Learn on PengiBig Ideas Math, Course 2Chapter 5: Ratios and Proportions

Lesson 1: Ratios and Rates

In this Grade 7 lesson from Big Ideas Math Course 2, Chapter 5, students learn to find ratios, rates, and unit rates, including complex fractions involving ratios of fractions. They practice writing and simplifying rates with different units, using ratio tables to find equivalent rates, and applying unit analysis to real-world problems.

Section 1

Ratios

Property

A ratio is a type of quotient used to compare two numerical quantities. The ratio of $a$ to $b$ is written $\frac{a}{b}$ . 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 $\frac{15}{12}$ , which simplifies to $\frac{5}{4}$ .

A recipe calls for 2 cups of sugar for every 5 cups of flour. The ratio of sugar to flour is $\frac{2}{5}$ .

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).

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 $a$ to $b$ is written $\frac{a}{b}$ . 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 $\frac{15}{12}$ , which simplifies to $\frac{5}{4}$ .

A recipe calls for 2 cups of sugar for every 5 cups of flour. The ratio of sugar to flour is $\frac{2}{5}$ .

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).

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Ratios

Property

A ratio is a type of quotient used to compare two numerical quantities. The ratio of $a$ to $b$ is written $\frac{a}{b}$ . 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 $\frac{15}{12}$ , which simplifies to $\frac{5}{4}$ .

A recipe calls for 2 cups of sugar for every 5 cups of flour. The ratio of sugar to flour is $\frac{2}{5}$ .

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).