# Ratio And Proportion

In this section we will discuss Ratio and proportion.

In daily life we come across situations where we need to compare quantities in terms of their magnitude/measurements. So, for comparing quantities we use ratio - proportion.

Thus, the ratio of two numbers ‘a’ and ‘b’ ( b≠ 0) is a ÷ b or a/b and is denoted by a : b.

In the ratio a : b, the quantities a and b are called the terms of the ratio. The former ‘a’ is called the

Thus in the ratio a : b, a ------> antecedent and b ---------> consequent.

We know that a fraction does not change when its numerator and denominator are multiplied or divided by the same non-zero number. So, a ratio does not alter, if its 1st and 2nd term are multiplied or divided by the same non-zero number.

45 : 15 = 90 : 30 [ Multiplying the 1st and 2nd term by 2 ]

24 : 36 = 8 : 12 [ Dividing the 1st term and 2nd term by 3 ]

1) Express the following in the form to ratio.

a) The length of rectangle is double of its width.

Ratio of length to width of the rectangle is 2 : 1 or length and width of the rectangle are in the ratio of 2 : 1.

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b) For preparing tea for 3 people, we need 3 cups of water and 1 cup of milk require.

Amount of water = 3 cups

Amount of milk = 1 cup

Ratio of water to milk = 3 : 1

Ratio of milk to water = 1 : 3

From ratio and proportion to number system

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In daily life we come across situations where we need to compare quantities in terms of their magnitude/measurements. So, for comparing quantities we use ratio - proportion.

**Ratio :**The ratio between two quantities of the same kind and in the same units is a fraction that shows how many times the one quantity is of the other.Thus, the ratio of two numbers ‘a’ and ‘b’ ( b≠ 0) is a ÷ b or a/b and is denoted by a : b.

In the ratio a : b, the quantities a and b are called the terms of the ratio. The former ‘a’ is called the

**first term or antecedent**and the later ‘b’ is known as the**2nd term or consequent.**Thus in the ratio a : b, a ------> antecedent and b ---------> consequent.

We know that a fraction does not change when its numerator and denominator are multiplied or divided by the same non-zero number. So, a ratio does not alter, if its 1st and 2nd term are multiplied or divided by the same non-zero number.

45 : 15 = 90 : 30 [ Multiplying the 1st and 2nd term by 2 ]

24 : 36 = 8 : 12 [ Dividing the 1st term and 2nd term by 3 ]

**Examples :**1) Express the following in the form to ratio.

a) The length of rectangle is double of its width.

**Solution :**Ratio of length to width of the rectangle is 2 : 1 or length and width of the rectangle are in the ratio of 2 : 1.

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b) For preparing tea for 3 people, we need 3 cups of water and 1 cup of milk require.

**Solution :**Amount of water = 3 cups

Amount of milk = 1 cup

Ratio of water to milk = 3 : 1

Ratio of milk to water = 1 : 3

**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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