Explore the Area Model Multiplication & the Distributive
See multiplication as a rectangle, split it into four easier parts and watch the partial products add up. Free, no signup, runs in your browser.
- Free to use
- No signup
- Nothing to install
- Runs in your browser
Illustration. Open the tool for the real thing.
See it in action
The Area Model Multiplication & the Distributive with sample data entered and the result showing.
What is the Area Model Multiplication & the Distributive?
See multiplication as a rectangle, split it into four easier parts and watch the partial products add up. It runs in your browser, so a change to a setting or a drag on an object shows up at once.
Mental math, algebra (multiplying brackets), and tiling floors or planning gardens all use the area idea.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
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.
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.
Used for
Pick one to see how it fits.
Math learners
Algebra, geometry, trigonometry and calculus students, teachers preparing demonstrations, and self-learners who want to see the maths move.
Try it freeTeachers
For teachers: project the Area Model Multiplication & the Distributive Property on the board, let students predict the result, then run it together and test this: Use Split into tens on 17 × 14 and add the four parts. For students: change one thing at a time and write down what changes.
Try it freeHow it compares
A plain look at this tool next to the usual alternative.
| This simulation | Textbook diagram | |
|---|---|---|
| Interactive | Drag, tap and change settings | Fixed picture |
| Install | Nothing to install | Not needed |
| Cost | Free to use | Depends on the book |
Questions people ask
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. The Area Model Multiplication & the Distributive Property is free, needs no signup or download and runs in your web browser. It is part of the Math group of AZRS simulations.
Does the Area Model Multiplication & the Distributive Property work on a phone or tablet?
Yes. The Area Model Multiplication & the Distributive Property takes touch input as well as mouse input, so you can use its 4 adjustable settings with a finger. A larger screen makes the controls and graphs easier to read.
How do I use the Area Model Multiplication & the Distributive?
1. In 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. 2. In the Area Model Multiplication & the Distributive Property, pick an option such as Unit squares, Plain colors to switch modes or load an example. 3. In the Area Model Multiplication & the Distributive Property, press "Split into tens", "Random problem", "Swap sides" to start, reset or change what is happening. 4. Start with this experiment: Compute 13 × 8 by cutting at 10. Drag any glowing handle, object or slider with your mouse or finger and the Area Model Multiplication & the Distributive Property responds in real time. 5. Change one setting at a time and watch which readout moves, then compare it with this idea: Multiplying a × b gives the area of an a by b rectangle.
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Try the Area Model Multiplication & the Distributive now
See multiplication as a rectangle, split it into four easier parts and watch the partial. Free to use.
Try it free