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:ba:b, multiply or divide both terms by the same non-zero number, cc.

a:b=(a×c):(b×c)a:b = (a \times c):(b \times c)
a:b=(a÷c):(b÷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.

Book overview

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Chapter 5: Understand and Use Ratio and Rate

  1. Lesson 1

    Lesson 1: Understand Ratios

  2. Lesson 2Current

    Lesson 2: Generate Equivalent Ratios

  3. Lesson 3

    Lesson 3: Compare Ratios

  4. Lesson 4

    Lesson 4: Represent and Graph Ratios

  5. Lesson 5

    Lesson 5: Understand Rates and Unit Rates

  6. Lesson 6

    Lesson 6: Compare Unit Rates

  7. Lesson 7

    Lesson 7: Solve Unit Rate Problems

  8. Lesson 8

    Lesson 8: Ratio Reasoning: Convert Customary Units

  9. Lesson 9

    Lesson 9: Ratio Reasoning: Convert Metric Units

  10. Lesson 10

    Lesson 10: Relate Customary and Metric Units

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Generating Equivalent Ratios

Property

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

a:b=(a×c):(b×c)a:b = (a \times c):(b \times c)
a:b=(a÷c):(b÷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.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 5: Understand and Use Ratio and Rate

  1. Lesson 1

    Lesson 1: Understand Ratios

  2. Lesson 2Current

    Lesson 2: Generate Equivalent Ratios

  3. Lesson 3

    Lesson 3: Compare Ratios

  4. Lesson 4

    Lesson 4: Represent and Graph Ratios

  5. Lesson 5

    Lesson 5: Understand Rates and Unit Rates

  6. Lesson 6

    Lesson 6: Compare Unit Rates

  7. Lesson 7

    Lesson 7: Solve Unit Rate Problems

  8. Lesson 8

    Lesson 8: Ratio Reasoning: Convert Customary Units

  9. Lesson 9

    Lesson 9: Ratio Reasoning: Convert Metric Units

  10. Lesson 10

    Lesson 10: Relate Customary and Metric Units