Learn on PengiEureka Math, Grade 5Chapter 16: Making Like Units Pictorially

Lesson 1: Add fractions with unlike units using the strategy of creating equivalent fractions.

In this Grade 5 Eureka Math lesson from Chapter 16, students learn how to add fractions with unlike denominators by converting them into equivalent fractions with common units. Using paper folding and rectangular area models, students practice renaming fractions such as one-half and one-fourth into like units before adding. The lesson builds on fluency with equivalent fractions and prepares students to add unlike unit fractions accurately and efficiently.

Section 1

The 'Like Units' Rule for Adding Fractions

Property

To add fractions, they must have like units, meaning a common denominator. You can only add the numerators when the denominators are the same.

ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}

Examples

Section 2

Adding Unlike Fractions with a Rectangular Model

Property

To add two fractions ab\frac{a}{b} and cd\frac{c}{d} using a rectangular model, partition a whole rectangle vertically into bb parts and horizontally into dd parts. This creates a common denominator of b×db \times d.
The sum is then calculated by adding the equivalent fractions:

ab+cd=a×db×d+c×bd×b=ad+cbbd\frac{a}{b} + \frac{c}{d} = \frac{a \times d}{b \times d} + \frac{c \times b}{d \times b} = \frac{ad + cb}{bd}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

The 'Like Units' Rule for Adding Fractions

Property

To add fractions, they must have like units, meaning a common denominator. You can only add the numerators when the denominators are the same.

ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}

Examples

Section 2

Adding Unlike Fractions with a Rectangular Model

Property

To add two fractions ab\frac{a}{b} and cd\frac{c}{d} using a rectangular model, partition a whole rectangle vertically into bb parts and horizontally into dd parts. This creates a common denominator of b×db \times d.
The sum is then calculated by adding the equivalent fractions:

ab+cd=a×db×d+c×bd×b=ad+cbbd\frac{a}{b} + \frac{c}{d} = \frac{a \times d}{b \times d} + \frac{c \times b}{d \times b} = \frac{ad + cb}{bd}

Examples