Maths · KS3 and GCSE · Interactive lesson
Fractions: add, subtract, multiply and divide
Explore fraction bars, shaded areas and equal groups. Understand all four operations, then practise with hints and small worked steps.
Choose your view
Explore an interactive example, then try the questions at your own pace.
KS3 / GCSE · start with the idea
By the end of this lesson: Explain why fractions need equal-sized pieces before you add or subtract.
The interactive diagram and controls are in Stage 2, “Explore one example”. Read the idea here, then try it next.
- The bottom number says how many equal pieces make a whole.
- The top number counts how many of those pieces you have.
- Before adding or subtracting, make both kinds of piece the same size.
Both whole bars are split into sixths, so the pieces match.
3/6 + 2/6 = 5/6Useful starting points
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What do the words mean?
- Numerator
- The top number: how many pieces you have.
- Denominator
- The bottom number: how many equal pieces make a whole.
- Equivalent
- Different-looking fractions with the same value, such as 1/2 and 2/4.
Change the example
This is the lesson example. Your practice question uses its own numbers.
Something to try
Keep the denominators the same. Add one more piece to the first fraction. What happens to the answer?
Notice what changes
How particle motion works +
Starts paused. Press Play, then add energy to see the warmer particles move faster.
Particles keep the same size. Liquid particles move around; solid particles vibrate around fixed positions. This is a simplified model, with the change in motion exaggerated to make it easier to see.
About the playback +
About this model
Each full bar is one whole. The upper bars show the original fractions; the lower bars show equivalent fractions with the common denominator. The answer uses the same-sized pieces. Each result bar is one whole; a second bar appears when the answer is greater than one.
More about this diagram
Still picture. Play particle motion in Stage 2.
1/2 + 1/3 = 5/6
Still picture of the example from Stage 2. Use the back arrow to change it.
Work through it
Starting example: read the steps below
- Choose 6 as a common denominator: both fractions now count the same-sized pieces.
- 1/2 = 3/6; 1/3 = 2/6. Multiply numerator and denominator by the same factor.
- 3 + 2 = 5. Keep the denominator 6.
- 5/6 is already in its simplest form. Decimal: 5/6 ≈ 0.833.
Try on your own
Your turn. No rush.
Question 1
What is 1/2 + 1/4? Give a fraction or decimal.
About these questions
Questions appear in a mixed order. Work at your own pace and stop whenever you like.
These questions use their own numbers, separate from the lesson example. You can stop whenever you like. Answers last for this visit to the page.
A good place to pause
This recap is for the activity you just tried. You can return to other activities in this topic later.
Can you explain the meaning of your chosen operation using equal pieces or groups?
Try one question and explain your first step. If you need help, use a hint, go back to the idea, or ask Maurice. You choose the pace.
Explain it in your own words and add a small example. This can help you remember and spot what to ask Maurice.
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Notes for parents and tutors
These lessons cover selected KS3 and GCSE ideas for England; they are not a complete course. The level notes explain where GCSE methods or optional extensions begin. Maurice can help you choose material for your course and exam board.
The content draws on the DfE Maths curriculum, DfE Science curriculum and AQA GCSE Physics specification. Level labels are guidance, not exam-board endorsements. For AQA Radioactivity, calculating net decline as a ratio is Higher-tier work. Net means the overall change; ask Maurice whether this extension is relevant to your course. Explanations and practice were reviewed during development on 21 October 2026; Maurice should check their fit before assigning work.
Topic labels and your lesson-view preference are saved in this browser. This tab also remembers the last lesson stage, so you can choose to continue there. If you choose revision, selected activities and suggested revisit dates are saved here too. Recent question codes are also kept to reduce repeats. Reflection notes are saved automatically per topic when you type them; you can delete a note in the recap. They stay in this browser and are visible to other people using it. Practice answers and enquiry details are not saved. Clearing browser data removes the labels.