HOW TO CHECK WHICH FRACTION IS GREATER

Whenever we compare two or more fractions, first we have to check the denominators.

Case 1 :

If the denominators are same, then we can decide that the fraction which is having the greater numerator is greater.

Case 2 :

If the denominators are different, then we have to make the denominators same and compare the fractions as said in case 1. 

To make the denominator same, we have to apply the concept of least common multiple. 

Example 1 :

Find which fraction is greater :

3/7 or 8/7

Solution : 

Because the denominators of the fractions are same, we can compare the numerators and decide which fraction is greater.

Comparing the numerators, we get

8 is greater than 3

So,

8/7 is greater than 3/7

Example 2 :

Find which fraction is greater :

3/8 or 5/12

Solution : 

Because the denominators are different, first we have to make the denominators same.

To make the denominator same.  we have find the least common multiple (LCM) of the denominators 8 and 12.

LCM of (8, 12)  =  24

Because the LCM is 24, we have to make each denominator as 24 using multiplication as shown below.

3/8  =  (3 ⋅ 3) / (8 ⋅ 3)  =  9/24

5/12  =  (5 ⋅ 2) / (12 ⋅ 2)  =  10/24

In 12/60 and 35/60, the denominator is same.

Now we can compare the numerators and decide which fraction is greater.

Then. we have

10/24 is greater than 9/24

So,

5/12 is greater than 3/8

Example 3 :

Find which fraction is greater :

2/3 or 4/7

Solution :

Because the denominators are different, first we have to make the denominators same.

To make the denominator same.  we have find the least common multiple (LCM) of the denominators 8 and 12.

LCM of (3, 7)  =  21

Because the LCM is 21, we have to make each denominator as 21 using multiplication as shown below.

2/3  =  14/21

4/7  =  12/21

In 14/21 and 12/21, the denominator is same.

Now we can compare the numerators and decide which fraction is greater.

Then. we have

14/21 is greater than 12/21

So,

2/3 is greater than 4/7

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