Area Model Multiplication Studio

See why multiplication works by drawing rectangles. Break numbers into tens and ones, find the area of each section, then add the pieces together for the full product.

Try an example

23 × 14 = ?

We want to multiply 23 × 14.

Press Next to break these numbers into tens and ones.

1
2
3
4

Step 1: See the problem

Area Model Reference

How the Area Model Works

The area model shows multiplication as a rectangle split into parts.

  • 23 × 14 = (20 + 3) × (10 + 4)
  • 20 × 10 = 200 (top-left)
  • 20 × 4 = 80 (top-right)
  • 3 × 10 = 30 (bottom-left)
  • 3 × 4 = 12 (bottom-right)
  • 200 + 80 + 30 + 12 = 322

Distributive Property

The area model uses the distributive property:

a × (b + c) = a × b + a × c

You break one factor into smaller pieces, multiply each piece, then add the results.

This is the same strategy used in the standard algorithm — the area model just makes it visible.