Learn on PengienVision, Mathematics, Grade 5Chapter 8: Apply Understanding of Multiplication to Multiply Fractions

Lesson 8: Multiplication as Scaling

In this Grade 5 lesson from enVision Mathematics Chapter 8, students learn to use multiplication as scaling to predict whether a product will be greater than, less than, or equal to a given number without calculating. Students discover that multiplying by a fraction less than 1 shrinks a value, multiplying by a fraction greater than 1 increases it, and multiplying by a fraction equal to 1 leaves it unchanged. Practice includes comparing products using inequality symbols and ordering expressions by size using number sense rather than computation.

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

Comparing Scaled Products

Property

To compare two products with a common factor, $a \times b$ and $a \times c$ (where $a > 0$ ), you only need to compare the scaling factors, $b$ and $c$ .
The relationship between the products will be the same as the relationship between the scaling factors.

If $b > c$ , then $a \times b > a \times c$ .

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

Comparing Scaled Products

Property

If $b > c$ , then $a \times b > a \times c$ .

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

Comparing Scaled Products

Property

If $b > c$ , then $a \times b > a \times c$ .