Learn on PengiReveal Math, Course 1Module 1: Ratios and Rates

1-2 Tables of Equivalent Ratios

In this Grade 6 lesson from Reveal Math, Course 1, students learn how to represent equivalent ratios using ratio tables and double number lines. They practice both the additive and multiplicative structures of ratio tables, including the process of scaling to find unknown quantities in equivalent ratios. The lesson builds skills in scaling forward and backward to solve real-world problems involving proportional relationships.

Section 1

Representing Equivalent Ratios in Tables

Property

Two ratios, a:ba : b and c:dc : d, are equivalent ratios if there is a positive number pp such that

c=p×a,d=p×b.c = p \times a, \quad d = p \times b.

This means you can create equivalent ratios by multiplying both parts of the ratio by the same positive number. Ratio tables organize these equivalent ratios in rows or columns to show the relationship clearly.

Examples

Section 2

Additive and Multiplicative Structures of Ratios

Property

You can generate equivalent ratios using two primary methods:

  1. Multiplication or Division: Multiply or divide both quantities in a ratio by the same non-zero number, cc.
a:b→(a⋅c):(b⋅c)a:b \rightarrow (a \cdot c) : (b \cdot c)
  1. Repeated Addition: Add the quantities of the original ratio to the previous ratio to generate a sequence.

Book overview

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Module 1: Ratios and Rates

  1. Lesson 1

    1-1 Understand Ratios

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  2. Lesson 2Current

    1-2 Tables of Equivalent Ratios

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  3. Lesson 3

    1-3 Graphs of Equivalent Ratios

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  4. Lesson 4

    1-4 Compare Ratio Relationships

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  5. Lesson 5

    1-5 Solve Ratio Problems

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  6. Lesson 6

    1-6 Convert Customary Measurement Units

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  7. Lesson 7

    1-7 Understand Rates and Unit Rates

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  8. Lesson 8

    1-8 Solve Rate Problems

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Lesson overview

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Expand

Section 1

Representing Equivalent Ratios in Tables

Property

Two ratios, a:ba : b and c:dc : d, are equivalent ratios if there is a positive number pp such that

c=p×a,d=p×b.c = p \times a, \quad d = p \times b.

This means you can create equivalent ratios by multiplying both parts of the ratio by the same positive number. Ratio tables organize these equivalent ratios in rows or columns to show the relationship clearly.

Examples

Section 2

Additive and Multiplicative Structures of Ratios

Property

You can generate equivalent ratios using two primary methods:

  1. Multiplication or Division: Multiply or divide both quantities in a ratio by the same non-zero number, cc.
a:b→(a⋅c):(b⋅c)a:b \rightarrow (a \cdot c) : (b \cdot c)
  1. Repeated Addition: Add the quantities of the original ratio to the previous ratio to generate a sequence.

Book overview

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

Continue this chapter

Module 1: Ratios and Rates

  1. Lesson 1

    1-1 Understand Ratios

    LearnPractice
  2. Lesson 2Current

    1-2 Tables of Equivalent Ratios

    LearnPractice
  3. Lesson 3

    1-3 Graphs of Equivalent Ratios

    LearnPractice
  4. Lesson 4

    1-4 Compare Ratio Relationships

    LearnPractice
  5. Lesson 5

    1-5 Solve Ratio Problems

    LearnPractice
  6. Lesson 6

    1-6 Convert Customary Measurement Units

    LearnPractice
  7. Lesson 7

    1-7 Understand Rates and Unit Rates

    LearnPractice
  8. Lesson 8

    1-8 Solve Rate Problems

    LearnPractice