Learn on PengienVision, Mathematics, Grade 7Chapter 2: Analyze and Use Proportional Relationships

Lesson 1: Connect Ratios, Rates, and Unit Rates

In this Grade 7 lesson from enVision Mathematics Chapter 2, students learn how to find and apply unit rates by dividing ratios to a per-unit value, and use equivalent ratios to compare rates and solve multi-step problems. Students practice calculating unit rates in real-world contexts such as hourly pay, consumption over time, and speed, then use those rates to make comparisons and draw conclusions. The lesson builds foundational understanding of how ratios, rates, and unit rates are interconnected tools for proportional reasoning.

Section 1

Ratios

Property

A ratio is a type of quotient used to compare two numerical quantities. The ratio of aa to bb is written ab\frac{a}{b}. A ratio can be expressed as a decimal instead of a common fraction.

Examples

  • In a class with 15 boys and 12 girls, the ratio of boys to girls is 1512\frac{15}{12}, which simplifies to 54\frac{5}{4}.
  • A recipe calls for 2 cups of sugar for every 5 cups of flour. The ratio of sugar to flour is 25\frac{2}{5}.

Section 2

Understanding Rates and Unit Rates

Property

A ratio compares two quantities, often of the same kind.

A rate is a special type of ratio that compares quantities with different units (like miles and gallons, or dollars and hours).

Book overview

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Chapter 2: Analyze and Use Proportional Relationships

  1. Lesson 1Current

    Lesson 1: Connect Ratios, Rates, and Unit Rates

  2. Lesson 2

    Lesson 2: Determine Unit Rates with Ratios of Fractions

  3. Lesson 3

    Lesson 3: Understand Proportional Relationships: Equivalent Ratios

  4. Lesson 4

    Lesson 4: Describe Proportional Relationships: Constant of Proportionality

  5. Lesson 5

    Lesson 5: Graph Proportional Relationships

  6. Lesson 6

    Lesson 6: Apply Proportional Reasoning to Solve Problems

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Ratios

Property

A ratio is a type of quotient used to compare two numerical quantities. The ratio of aa to bb is written ab\frac{a}{b}. A ratio can be expressed as a decimal instead of a common fraction.

Examples

  • In a class with 15 boys and 12 girls, the ratio of boys to girls is 1512\frac{15}{12}, which simplifies to 54\frac{5}{4}.
  • A recipe calls for 2 cups of sugar for every 5 cups of flour. The ratio of sugar to flour is 25\frac{2}{5}.

Section 2

Understanding Rates and Unit Rates

Property

A ratio compares two quantities, often of the same kind.

A rate is a special type of ratio that compares quantities with different units (like miles and gallons, or dollars and hours).

Book overview

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

Continue this chapter

Chapter 2: Analyze and Use Proportional Relationships

  1. Lesson 1Current

    Lesson 1: Connect Ratios, Rates, and Unit Rates

  2. Lesson 2

    Lesson 2: Determine Unit Rates with Ratios of Fractions

  3. Lesson 3

    Lesson 3: Understand Proportional Relationships: Equivalent Ratios

  4. Lesson 4

    Lesson 4: Describe Proportional Relationships: Constant of Proportionality

  5. Lesson 5

    Lesson 5: Graph Proportional Relationships

  6. Lesson 6

    Lesson 6: Apply Proportional Reasoning to Solve Problems