Ratio And Proportions

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Ratio is the quantitative comparison between quantitates. Proportion is a fixed ratio between two substances. Proportion always maintains a fixed ratio between two fractions. For example, a / b = c / d. It can be written as a : b = c : d. This can also be called as the proportion formula. Proportion in math is defined as the similarity while comparison between two quantities or substances.

Example 1: Find the y in the given ratio and proportion 4 : y = 2 : 5.

Solution: Here the given proportion is 4 : y = 2 : 5.

It can be expressed as a fraction in the form.

4 / y = 2 / 5

Now multiply both sides of the equation by y.

This gives 4 = 2 y / 5.

Now multiply both sides of the equation by 5.

This gives 2 y = 10.

Now divide both sides of the equation by 2.

So y = 5.

Hence the value of y for the given proportion = 5.
 
Example 2: Find the x in the proportion x : 6 = 4 : 3.

Solution: Here the given proportion is x : 6 = 4 : 3.

It can be expressed as a fraction in the form.

This gives, x / 6 = 4 / 3

Now multiply both sides of the equation by 6.

This gives 6 (x/ 6) = (4 / 3) (6).

 x = 24 / 3 = 8.

Hence the value of x for the given proportion is 8.

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