Ratio In The Simplest Form

Ratio in the simplest form : A ratio a : b is said to be in the simplest form if its antecedent ‘a’ and consequent ‘b’ have no common factor other than 1.
A ratio in the simplest form is also called the ratio in the lowest terms.

Example : The ratio 32 :48 is not in the simplest form, because 16 is a common factor of its antecedent and consequent. The simplest form of this ratio is 2 : 3 ( dividing the 1st term and 2nd term by 16).

Note 1 : To find the ratio of two quantities, they must be expressed in the same units.
Note 2 : As the ratio of two quantities are in same units so ratio has no unit or it is independent of the units used in the quantities compared.
Note 3 : The order of the terms in a ratio a : b is very important. The ratio
3 : 2 is different from the ratio 2 : 3.

Examples :
1) Express the following ratios in the simplest form.
a) 150 : 400
Solution :
The given ratio is 150 : 400 = 150/400
The common factor of 150 and 400 is 50.
(150 ÷ 50)/ (400 ÷ 50) = 3/8 = 3 : 8.
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b) A dozen to score
Solution :
One dozen = 12 and one score = 20.
So, a dozen to score = 12/20 = 12 : 20.
(12 ÷ 4)/ (20 ÷ 4) [ As the common factor is 4]
= 3/5 = 3 : 5.
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c) 200 grams to 4 kg
Solution :
200 g to 4 kg
As both the quantities are in different units, first make their units same.
1kg = 1000 g
∴ 4 kg = 4000 g.
200 g to 4000 g = 200 / 4000
Common factor of 200 and 4000 is 200.
(200 ÷ 200)/(4000 ÷ 200) = 1/20 = 1 : 20.
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d) Sam earned $4000 and paid $500 as income tax and spent $1500 on household expenses. Find the ratio of : 1) income tax to income 2) household expenses to income 3) savings to earnings
Solution
Sam’s income = $4000
Income tax = $500
∴ income tax to income = 500/4000
(500 ÷ 500)/(4000 ÷ 500) = 1/8
Ratio of Income tax to income is 1 : 8
Expenses = $1500
∴ Household expenses to income = 1500/4000
(1500 ÷ 500)/ (4000 ÷ 500) = 3/8
Ratio of Household expenses to income = 3 : 8.
Savings = Income – (expenses + income tax)
Savings = 4000 – (1500 + 500) = $2000.
∴ Savings to earnings = 2000/4000
(2000 ÷ 2000)/(4000 ÷ 2000) = ½
Ratio of savings to expenses = 1 : 2.

Ratio - Proportion

Ratio and Proportion
Ratio in the simplest form
Comparison of ratios
Equivalent ratios
Proportion
Continued Proportion

From ratio in the simplest form to number system

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