Learn on PengiEureka Math, Grade 5Chapter 15: Equivalent Fractions

Lesson 1: Make equivalent fractions with the number line, the area model, and numbers.

In this Grade 5 Eureka Math lesson from Chapter 15, students learn to create equivalent fractions using three representations: the number line, the area model, and multiplication of the numerator and denominator by the same factor. Through hands-on activities with paper strips and visual models, students explore why fractions like one-half and two-fourths name the same value and occupy the same point on the number line.

Section 1

Identifying Equivalent Fractions with Models

Property

Equivalent fractions are different fractions that name the same number.
They represent the same part of a whole or the same point on a number line, so they have the same value: ab=cd\frac{a}{b} = \frac{c}{d}.

Examples

Section 2

Connecting Area Models and Multiplication for Equivalent Fractions

Property

To generate an equivalent fraction from an area model, you can partition the model with horizontal lines.
If you create nn new horizontal sections, you are multiplying the number of shaded parts (numerator) and the total number of parts (denominator) by nn.
This visual process is represented by the numerical formula:

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Identifying Equivalent Fractions with Models

Property

Equivalent fractions are different fractions that name the same number.
They represent the same part of a whole or the same point on a number line, so they have the same value: ab=cd\frac{a}{b} = \frac{c}{d}.

Examples

Section 2

Connecting Area Models and Multiplication for Equivalent Fractions

Property

To generate an equivalent fraction from an area model, you can partition the model with horizontal lines.
If you create nn new horizontal sections, you are multiplying the number of shaded parts (numerator) and the total number of parts (denominator) by nn.
This visual process is represented by the numerical formula:

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Examples