---
title: "Area with Fractions"
description: "Find the area of a rectangle with fractional side lengths by tiling with unit-fraction squares; show that the area equals the product of the side lengths"
canonical: https://lightmysky.com/learn/mathematics/area-with-fractions-mt_gx6KQK5-Kx
source: https://lightmysky.com/learn/mathematics/area-with-fractions-mt_gx6KQK5-Kx.md
retrieved: 2026-10-19
---

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# Area with Fractions

Find the area of a rectangle with fractional side lengths by tiling with unit-fraction squares; show that the area equals the product of the side lengths

Subject: Mathematics · Area: Fractions · Ages 10 to 11
Page: https://lightmysky.com/learn/mathematics/area-with-fractions-mt_gx6KQK5-Kx

## Ready when they can

- Tile a 2/3 × 3/4 rectangle with 1/12 squares and count to find area = 6/12 = 1/2
- Explain why the number of unit-fraction tiles equals the product of the two fractions
- Calculate the area of a rectangle with sides 1 1/2 and 2/3 using fraction multiplication

## Lesson: Area with Fraction Sides

You already know how to multiply fractions. Today you will use that skill to find the area of a rectangle when the length and width are both fractions, like a rug that is 2/3 meter long and 3/4 meter wide.

*(drawing: Cut a whole square into 3 columns and 4 rows. That makes 12 equal tiles, and each tile is 1/12 of the square.)*

**Example.** A rectangle is 2/3 m long and 3/4 m wide. Line up 2 of the 3 columns and 3 of the 4 rows. That covers 6 of the 12 tiles, so the area is 6/12 square meters, which is the same as 1/2 square meter.

**Example.** A garden bed is 1 1/2 m long and 2/3 m wide. First write 1 1/2 as 3/2. Then multiply: 3/2 x 2/3 = 6/6 = 1. The bed's area is 1 square meter, the same answer tiling would give.

**Tip.** Turn mixed numbers into improper fractions before you multiply. Then estimate first: since 2/3 and 3/4 are both less than 1, the area has to be smaller than 3/4. That helps you catch mistakes.

**Recap.** Area with fraction sides follows the same rule as always, length times width, and tiling with tiny fraction squares shows exactly why it works.

## Practice

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

## Needs first

- [Multiplying fractions (age 10+)](https://lightmysky.com/learn/mathematics/multiplying-fractions-age-10-mt_AabJisinfi)
- [Area and perimeter of rectangles](https://lightmysky.com/learn/mathematics/area-and-perimeter-of-rectangles-mt_eiB3-6pu6a)
- [Fractions as parts of shapes](https://lightmysky.com/learn/mathematics/fractions-as-parts-of-shapes-mt_idbKDrf9qZ)

## Opens up

- [Real-world fraction multiplication](https://lightmysky.com/learn/mathematics/real-world-fraction-multiplication-mt_lvaSGHwvQ5)
- [Multiplication as scaling](https://lightmysky.com/learn/mathematics/multiplication-as-scaling-mt_VKW8lOcFaw)