Multiplying and Dividing Fractions

What is Multiplying and Dividing Fractions?

Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Multiplying and Dividing Fractions. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.

Check that you can explain Multiplying and Dividing Fractions in your own words and give one example from everyday life. If you can do that, you have understood the core idea.

Understanding Multiplying and Dividing Fractions gives you a reliable method you will reuse in later maths units, in science lessons and in data work.

Multiplying and Dividing Fractions in detail

To multiply fractions, multiply the numerators together and the denominators together, simplifying first by cancelling common factors if you can. So 2/3 × 3/5 = 6/15 = 2/5. No common denominator is needed.

To divide by a fraction, multiply by its reciprocal, which is the fraction turned upside down: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. Remember that dividing by a number less than 1 makes the result larger. These skills are used when scaling recipes, finding fractions of amounts and later in algebraic fractions.

How the interactive helps you understand Multiplying and Dividing Fractions

Watch the pie chart in the interactive. Use any sliders or buttons it offers to change the values and see how the pie chart responds.

Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Multiplying and Dividing Fractions.

Real-life uses and examples

• Spot Multiplying and Dividing Fractions in exam questions, where it often sits inside a short word problem.
• Check a homework answer about Multiplying and Dividing Fractions by estimating first, then working it out step by step.
• Use Multiplying and Dividing Fractions when comparing prices, discounts or recipe quantities in everyday life.

Common mistakes to avoid

• Forgetting units, signs or brackets when you apply Multiplying and Dividing Fractions.
• Memorising the steps for Multiplying and Dividing Fractions without checking why they work.
• Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.