Finding Missing Values in a Table of Equivalent Ratios

Introduction

You can find equivalent ratios by multiplying or dividing both terms of a ratio by the same number. This is similar to finding equivalent fractions of a given fraction. All the ratios in the tables below are equivalent.

The table below represent the equivalent ratios 1:3, 2:6, 3:9

1	3
2	6
3	9

The table below represent the equivalent ratios 1:4, 3:12, 5:20

1	4
3	12
5	20

Such tables of equivalent ratios can be used to find missing values as follows.

Example 1

Find the missing values in the following table of equivalent ratios:

3	10
6	x
9	30
y	40

Solution

Step 1:

Find the missing values in the following table of equivalent ratios :

$\frac{x}{6} = \frac{10}{3}; x = \frac{10}{3} \times 6 = \frac{10}{3} \times \frac{6}{1} = 20$

$\frac{y}{40} = \frac{3}{10}; y = \frac{3}{10} \times 40 = \frac{3}{10} \times \frac{40}{1} = 12$

Step 2:

So, $x = 9; y = 28$

Example 2

Find the missing values in the following table of equivalent ratios:

2	3
4	6
6	x
y	12

Solution

Step 1:

Since the table gives values of equivalent ratios

$\frac{x}{6} = \frac{3}{2}; x = \frac{3}{2} \times \frac{6}{1} = \frac{3}{2} \times \frac{6}{1} = 9$

$\frac{y}{12} = \frac{2}{3}; y = \frac{2}{3} \times 12 = \frac{2}{3} \times \frac{12}{1} = 8$

Step 2:

So, $x = 9; y = 8$