Comparing Fractions

Sohni has 3 x 12 rotis in her plate and Rita has 2 x 34 rotis in her plate. Who has more rotis in her plate?

Clearly, Sohni has 3 full rotis and more and Rita has less than 3 rotis. So, Sohni has more rotis.

Try representing the fractions: 12 and 13 below. We see that, the portion corresponding to 12 is clearly larger than the portion corresponding to 13.

So 12 than 13.

But often it is not easy to say which one out of a pair of fractions is larger. For example, which is greater, 14 or 310 ?

For this, we may wish to show the fractions using figures but drawing figures may not be easy especially with denominators like 13. Therefore, we need to have a systematic procedure to compare fractions.

On the other hand, it is particularly easy to compare like fractions.

Try these

You get one-fifth of a bottle of juice and your sister gets one third of the same size of a bottle of juice. Who gets more?

Given that a person gets one-fourth of a bottle of juice and his sister gets one-third of a bottle of juice.

One-fourth of a bottle of juice can be written as .

Similarly, one-third of a bottle of juice can be written as .

Here, the numerators of both fractions are , but the denominators are .

Both 14 and 13 are proper fractions, because their numerators are lesser than denominators.

So, the fraction which has lesser denominator has greater value.

Thus, 13

14.

Hence, we conclude that sister gets more juice.

Comparing like fractions

Like fractions are fractions with the same denominator. Which of these are like fractions?

Let us compare two like fractions: 38 and 58

In both the fractions the whole is divided into equal parts.

For 38 and 58we take 3 and 5 parts respectively out of the equal parts.

Clearly, out of 8 equal parts, the portion corresponding to parts is larger than the portion corresponding to 3 parts.

Hence, 58

38 . Note the number of the parts taken is given by the numerator.

It is, therefore, clear that for two fractions with the same denominator, the fraction with the greater numerator is greater.

Let's Answer the below questions.

Answer this questions

Now drag the following events into the ascending order and descending order.

ascending order :

descending order :

Comparing unlike fractions

Two fractions are unlike if they have different denominators. For example 13 and 15 are unlike fractions. So are 23 and 45

Unlike fractions with the same numerator:

Consider a pair of unlike fractions 13 and 15 , in which the numerator is the same.

which is greater 13 or 15 ? Answer : .

In 13, we divide the whole into 3 equal parts and take one. In 15 we divide the whole into 5 equal parts and take one. Note that in 13 , the whole is divided into a lesser number of parts than in 15. The equal part that we get in 13 is, therefore, larger than the equal part we get in 15 Since in both cases we take the same number of parts (i.e. one), the portion of the whole showing 13 is larger than the portion showing 15 , and therfore 13 15.

Let us arrange 21,213,29,25,27 in increasing order.

2/5

2/1

2/9

2/7

2/13

Solution: All these fractions are unlike, but their numerator is the same. Hence, in such case, the larger the denominator, the smaller is the fraction. The smallest is 213 as it has the largest denominator. The next three fractions in order are 29 27 25. The greatest fraction is 21 (It is with the smallest denominator).

Try these questions

1. Arrange the following in ascending and descending order :

(a) 112, 123,15,17,150,19,17

ascending order =

1/12

1/23

1/7

1/9

1/5

1/17

1/50

descending order =