COMPARING FRACTIONS

Whenever we compare two 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 :

6/19 and 16/19

Solution :

In the fractions 6/19 and 16/19, the denominator is same. So, the fraction which has greater numerator will greater in value. 

16/9 > 6/19

16/19 is greater than 6/19

Example 2 :

1/2 and 3/5

Solution :

In the fractions 1/2 and 3/5, the denominators are different. 

Make the denominators same using least common multiple. 

Least common multiple of (2, 5) = 10. 

1/2 = (1 ⋅ 5)/(2 ⋅ 5) = 5/10

3/5 = (3 ⋅ 2)/(5 ⋅ 2) = 15/10

Compare the numerators of like fractions 5/10 and 15/10. 

15/10 > 5/10

Substitute the corresponding original fractions. 

3/5 > 1/2

3/5 is greater than 1/2

Example 3 :

7/12 and 11/18

Solution :

In the fractions 7/12 and 11/18, the denominators are different. 

Make the denominators same using least common multiple. 

Least common multiple of (12, 18) = 36. 

7/12 = (7 ⋅ 3)/(12 ⋅ 3) = 21/36

11/18 = (11 ⋅ 2)/(18 ⋅ 2) = 22/36

Compare the numerators of like fractions 21/36 and 22/36. 

22/36 > 21/36

Substitute the corresponding original fractions. 

11/18 > 7/12

11/18 is greater than 7/12

Example 4 :

5/12 and 3/8

Solution :

In the fractions 5/12 and 3/8, the denominators are different. 

Make the denominators same using least common multiple. 

Least common multiple of (12, 8) = 24. 

5/12 = (5 ⋅ 2)/(12 ⋅ 2) = 10/24

3/8 = (3 ⋅ 3)/(8 ⋅ 3) = 9/24

Compare the numerators of like fractions 10/24 and 9/24. 

10/24 > 9/24

Substitute the corresponding original fractions. 

5/12 > 3/8

5/12 is greater than 3/8

Example 5 :

3/14 and 5/21

Solution :

In the fractions 3/14 and 5/21, the denominators are different. 

Make the denominators same using least common multiple. 

Least common multiple of (14, 21) = 42. 

3/14 = (3 ⋅ 3)/(14 ⋅ 3) = 9/42

5/21 = (5 ⋅ 2)/(21 ⋅ 2) = 10/42

Compare the numerators of like fractions 9/42 and 10/42. 

10/42 > 9/42

Substitute the corresponding original fractions. 

5/21 > 3/14

5/21 is greater than 3/14

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