Number
Grade 4-5Multiplying & Dividing Fractions
Multiplying fractions is more straightforward than adding them, since there is no common denominator to find, but dividing fractions has its own rule that catches students out if it is applied without understanding it. This lesson covers multiplying fractions, multiplying by whole numbers, dividing using the reciprocal, and mixed numbers.
What you need to know
- To multiply, multiply the numerators and multiply the denominators; no common denominator needed.
- To divide, flip the second fraction and multiply (keep, change, flip).
- Turn mixed numbers into improper fractions before multiplying or dividing.
- Cancel common factors before multiplying to keep the numbers small.
Written by Asad, co-founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Multiplying fractions
Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. There is no need to find a common denominator first. Simplify the result fully.
2/3 × 3/5: multiply the numerators, 2 × 3 = 6, and the denominators, 3 × 5 = 15, giving 6/15, which simplifies to 2/5.
Multiplying a fraction by a whole number
Write the whole number as a fraction over 1, then multiply as normal by multiplying the numerators and the denominators.
2/5 × 20: write 20 as 20/1, then multiply: 2 × 20 = 40, and 5 × 1 = 5, giving 40/5, which simplifies to 8.
Dividing fractions
To divide by a fraction, keep the first fraction the same, change the divide sign to a multiply sign, and flip the second fraction upside down (its reciprocal). Then multiply as normal.
2/3 ÷ 1/6: keep 2/3, change ÷ to ×, and flip 1/6 to 6/1, giving 2/3 × 6/1 = 12/3 = 4.
Multiplying and dividing mixed numbers
Convert each mixed number to an improper fraction first, then multiply or divide using the same rules as for ordinary fractions. Convert the final answer back to a mixed number if the question asks for one.
2 1/4 ÷ 1 1/2: convert to improper fractions, 9/4 ÷ 3/2. Keep 9/4, change ÷ to ×, and flip 3/2 to 2/3, giving 9/4 × 2/3 = 18/12, which simplifies to 3/2, or 1 1/2 as a mixed number.
Worked examples
Three exam-style questions, fully solved
Work out 2/3 × 3/5. Give your answer in its simplest form.
Easy- 1.Multiply the numerators: 2 × 3 = 6
- 2.Multiply the denominators: 3 × 5 = 15
- 3.Simplify 6/15 by dividing both by their highest common factor, 3
Answer: 2/5
Work out 2/3 ÷ 1/6.
Medium- 1.Keep the first fraction the same: 2/3
- 2.Change ÷ to × and flip the second fraction: 1/6 becomes 6/1
- 3.Multiply: 2/3 × 6/1 = 12/3
Answer: 4
Work out 2 1/4 ÷ 1 1/2. Give your answer as a mixed number in its simplest form.
Hard- 1.Convert both mixed numbers to improper fractions: 2 1/4 = 9/4, and 1 1/2 = 3/2
- 2.Keep 9/4, change ÷ to ×, and flip 3/2 to 2/3
- 3.Multiply: 9/4 × 2/3 = 18/12, which simplifies to 3/2
Answer: 1 1/2
Practice
6 questions, marked instantly
Type an answer and check it. The worked solution appears once you have had a go. No login needed, and your progress saves in this browser.
Practice
Now try these yourself.
Type your answer and check it. The worked solution appears once you have had a go.
Work out 2/3 × 3/4. Give your answer in its simplest form.
Work out 1/2 ÷ 1/4
Work out 3/5 of 20
Work out 2/3 ÷ 4
Work out 1 1/2 × 2/3
A jug holds 3/4 of a litre. How many 1/8 litre cups can be filled from it?
Avoid these
The mistakes students make most often
Trying to find a common denominator before multiplying fractions, which is only needed for adding and subtracting, not multiplying.
Dividing straight across instead of flipping the second fraction and multiplying, which only works for multiplication, not division.
Forgetting to write a whole number as a fraction over 1 before multiplying it by another fraction.
Multiplying or dividing mixed numbers directly without converting them to improper fractions first.
Leaving the final answer as an improper fraction when the question specifically asks for a mixed number, or not simplifying the answer fully.
FAQ
Questions students and parents ask
Before this topic, make sure you know
What to learn next
Teachably is a GCSE Maths tutoring practice
This hub is our free resource and it stays free. If you would like one-to-one help alongside it, a short call is the best place to start. There is also a free video course for parents.