Multiplying Fractions
Get to grips with multiplying fractions using these Foundation and Higher GCSE Maths practice questions. The worksheet focuses on multiplying fractions, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. To multiply fractions, multiply numerators and denominators straight across.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
Multiplying fractions is the most straightforward of the four operations: multiply the numerators together and multiply the denominators together. There is no need for a common denominator.
The word of signals multiplication in fraction questions. Finding three quarters of a number means multiplying by \(\frac{3}{4}\), which is why fractions of amounts and multiplying fractions are really the same skill.
Cancelling before you multiply saves a great deal of work. If a numerator and a denominator share a factor, divide both by it first. The answer is the same but the numbers stay small, which reduces arithmetic slips and often removes the need to simplify at the end.
Revision notes
The basic method
Multiply straight across: numerators together, denominators together.
So \(\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}\). Notice the answer is smaller than either fraction, which makes sense because you are taking a part of a part.
Cancelling first
Before multiplying, look for a common factor between any numerator and any denominator, including diagonally across the multiplication sign.
In \(\frac{3}{4} \times \frac{8}{9}\), the \(3\) and \(9\) share a factor of \(3\), and the \(4\) and \(8\) share a factor of \(4\). Cancelling gives \(\frac{1}{1} \times \frac{2}{3} = \frac{2}{3}\).
Mixed numbers and whole numbers
Convert mixed numbers to improper fractions before multiplying. A whole number can be written over \(1\).
So \(1\frac{1}{2} \times \frac{2}{5}\) becomes \(\frac{3}{2} \times \frac{2}{5} = \frac{6}{10} = \frac{3}{5}\).
Key points
- Multiply numerators together and denominators together.
- No common denominator is needed.
- The word of means multiply.
- Cancel common factors before multiplying to keep numbers small.
- Convert mixed numbers to improper fractions first.
- A whole number can be written over 1.
Worked examples
Example 1
Work out \(\frac{3}{5} \times \frac{2}{7}\).
Working
Example 2
Work out \(\frac{4}{9} \times \frac{3}{8}\), cancelling first.
Working
Example 3
Work out \(2\frac{1}{4} \times \frac{2}{3}\).
Working
Common mistakes
Finding a common denominator before multiplying.
That step belongs to addition and subtraction. Multiplying needs no common denominator.
Multiplying mixed numbers whole-by-whole.
1½ × 2½ is not 2¼. Convert to 3/2 × 5/2 = 15/4 = 3¾.
Cancelling across an addition sign.
Cancelling only works with multiplication. In 2/3 + 4/9 nothing may be cancelled diagonally.
Expecting the answer to be larger.
Multiplying by a fraction less than 1 makes a number smaller, which is correct, not an error.
Exam tips
- Cancel before multiplying — it is faster and reduces mistakes.
- Rewrite any mixed number as an improper fraction on its own line.
- Read of as a multiplication sign.
- Check whether the answer needs simplifying or converting back to a mixed number.
Key terms
- Numerator
- The top number of a fraction.
- Cancelling
- Dividing a numerator and a denominator by a common factor before multiplying.
- Improper fraction
- A fraction with a numerator larger than its denominator.
- Simplify
- Write a fraction with the smallest possible whole numbers.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.