Learn on PengiBig Ideas Math, Advanced 1Chapter 5: Ratios and Rates

Lesson 2: Ratio Tables

In this Grade 6 lesson from Big Ideas Math Advanced 1, Chapter 5, students learn how to use ratio tables to find and organize equivalent ratios. They practice completing ratio tables by applying addition, subtraction, multiplication, and division to generate ratios that describe the same relationship. The lesson connects to Common Core standards 6.RP.1 and 6.RP.3a through real-life contexts such as mixing beverages and measuring ingredients for hummingbird feeders.

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

Adding Columns in Ratio Tables

Property

When two columns in a ratio table represent equivalent ratios, adding the corresponding values from these columns creates a new column that is also an equivalent ratio.

Examples

Section 3

Real-World Applications of Ratio Tables

Property

Ratio tables can solve real-world problems by organizing given ratios and finding equivalent ratios that match the problem's constraints.

Set up the table with the original ratio, then use multiplication or addition of columns to find the desired quantities.

Book overview

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Continue this chapter

Chapter 5: Ratios and Rates

  1. Lesson 1

    Lesson 1: Ratios

  2. Lesson 2Current

    Lesson 2: Ratio Tables

  3. Lesson 3

    Lesson 3: Rates

  4. Lesson 4

    Lesson 4: Comparing and Graphing Ratios

  5. Lesson 5

    Lesson 5: Percents

  6. Lesson 6

    Lesson 6: Solving Percent Problems

  7. Lesson 7

    Lesson 7: Converting Measures

Lesson overview

Expand to review the lesson summary and core properties.

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

Adding Columns in Ratio Tables

Property

When two columns in a ratio table represent equivalent ratios, adding the corresponding values from these columns creates a new column that is also an equivalent ratio.

Examples

Section 3

Real-World Applications of Ratio Tables

Property

Ratio tables can solve real-world problems by organizing given ratios and finding equivalent ratios that match the problem's constraints.

Set up the table with the original ratio, then use multiplication or addition of columns to find the desired quantities.

Book overview

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

Continue this chapter

Chapter 5: Ratios and Rates

  1. Lesson 1

    Lesson 1: Ratios

  2. Lesson 2Current

    Lesson 2: Ratio Tables

  3. Lesson 3

    Lesson 3: Rates

  4. Lesson 4

    Lesson 4: Comparing and Graphing Ratios

  5. Lesson 5

    Lesson 5: Percents

  6. Lesson 6

    Lesson 6: Solving Percent Problems

  7. Lesson 7

    Lesson 7: Converting Measures