WRITING AND SIMPLIFYING RATIOS

A ratio is a comparison of the sizes of two or more quantities of same kind by division. 

The quantities we compare must be in same units. 

Both terms of a ratio can be multiplied or divided by the same non zero number.

Usually a ratio is expressed to its lowest term or in its simplest form. 

Solved Examples 

Example 1 : 

Jacob earns $2500 per month and John earns $3000 per month. Find the ratio between the earning of Jacob and John.   

Solution : 

Ratio between the earnings of Jacob and John : 

=  $2500 / $3000

=  2500 / 3000

Simplify. 

=  5 / 6

Example 2 : 

Find the ratio between 150 grams and 2 kilograms.   

Solution : 

The quantities we compare must be in same units.

Convert 2 kilograms into grams : 

2 kilograms  =  2 ⋅ 1000 grams

2 kilograms  =  2000 grams

Ratio between 150 grams and 2 kilograms : 

=  150 grams / 2000 grams

=  150 / 2000

Simplify. 

=  3 / 40

Example 3 : 

Train A takes 35 minutes to travel its route. Train B, traveling the same route but making more stops, takes 45 minutes. What is the ratio of the time of Train A to Train B ?

Solution : 

Ratio of the time of Train A to Train B is 

=  35 minutes / 45 minutes

=  35 / 45

Simplify. 

=  7 / 9

Example 4 : 

Lily's height is 4 feet, 7 inches. Her younger sister’s height is 25 inches. Find the ratio of Lily’s height to her sister’s. 

Solution : 

The quantities we compare must be in same units.

Convert 4 feet 7 inches into inches. 

4 feet 7 inches  =  4(12) + 7

4 feet 7 inches  =  48 + 7

4 feet 7 inches  =  55 inches

Ratio of Lily’s height to her sister’s  :

=  55 inches / 25 minutes

Simplify. 

=  11 / 5

Example 5 : 

Two sunflowers’ growth was measured daily. At the end of the experiment,Sunflower A had grown from 2 inches to 2 feet, 3 inches. Sunflower B had grown from 3 inches to 2 feet, 6 inches. Find the ratio of the growth in height of Sunflower A to Sunflower B.

Solution : 

First, we have to find the growth of each Sunflower

Convert 2 feet 3 inches to inches : 

2 feet 3 inches  =  2(12) + 3

2 feet 3 inches  =  24 + 3

2 feet 3 inches  =  27 inches

Convert 2 feet 6 inches to inches : 

2 feet 6 inches  =  2(12) + 6

2 feet 6 inches  =  24 + 6

2 feet 6 inches  =  30 inches

Growth of Sunflower A : 

=  Height at the end - Height at the beginning

=  27 - 2

=  25 inches

Growth of Sunflower B : 

=  Height at the end - Height at the beginning

=  30 - 3

=  27 inches

Ratio of the growth in height of Sunflower A to Sunflower B :

=  25 inches / 27 inches

=  25 / 27

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