Adding and Subtracting Fractions

What is Adding and Subtracting Fractions?

Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Adding and Subtracting 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 Adding and Subtracting Fractions in your own words and give one example from everyday life. If you can do that, you have understood the core idea.

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

Adding and Subtracting Fractions in detail

To add or subtract fractions, they must have the same denominator. If they do not, rewrite each as an equivalent fraction over a common denominator, usually the lowest common multiple of the denominators, then add or subtract the numerators and keep the denominator unchanged. Simplify the result if possible.

For example, 1/3 + 1/4 becomes 4/12 + 3/12 = 7/12. A common error is to add the denominators as well, giving 2/7, which is wrong because the size of the parts has not changed. Mixed numbers can be converted to improper fractions first.

How the interactive helps you understand Adding and Subtracting 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 Adding and Subtracting Fractions.

Real-life uses and examples

• Check a homework answer about Adding and Subtracting Fractions by estimating first, then working it out step by step.
• Use Adding and Subtracting Fractions when comparing prices, discounts or recipe quantities in everyday life.
• Explain Adding and Subtracting Fractions to a friend with a simple picture, such as a row of tiles or a bag of sweets.

Common mistakes to avoid

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