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.

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.
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
Continued Proportion

Number system

7th grade math

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