REDUCING RATIOS TO LOWEST TERMS

Simplify each of the following ratios.

Problem 1 :

12 to 48

Solution:

Given ratio is 12 : 48

Highest common factor of 12 and 48 is 12.

So, the simplest form is 1 : 4.

Problem 2 :

81 : 27

Solution:

Given ratio is 81 : 27

Highest common factor of 81 and 27 is 27.

So, the simplest form is 3 : 1.

Problem 3 :

4 to 24 to 64

Solution:

Given ratio is 4 : 24 : 64

Highest common factor of 4, 24 and 64 is 4.

So, the simplest form is 1 : 6 : 16.

Problem 4 :

21 : 42 : 14

Solution:

Given ratio is 21 : 42 : 14

Highest common factor of 21, 42 and 14 is 7.

So, the simplest form is 3 : 6 : 2.

Set up a ratio for each of the following and reduce to lowest terms. Eliminate decimals and fractions by using equivalent ratios.

Problem 5 :

13 dimes to 8 nickels

Solution:

The quantities we compare must be in same units.

Convert dimes into nickels.

1 dime = 2 nickles

13 dimes = 26 nickels

Ratio between 13 dimes and 8 nickels

= 13 : 4

Problem 6 :

10 days to 4 weeks

Solution:

Convert weeks into days.

4 weeks = 28 days

= 5 : 14

Problem 7 :

1.25 to 8

Solution:

Given ratio is 1.25 to 8

1.25 = 1.25 × 100 = 125

Problem 8 :

0.8 to 2.3 to 4.1

Solution:

Given ratio is decimal 0.8 : 2.3 : 4.1

Multiplying by 10, we get

= 8 : 23 : 41

So, the simplest for is 8 : 23 : 41.

Problem 9 :

Solution:

Multiplying by 10 on both sides, we get

= 5 : 6

So, the simplest form is 5 : 6.

Problem 10 :

Solution:

LCM of 8, 4 and 3 is 24.

Multiplying by 24, we get

Problem 11 :

Solution:

Given ratio is mixed numbers 2 2/3 : 3 1/5

Changing the mixed numbers as improper fractions, we get

LCM of 3 and 5 is 15.

So, the simplest form is 5 : 6.

Problem 12 :

There are 60 red and blue balls in a ball pit. 21 of them are blue.  What fraction of the balls are red?

Represent this as a simplified fraction.

Solution :

Total number of balls are in red and blue color = 60

Number of blue balls = 21

number of blue balls : number of red balls

Number of red balls = 60 - 21

= 39

Number of blue balls : number of red balls

60 : 39

20 : 13

Problem 13 :

Nancy and Lisa played 20 sets of tennis. Nancy won 12 of them. Write the ratio of Nancy’s wins to the total number of sets in simplest form.

Solution :

Total number of sets = 20

Number wins Nancy got = 12

Required ratio :

12 : 20

Simplifying using 2 times table, we get

= 6 : 10

= 3 : 5