## Introduction

In many situations two fractions are compared. The comparison follows certain basic rules. This concept helps us to find out the unknown part of a fraction by comparing to a fraction equivalent to that. This method of finding the unknown quantity is helpful in solving the problems related to operation with fractions, proportions, scale factors, finding a percentage etc.

## Operations with Fractions Using Division

When two fractions are added or added or subtracted, just the numerators are added or subtracted over a common denominator if both the denominators are same. But if the denominators are different, then we need to convert one of the fractions with the denominator same as that of the other fraction. This converted fraction is called as the ‘equivalent fraction’ of the original fraction.

EXAMPLE

What is the sum of 1/2 and 1/4?

The denominator of the first fraction is 2 and that of the second is 4. Let n/4 be a fraction whose value is the same as 1/2.

Therefore we can say that n/4 = 1/2 and by cross multiplication and simplification we figure out the value of ‘n’ as 2. Hence the equivalent fraction of 1/2 is 2/4.

So, 1/2 + 1/4 = 2/4 + 1/4 = 3/4.

## Finding a Proportional Value by Division

Some times we come across two quantities that are proportional under a certain rule. If we know the ratio, we can find out the value of one item if the corresponding value of the other item is known.

EXAMPLE

If v = 10 when w = 15, what is the value of ‘w’?, when v =12 and if the variation is direct.

Let us assume the value of ‘w’ as ‘n’ when v = 12. Since the variation is direct, the unknown fraction 15/n is equivalent to 10/12 and by cross multiplication and simplification we find the value of ‘n’ as 18.

Therefore, w = 18 when v = 12.

## Using Division in Finding a Scale Factor

In a drawing the shape of an object is drawn to a certain scale. The ratio of the actual dimension of the object to the dimension drawn in the drawing is called as the scale factor.

EXAMPLE

The actual length of a room is 20 ft. In the plan drawing of the room, it is drawn as 2 in.

What is the scale factor?

Let ‘n’ be the scale factor.

Therefore, n = (20 x 12) in./ 2in. = 120. That is 1 in. in the drawing represents 120 in. of the object. Usually it is described as 1in. = 10 ft.

## Percentage of a Quantity as a Division

The actual value of a quantity can be calculated if the percentage to another quantity is known.

EXAMPLE

How much is 20% of 150?

Let ‘n’ be 20% of 150

Therefore, n/150 = 20/100 and by simplifying we get, n= 30.

So, 30 is 20% of 150.