Multiplying Fractions
Learn how to find a fraction of a whole number and how to multiply fractions together.
Finding a Fraction of a Whole Number
When we find a fraction of a whole number, we are dividing and then multiplying. The word "of" in maths means multiply.
3/4 of 20 means 3/4 × 20
Visualising 3/4 of 20
Step 1: Divide 20 into 4 equal groups (20 ÷ 4 = 5)
5
Group 1
5
Group 2
5
Group 3
5
Group 4
Step 2: Take 3 of those groups: 5 × 3 = 15
Quick Method
- Divide the whole number by the denominator.
- Multiply the result by the numerator.
Multiplying a Fraction by a Fraction
To multiply two fractions, simply multiply the numerators together and multiply the denominators together.
a/b × c/d = a × c/b × d
Example: 1/2 × 3/4
The grid shows 1/2 (top half) overlapping with 3/4 (first 3 columns).
Green area = 3 out of 8 squares = 3/8
Check: 1 × 3 = 3, and 2 × 4 = 8, so 1/2 × 3/4 = 3/8
Simplifying Your Answer
After multiplying, always check if you can simplify (make the fraction smaller) by dividing both the numerator and denominator by the same number.
Example: 2/3 × 3/4 = 6/12
Both 6 and 12 can be divided by 6: 6 ÷ 6/12 ÷ 6 = 1/2
Key Vocabulary
Numerator
The top number of a fraction — tells how many parts we are talking about.
Denominator
The bottom number of a fraction — tells how many equal parts the whole is split into.
Simplify
To reduce a fraction by dividing numerator and denominator by their common factor.
Product
The answer when you multiply two or more numbers together.
Worked Examples
Find 2/5 of 30.
Step 1: Divide 30 by 5: 30 ÷ 5 = 6
Step 2: Multiply by 2: 6 × 2 = 12
Answer: 2/5 of 30 = 12
Calculate 3/4 × 2/5.
Step 1: Multiply numerators: 3 × 2 = 6
Step 2: Multiply denominators: 4 × 5 = 20
Step 3: Simplify: 6/20 = 3/10
Answer: 3/10
A recipe needs 3/4 of a cup of flour. You want to make half the recipe. How much flour do you need?
Step 1: Find 1/2 × 3/4
Step 2: Multiply: 1 × 3 = 3, and 2 × 4 = 8
Answer: You need 3/8 of a cup of flour.
Knowledge Check
Select the correct answer for each question.
Question 1
What is 1/3 of 24?
Question 2
What is 3/4 of 16?
Question 3
Calculate 1/2 × 1/3.
Question 4
Calculate 2/3 × 3/4. Give your answer in simplest form.
Question 5
There are 40 students in Year 5. 3/8 of them walk to school. How many students walk to school?
Key Concepts Summary
- ●"Of" means multiply in maths.
- ●Fraction of a whole: divide by the denominator, multiply by the numerator.
- ●Fraction × Fraction: multiply numerators and multiply denominators.
- ●Always simplify your answer if possible.
- ●When you multiply a fraction by a fraction, the answer is smaller than either fraction.