Learn on PengiBig Ideas Math, Advanced 1Chapter 14: Ratios and Proportions

Lesson 3: Writing Proportions

In this Grade 6 lesson from Big Ideas Math Advanced 1, students learn how to write proportions by setting up equivalent ratios using tables to organize real-world information, then solving for unknown quantities using mental math. Drawing on contexts like baseball batting averages and recipe scaling, students practice expressing proportional relationships in the form of equivalent fractions with consistent units across numerators and denominators. The lesson aligns with standards 7.RP.2c and 7.RP.3, building foundational skills in recognizing and applying proportional reasoning.

Section 1

Writing Proportions

Property

Two quantities xx and yy are in a proportional relationship if the quotient yx\frac{y}{x} is a fixed number kk whenever xx is not zero.

This relationship can be written as a proportion: yx=k\frac{y}{x} = k or y=kxy = kx.

Section 2

Mental Math Strategies for Solving Proportions

Property

To solve proportions using mental math, identify the multiplication factor between known values and apply it to find the unknown: if ab=cd\frac{a}{b} = \frac{c}{d} and you know three values, find what number multiplies the known denominator to get the unknown denominator, then multiply the corresponding numerator by the same factor.

Examples

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Chapter 14: Ratios and Proportions

  1. Lesson 1

    Lesson 1: Ratios and Rates

  2. Lesson 2

    Lesson 2: Proportions

  3. Lesson 3Current

    Lesson 3: Writing Proportions

  4. Lesson 4

    Lesson 4: Solving Proportions

  5. Lesson 5

    Lesson 5: Slope

  6. Lesson 6

    Lesson 6: Direct Variation

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Writing Proportions

Property

Two quantities xx and yy are in a proportional relationship if the quotient yx\frac{y}{x} is a fixed number kk whenever xx is not zero.

This relationship can be written as a proportion: yx=k\frac{y}{x} = k or y=kxy = kx.

Section 2

Mental Math Strategies for Solving Proportions

Property

To solve proportions using mental math, identify the multiplication factor between known values and apply it to find the unknown: if ab=cd\frac{a}{b} = \frac{c}{d} and you know three values, find what number multiplies the known denominator to get the unknown denominator, then multiply the corresponding numerator by the same factor.

Examples

Book overview

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

Continue this chapter

Chapter 14: Ratios and Proportions

  1. Lesson 1

    Lesson 1: Ratios and Rates

  2. Lesson 2

    Lesson 2: Proportions

  3. Lesson 3Current

    Lesson 3: Writing Proportions

  4. Lesson 4

    Lesson 4: Solving Proportions

  5. Lesson 5

    Lesson 5: Slope

  6. Lesson 6

    Lesson 6: Direct Variation