Learn on PengiEureka Math, Grade 5Chapter 24: Multiplication with Fractions and Decimals as Scaling and Word Problems

Lesson 2: Compare the size of the product to the size of the factors.

In this Grade 5 Eureka Math lesson from Chapter 24, students learn to compare the size of a product to the size of its factors when multiplying by fractions, exploring how multiplying by a fraction less than 1, equal to 1, or greater than 1 affects the result. Using concrete examples like multiplying 12 inches by fractions such as 1/4, 3/4, and 5/4, students discover that a factor less than 1 shrinks the product, a factor equal to 1 leaves it unchanged, and a factor greater than 1 enlarges it. Fluency practice with unit conversions and multiplying fractions by whole numbers reinforces the skills needed to reason about scaling with fractions and decimals.

Section 1

Predicting Product Size Using a Scaling Factor

Property

When a number $a$ is multiplied by a fractional scaling factor $f$ :

If $f < 1$ , the product is smaller than $a$ . ( $a \times f < a$ )
If $f = 1$ , the product is equal to $a$ . ( $a \times f = a$ )
If $f > 1$ , the product is larger than $a$ . ( $a \times f > a$ )

Examples

Section 2

Applying Scaling to Real-World Measurements

Property

To find a new, scaled measurement, multiply the original measurement by the scaling factor.

\text{New Measurement} = \text{Original Measurement} \times \text{Scaling Factor}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Predicting Product Size Using a Scaling Factor

Property

When a number $a$ is multiplied by a fractional scaling factor $f$ :

If $f < 1$ , the product is smaller than $a$ . ( $a \times f < a$ )
If $f = 1$ , the product is equal to $a$ . ( $a \times f = a$ )
If $f > 1$ , the product is larger than $a$ . ( $a \times f > a$ )

Examples

Section 2

Applying Scaling to Real-World Measurements

Property

To find a new, scaled measurement, multiply the original measurement by the scaling factor.

\text{New Measurement} = \text{Original Measurement} \times \text{Scaling Factor}

Examples

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Predicting Product Size Using a Scaling Factor

Property

When a number $a$ is multiplied by a fractional scaling factor $f$ :

If $f < 1$ , the product is smaller than $a$ . ( $a \times f < a$ )
If $f = 1$ , the product is equal to $a$ . ( $a \times f = a$ )
If $f > 1$ , the product is larger than $a$ . ( $a \times f > a$ )

Examples

Section 2

Applying Scaling to Real-World Measurements

Property

To find a new, scaled measurement, multiply the original measurement by the scaling factor.

\text{New Measurement} = \text{Original Measurement} \times \text{Scaling Factor}