SIMPLIFYING RATIOS

Express the following ratios in simplest form :

Example 1 :

8 : 16

Solution :

Given ratio is 8 : 16 

Highest Common factor of 8 and 16 is 8.

=  (8/8) : (16/8)

=  1 : 2

So, the simplest form is 1 : 2

Example 2 :

18 : 24

Solution :

Given ratio is 18 : 24 

Highest Common factor of 18 and 24 is 6.

=  (18/6) : (24/6)

=  3 : 4

So, the simplest form is 3 : 4

Example 3 :

6 : 12 : 24

Solution :

Given ratio is 6 : 12 : 24 

Highest Common factor of 6, 12 and 24 is 6.

=  (6/6) : (12/6) : (24/6)

=  1 : 2 : 4

So, the simplest form is 1 : 2 : 4

Example 4 :

2 : 4 : 6

Solution :

Given ratio is 2 : 4 : 6 

Highest Common factor of 2, 4 and 6 is 2

=  (2/2) : (4/2) : (6/2)

=  1 : 2 : 3

So, the simplest form is 1 : 2 : 3

Example 5 :

1000 : 50

Solution :

Given ratio is 1000 : 50 

Highest Common factor of 1000 and 50 is 50

=  (1000/50) : (50/50)

=  20 : 1

So, the simplest form is 20 : 1

Example 6 :

0.5 : 0.2

Solution :

Given ratio is decimal 0.5 : 0.2

Multiplying both by 10, we get

=  5 : 2

So, the simplest form is 5 : 2

Example 7 :

0.3 : 0.7

Solution :

Given ratio is decimal 0.3 : 0.7

Multiplying both by 10, we get

=  3 : 7

So, the simplest form is 3 : 7

Example 8 :

0.7 : 1.2

Solution :

Given ratio is decimal 0.7 : 1.2

Multiplying both by 10, we get

=  7 : 12

So, the simplest form is 7 : 12

Example 9 :

0.03 : 0.12

Solution :

Given ratio is decimal 0.03 : 0.12

Multiplying both by 100, we get

=  3 : 12

Highest Common factor of 3 and 12 is 3

=  (3/3) : (12/3)

=  1 : 4

So, the simplest form is 1 : 4

Example 10 :

1  1/2 : 2  1/2

Solution :

Given ratio is mixed numbers 1 1/2 : 2 1/2

Changing the mixed numbers as improper fractions, we get

=  3/2 : 5/2

Multiplying by 2 on both sides, we get

=  3 : 5

So, the simplest form is 3 : 5

Example 11 :

Daisy mixes 50 ml of orange juice with 200 ml of water. Write down the ratio of orange juice to water. Give your answer in its simplest form.

Solution :

Quantity of orange juice = 50 ml

Quantity of water = 200 ml

Ration between juice and water = 50 : 200

= 50/200

= 5/20

= 1/4

Writing it as ratio, we get 

1 : 4

Example 12 :

At a football match, there are 3000 men and 1800 women. Write down the ratio of male fans to female fans. Give your answer in its simplest form.

Solution :

Number of males = 3000

Number of women = 1800

Ratio between male to female = 3000 : 1800

= 3000/1800

= 30/18

= 5/3

Example 13 :

Aidan, Bill and Cara share sweets in the ratio of their ages. Aidan is 12 years old. Bill is 9 years old. Cara is 3 years old. Write down the ratio of their ages. Give your answer in its simplest form.

Solution :

Aidan's age = 12

Bill's age = 9

Cara's age = 3

Ratio between their ages,

= 12 : 9 : 3

= 4 : 3 : 1

Example 14 :

In a nursery, there are 5 adults and 14 children. Write the ratio of adults to children in the form 1 : n.

Solution :

Number of adults = 5

Number of children = 14

Ratio between adults : children = 5 : 14

Example 15 :

Ellie is making a cake. The instructions say that the ratio of sugar to flour should be 1 : 3 Ellie uses 250 g of sugar and 650 g of flour. Has Ellie used the correct ratio of sugar to flour ?

Solution :

Quantity of sugar = 250 g

quantity of flour = 650 g

Ratio between sugar to flour = 250 : 650

= 250/650

= 25/65

= 5/13

= 5 : 13

She has not used the correct ratio.

Example 16 :

There are 32 pupils in a class. 20 of them are girls. What is the ratio of boys to girls in its simplest form?

Solution :

Number of pupils in the class = 32

Number of girls = 20

Number of boys = 32 - 20

= 12

Ratio of number of boys to girls = 12 : 20

= 12/20

= 3/4

= 3 : 4

Hence 3 : 4 is the ratio between number of boys to girls.

Example 17 :

There are 50 sweets in a mixed pack. 25 are jellies, 10 are fizzy cola bottles and the rest are boiled. Write the ratio of each type of sweet in its simplest form.

Solution :

Total number of sweets = 50

Number of jellies = 25

Number of fizzy cola = 10

Number of boiled = 50 - (25 + 10)

= 50 - 35

= 15

Ratio between the sweets = 25 : 10 : 15

Simplifying using 5 times table, we get

= 5 : 2 : 3

Example 18 :

A fruit drink is made by mixing 60 ml of orange juice with 180 ml of pineapple juice. What is the ratio of orange juice to pineapple juice in its simplest form?

Solution :

Quantity of orange juice = 60 ml

Quantity of pineapple juice = 180 ml

Ratio between them = 60 : 180

= 60/180

= 1/3

= 1 : 3

So, the ratio between orange juice to pineapple juice is 1 : 3.

Example 19 :

Concrete is made by mixing sand, water and concrete mix in the ratio of 6 parts sand, 3 parts water and 3 parts concrete mix. What ratio is this in its simplest form?

Solution :

Ratio between sand, water and concrete mix = 6 : 3 : 3

simplifying using 3 times table, we get

= 2 : 1 : 1

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