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

1-1 Understand Ratios

In this Grade 6 lesson from Reveal Math, Course 1, students learn how to define and represent ratios as multiplicative comparisons between two quantities, distinguishing between part-to-whole and part-to-part ratios. Using real-world contexts like lemonade recipes and paint mixtures, students practice writing ratios in three forms — word form, colon notation, and fraction notation — while exploring how equivalent ratios scale across multiple batches. This lesson builds the foundational ratio language and reasoning skills central to Module 1: Ratios and Rates.

Section 1

Describing Ratios with "For Every" and "For Each"

Property

A ratio is a comparison between two quantities. The phrases for every and for each are used to define and describe this relationship verbally.

If a ratio compares quantity $a$ to quantity $b$ , it can be stated as:

a \text{ for every } b

a \text{ for each } b

Section 2

Writing Ratios in Three Notations

Property

A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of $a$ to $b$ is written $a$ to $b$ , $\frac{a}{b}$ , or $a:b$ .

Examples

The ratio 20 to 36 can be written as $20\ \text{to}\ 36$ , $20:36$ , and $\frac{20}{36}$ , which simplifies to $\frac{5}{9}$ .

The ratio 45 to 18 can be written as $45\ \text{to}\ 18$ , $45:18$ , and $\frac{45}{18}$ , which simplifies to $\frac{5}{2}$ .

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Describing Ratios with "For Every" and "For Each"

Property

A ratio is a comparison between two quantities. The phrases for every and for each are used to define and describe this relationship verbally.

If a ratio compares quantity $a$ to quantity $b$ , it can be stated as:

a \text{ for every } b

a \text{ for each } b

Section 2

Writing Ratios in Three Notations

Property

A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of $a$ to $b$ is written $a$ to $b$ , $\frac{a}{b}$ , or $a:b$ .

Examples

The ratio 20 to 36 can be written as $20\ \text{to}\ 36$ , $20:36$ , and $\frac{20}{36}$ , which simplifies to $\frac{5}{9}$ .

The ratio 45 to 18 can be written as $45\ \text{to}\ 18$ , $45:18$ , and $\frac{45}{18}$ , which simplifies to $\frac{5}{2}$ .

Overview

Lesson overview

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

Overview

Section 1

Describing Ratios with "For Every" and "For Each"

Property

A ratio is a comparison between two quantities. The phrases for every and for each are used to define and describe this relationship verbally.

If a ratio compares quantity $a$ to quantity $b$ , it can be stated as:

a \text{ for every } b

a \text{ for each } b

Section 2

Writing Ratios in Three Notations

Property

A ratio compares two numbers or two quantities that are measured with the same unit. The ratio of $a$ to $b$ is written $a$ to $b$ , $\frac{a}{b}$ , or $a:b$ .

Examples

The ratio 20 to 36 can be written as $20\ \text{to}\ 36$ , $20:36$ , and $\frac{20}{36}$ , which simplifies to $\frac{5}{9}$ .

The ratio 45 to 18 can be written as $45\ \text{to}\ 18$ , $45:18$ , and $\frac{45}{18}$ , which simplifies to $\frac{5}{2}$ .