Ratio In The Simplest Form

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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.

3 : 2 is different from the ratio 2 : 3.

1) Express the following ratios in the simplest form.

a) 150 : 400

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

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

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

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 and Proportion

• Ratio in the simplest form

• Comparison of ratios

• Equivalent ratios

• Proportion

• Continued Proportion

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