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

Lesson 2: Ratio Tables

In this Grade 6 lesson from Big Ideas Math, Course 1 (Chapter 5: Ratios and Rates), students learn how to use ratio tables to find and organize equivalent ratios by applying addition, subtraction, multiplication, and division. Through hands-on activities and worked examples, students practice completing ratio tables and solving real-life problems such as scaling mixtures and calculating ingredient amounts. The lesson addresses standards 6.RP.1 and 6.RP.3a, building foundational skills in proportional reasoning.

Section 1

Equivalent Ratios

Property

Two ratios, $a : b$ and $c : d$ , are equivalent ratios if there is a positive number $p$ such that

c = p \times a, \quad d = p \times b.

This means you can create equivalent ratios by multiplying or dividing both parts of the ratio by the same positive number. This is often used to simplify a ratio by dividing both numbers by their greatest common factor.

Examples

The ratio 3:7 is equivalent to 9:21 because both parts were multiplied by 3. ( $3 \times 3 = 9$ and $7 \times 3 = 21$ ).
To simplify the ratio 20:15, find the greatest common factor, which is 5. Dividing both parts by 5 gives the equivalent ratio 4:3.
A map scale is 1 inch to 5 miles (1:5). An equivalent ratio shows that 4 inches on the map represents 20 miles, since both parts are multiplied by 4.

Explanation

Equivalent ratios are like different-sized versions of the same recipe. The proportions stay the same whether you're making a small snack or a giant feast. You create them by multiplying or dividing both numbers in the ratio by the same amount.

Section 2

Constructing and Using Ratio Tables

Property

A ratio table organizes equivalent ratios in rows or columns, where each ratio maintains the same proportional relationship: $\frac{a}{b} = \frac{2a}{2b} = \frac{3a}{3b} = \frac{ka}{kb}$ for any multiplier $k$ .

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Equivalent Ratios

Property

Two ratios, $a : b$ and $c : d$ , are equivalent ratios if there is a positive number $p$ such that

c = p \times a, \quad d = p \times b.

Examples

The ratio 3:7 is equivalent to 9:21 because both parts were multiplied by 3. ( $3 \times 3 = 9$ and $7 \times 3 = 21$ ).
To simplify the ratio 20:15, find the greatest common factor, which is 5. Dividing both parts by 5 gives the equivalent ratio 4:3.
A map scale is 1 inch to 5 miles (1:5). An equivalent ratio shows that 4 inches on the map represents 20 miles, since both parts are multiplied by 4.

Explanation

Section 2

Constructing and Using Ratio Tables

Property

Examples

Overview

Lesson overview

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

Overview

Section 1

Equivalent Ratios

Property

Two ratios, $a : b$ and $c : d$ , are equivalent ratios if there is a positive number $p$ such that

c = p \times a, \quad d = p \times b.

Examples

The ratio 3:7 is equivalent to 9:21 because both parts were multiplied by 3. ( $3 \times 3 = 9$ and $7 \times 3 = 21$ ).
To simplify the ratio 20:15, find the greatest common factor, which is 5. Dividing both parts by 5 gives the equivalent ratio 4:3.
A map scale is 1 inch to 5 miles (1:5). An equivalent ratio shows that 4 inches on the map represents 20 miles, since both parts are multiplied by 4.