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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

• Ratio and Proportion

• Ratio in the simplest form

• Comparison of ratios

• Equivalent ratios

• Proportion

• Continued Proportion

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