Ratio will be in the form a : b.
How to reduce ratio to the 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
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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