Area Model Multiplication & the Distributive Property
See multiplication as a rectangle, split it into four easier parts and watch the partial products add up.
Multiply by drawing a rectangle. Drag the yellow cut lines to split each side into two easier parts. The four smaller areas add up to the whole product (the distributive property).
About the Area Model Multiplication & the Distributive Property
Free area model multiplication & the distributive property. See multiplication as a rectangle, split it into four easier parts and watch the partial products add up. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for math, the area model multiplication & the distributive property runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
See multiplication as a rectangle, split it into four easier parts and watch the partial products add up. Use it to explore math ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Area Model Multiplication & the Distributive Property
- Use the controls to change Width (first number), Height (second number), Cut the width at, Cut the height at. The simulation reacts instantly.
- Pick an option such as Unit squares, Plain colors to switch modes or load an example.
- Press "Split into tens", "Random problem" to start, reset or change what is happening.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Compute 13 × 8 by cutting at 10.
- Use Split into tens on 17 × 14 and add the four parts.
- Try a random problem and predict the product before looking.
- Cut in different places and check that the total never changes.
Key ideas you can learn
- Multiplying a × b gives the area of an a by b rectangle.
- You can split the rectangle into smaller rectangles and add their areas.
- This is the distributive property: (x + y) × (u + v) = xu + xv + yu + yv.
- Splitting into tens and ones makes big products easier to do in your head.
Where this is used in the real world
Mental math, algebra (multiplying brackets), and tiling floors or planning gardens all use the area idea.
Who is this simulation for?
Algebra, geometry, trigonometry and calculus students, teachers preparing demonstrations, and self-learners who want to see the maths move.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
What is the area model?
A picture of multiplication as the area of a rectangle, cut into parts whose areas are easy to work out.
Is this the same as the box method?
Yes. The box method is the same idea written as a table.
Is the Area Model Multiplication & the Distributive Property free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Area Model Multiplication & the Distributive Property work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.