---
title: "Area and the distributive property"
description: "Use tiling to demonstrate the distributive property: the area of a rectangle with sides a and (b+c) equals a×b + a×c; use area models to represent the distributive property"
canonical: https://lightmysky.com/learn/mathematics/area-and-the-distributive-property-mt_AQo4u7O4sM
source: https://lightmysky.com/learn/mathematics/area-and-the-distributive-property-mt_AQo4u7O4sM.md
retrieved: 2026-10-19
---

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# Area and the distributive property

Use tiling to demonstrate the distributive property: the area of a rectangle with sides a and (b+c) equals a×b + a×c; use area models to represent the distributive property

Subject: Mathematics · Area: Measurement · Ages 8 to 9
Page: https://lightmysky.com/learn/mathematics/area-and-the-distributive-property-mt_AQo4u7O4sM

## Ready when they can

- Tile a 3×(4+2) rectangle and show it decomposes into 3×4 and 3×2
- Use an area model to compute 6×13 as 6×10 + 6×3
- Draw an area model showing 5×(7+3) = 5×7 + 5×3

## Lesson: Splitting a rectangle to find its area

A rectangle's area is one side times the other side. But a big rectangle, like a school garden that is 6 meters by 13 meters, can be hard to multiply in your head. Split one side into two smaller parts, find the area of each part, then add them together to get the same total.

*(drawing: This 3-by-6 rectangle splits into a 3×4 part and a 3×2 part. 3×4 + 3×2 = 12 + 6 = 18, the same as 3×6.)*

**Example.** To work out 6×13, split 13 into 10 and 3. Then 6×13 = 6×10 + 6×3 = 60 + 18 = 78.

**Tip.** You can split either side of the rectangle, not just one way. Splitting only breaks the counting into easier steps. It does not change how much space is inside.

**Recap.** Split one side of a rectangle into parts, multiply each part separately, then add the results to get the same total area.

## Practice

18 questions on this page, each with its working shown.

## Needs first

- [Rectangle area by multiplying](https://lightmysky.com/learn/mathematics/rectangle-area-by-multiplying-mt_GzcJEVkNRn)

## Opens up

- [Moving between diagrams and equations with fractions](https://lightmysky.com/learn/mathematics/moving-between-diagrams-and-equations-with-fractions-mt_3VmBdlAeOZ)
- [Long multiplication](https://lightmysky.com/learn/mathematics/long-multiplication-mt_q9EaJc2FP8)