jar is 23 full of marbles. If the jar holds 24 marbles when completely full, how many marbles are currently in the jar?

  8. Missing Value

    Fill in the missing value: ______ × 35 = 920

  9. Garden Area

    A garden is 34 km long and 25 km wide. What is its area in km²?

  10. Reading a Book

    Tom reads 35 of a book on Monday. On Tuesday he reads 23 of what remains. What fraction of the whole book did he read on Tuesday?

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