# COMPARING FRACTIONS WITH DIFFERENT DENOMINATORS

To compare two fractions, first we should have the denominators same.

If the denominators are same, we can compare the numerators and decide which is greater.

If the denominators are not same, we have to take the least common multiple and make the denominators same.

Problem 1 :

5/6, 7/9

Solution :

By considering the denominator (6 and 9), they are not same. So, we will take the least common multiple.

LCM (6, 9) = 18

= (5/6) x (3/3) ==> 15/18

= (7/9) x (2/2) ==> 14/18

Now the denominators are same, so we can compare the numerators and decide which fraction is greater.

15/18 > 14/18

5/6 > 7/9

Determine which fraction is greater.

Problem 2 :

5/8, 13/20

Solution :

By considering the denominator (8 and 20), they are not same. So, we will take the least common multiple.

LCM (8, 20) = 40

= (5/8) x (5/5) ==> 25/40

= (13/20) x (2/2) ==> 26/40

Now the denominators are same, so we can compare the numerators and decide which fraction is greater.

26/40 > 25/40

13/20 > 5/8

Problem 3 :

7/12, 11/15

Solution :

By considering the denominator (12 and 15), they are not same. So, we will take the least common multiple.

LCM (12, 15) = 60

= (7/12) x (5/5) ==> 35/60

= (11/15) x (4/4) ==> 44/60

Now the denominators are same, so we can compare the numerators and decide which fraction is greater.

44/60 > 35/60

11/15 > 7/12

Problem 4 :

5/16, 3/10

Solution :

By considering the denominator (16 and 10), they are not same. So, we will take the least common multiple.

LCM (16, 10) = 80

= (5/16) x (5/5) ==> 25/80

= (3/10) x (8/8) ==> 24/80

Now the denominators are same, so we can compare the numerators and decide which fraction is greater.

25/80 > 24/80

5/16 > 3/10

Problem 5 :

3/4, 5/8

Solution :

By considering the denominator (4 and 8), they are not same. So, we will take the least common multiple.

LCD (4, 8) = 8

= (3/4) x (2/2) ==> 6/8

= (5/8) x (1/1) ==> 5/8

Now the denominators are same, so we can compare the numerators and decide which fraction is greater.

6/8 > 5/8

3/4 > 5/8

Problem 6 :

2/3, 13/16

Solution :

By considering the denominator (3 and 16), they are not same. So, we will take the least common multiple.

LCD (3, 16) = 48

= (2/3) x (16/16) ==> 32/48

= (13/16) x (3/3) ==> 39/48

Now the denominators are same, so we can compare the numerators and decide which fraction is greater.

39/48 > 32/48

13/16 > 2/3

Problem 7 :

2/5, 3/8

Solution :

By considering the denominator (5 and 8), they are not same. So, we will take the least common multiple.

LCD (5, 8) = 40

= (2/5) x (8/8) ==> 16/40

= (3/8) x (5/5) ==> 15/40

Now the denominators are same, so we can compare the numerators and decide which fraction is greater.

16/40 > 15/40

2/5 > 3/8

Problem 8 :

3/4, 7/10

Solution :

By considering the denominator (4 and 10), they are not same. So, we will take the least common multiple.

LCD (4, 10) = 20

= (3/4) x (5/5) ==> 15/20

= (7/10) x (2/2) ==> 14/20

15/20 > 14/20

3/4 > 7/10

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