Learn on PengienVision, Mathematics, Grade 6Chapter 5: Understand and Use Ratio and Rate

Lesson 2: Generate Equivalent Ratios

In this Grade 6 lesson from enVision Mathematics Chapter 5, students learn how to generate equivalent ratios by multiplying or dividing both terms of a ratio by the same nonzero number. Using tables and direct calculations, students practice finding equivalent ratios in real-world contexts such as mixing paint colors, sports statistics, and the ratio of a circle's circumference to its diameter (pi). The lesson builds foundational understanding of proportional relationships essential for ratio and rate reasoning.

Section 1

Generating Equivalent Ratios

Property

To find a ratio equivalent to $a:b$ , multiply or divide both terms by the same non-zero number, $c$ .

a:b = (a \times c):(b \times c)

a:b = (a \div c):(b \div c)

Examples

Section 2

Common Error: Adding the Same Number to Both Terms

Property

Ratios represent a multiplicative relationship, not an additive one.

Adding or subtracting the same non-zero number to both terms of a ratio changes the relationship and does not create an equivalent ratio.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Generating Equivalent Ratios

Property

To find a ratio equivalent to $a:b$ , multiply or divide both terms by the same non-zero number, $c$ .

a:b = (a \times c):(b \times c)

a:b = (a \div c):(b \div c)

Examples

Section 2

Common Error: Adding the Same Number to Both Terms

Property

Ratios represent a multiplicative relationship, not an additive one.

Adding or subtracting the same non-zero number to both terms of a ratio changes the relationship and does not create an equivalent ratio.