Topics
4. Ratios & Proportions
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United States of America
Grade 6

4.03 Ratio tables

Lesson
Practice

Introduction

Previously, We have learned about  equivalent ratios and simplified ratios  . We'll now make tables of equivalent ratios to relate quantities, find missing values in tables and compare ratios.

Ratio tables

We can use a ratio table to represent equivalent ratios, as well as determine unknown values.

For example, if a pie recipe calls for 1 tablespoons of brown sugar per 2 cups of flour, we could write this as a ratio: 2:1.

In a ratio table we have:

Sugar2468
Flour1234

We can also use a ratio table to help us determine unknown values. For example, if we wanted to find out how much flour is needed when we use 12 tablespoons of brown sugar, we have the following:

Sugar246812
Flour1234⬚

We can determine the corresponding amount of flour to 12 tablespoons of brown sugar by finding equivalent ratios.

\displaystyle 6:3\displaystyle =\displaystyle 12 : ⬚Equivalent ratios
\displaystyle 6:3\displaystyle =\displaystyle 6\times 2 : 3 \times 2Multiply both parts of the ratio by 2
\displaystyle =\displaystyle 12:6

Therefore, for every 12 tablespoons of brown sugar, we can use 6 cups of flour.

You may have noticed that there was another way to find this using the table.

Sugar246812
Flour1234⬚

We can see in the table that for 4 cups of flour we need 2 tablespoons of brown sugar, and for 8 cups of flour we need 4 tablespoons of brown sugar.

We know that 4 + 8 = 12 so we could have added 2 + 4 to get the 6 tablespoons of brown sugar.

Examples

Example 1

The following table shows the ratio of dogs to cats:

DogstoCats
9:5
18:10
27:
45:
:50
a

Complete the table of equivalent ratios.

Worked Solution
Create a strategy

We can find the equivalent ratios by multiplying or dividing both sides of a ratio by the same value.

Apply the idea
\displaystyle 9:5\displaystyle =\displaystyle 9 \times 3:5 \times 3Multiply by 3
\displaystyle =\displaystyle 27:15Evaluate
\displaystyle =\displaystyle 9\times 5: 5 \times 5Multiply by 5
\displaystyle =\displaystyle 45: 25Evaluate
\displaystyle =\displaystyle 9\times 10: 5 \times 10Multiply by 10
\displaystyle =\displaystyle 90: 50Evaluate
DogstoCats
9:5
18:10
27:15
45:25
90:50
b

If there are 270 dogs, how many cats are there expected to be?

A
150
B
30
C
270
D
266
Worked Solution
Create a strategy

Find the multiple number and multiply to the number of cats.

Apply the idea

We can find the multiple by which the number of dogs has increased, by dividing 270 by 9. We get a multiple of 30 and multiply to the number of cats which is 30 \times 5 = 150.

So, If there are 270 dogs, there are 150 cats. The correct option is A.

Example 2

Kate and Laura are selling cakes at a bake sale. For every 6 cakes that Kate sells, she will make \$15. For every 24 cakes that Laura sells, she will make \$53. Whose cakes are more expensive?

a

Fill in the missing gaps in the table for Kate.

\text{Cakes sold}61830
\text{Earning } (\$)306075
Worked Solution
Create a strategy

For Kate, the cakes and earnings is in the ratio 6:15.

Find the equivalent fractions to fill in missing gaps in the table.

Apply the idea

Each time the number of cakes increase by 6, earnings increase by 15. This means we get:

\text{Cakes sold}612182430
\text{Earning } (\$)1530456075
b

Fill in the missing gaps in the table for Laura.

\text{Cakes sold}487296120
\text{Earning } (\$)53159212265
Worked Solution
Create a strategy

For Laura, the cakes and earnings should increase in the ratio 24:53.

Apply the idea

Each time the number of cakes increase by 24, earnings increase by 53. This means we get:

\text{Cakes sold}24487296120
\text{Earning } (\$)53106159212265
c

Whose cakes are more expensive?

Worked Solution
Create a strategy

Use the tables from part (a) and part (b).

Apply the idea

Comparing the two tables from part (a) and (b), Kate makes \$60 from 24 cakes, and Laura only makes \$53 from 24 cakes. This means that Kate's cakes are more expensive than Laura's.

Idea summary

We can use ratio tables to determine unknown values by multiplying or dividing. All of the values in the table will be equivalent ratios.

Outcomes

6.RP.A.3

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g. By reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

6.RP.A.3.A

Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

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