# COMPARING UNLIKE FRACTIONS

To compare two or more 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 :

1/4, 2/7

Solution :

By considering the denominator (4 and 7), they are not same. So, we will take the least common multiple.

LCD (4, 7) = 28

= (1/4) x (7/7) ==> 7/28

= (2/7) x (4/4) ==> 8/28

Now we can compare the fractions 7/28 and 8/28 since  the denominators are same.

8/28 > 7/28

2/7 > 1/4

Compare fractions and decide which is greater fraction :

Problem 2 :

2/3, 5/8

Solution :

By considering the denominator (3 and 8), they are not same. So, we will take the least common multiple.

LCD (3, 8) = 24

(2/3) x (8/8) ==> 16/24

(5/8) x (3/3) ==> 15/24

Now we can compare the fractions 7/28 and 8/28 since the denominators are same.

16/24 > 15/24

2/3 > 5/8

Problem 3 :

7/10, 11/15

Solution :

By considering the denominator (10 and 15), they are not same. So, we will take the least common multiple.

LCD (10, 15) = 30

= (7/10) x (3/3) ==> 21/30

= (11/15) x (2/2) ==> 22/30

Now we can compare the fractions 21/30 and 22/30 since we can compare the denominators are same.

22/30 > 21/30

11/15 > 7/10

Problem 4 :

3/5, 6/11

Solution :

By considering the denominator (5 and 11), they are not same. So, we will take the least common multiple.

LCD (5, 11) = 55

(3/5) x (11/11) ==> 33/55

(6/11) x (5/5) ==> 30/55

Now we can compare the fractions 33/55 and 30/55 since we can compare the denominators are same.

33/55 > 30/55

3/5 > 6/11

Problem 5 :

5/12, 4/15

Solution :

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

LCD (12, 15) = 60

(5/12) x (5/5) ==> 25/60

(4/15) x (4/4) ==> 16/60

Now we can compare the fractions 25/60 and 16/60 since we can compare the denominators are same.

25/60 > 16/60

5/12 > 4/15

Problem 6 :

7/20, 9/25

Solution :

By considering the denominator (20 and 25), they are not same. So, we will take the least common multiple.

LCD (20, 25) = 100

(7/20) x (5/5) ==> 35/100

(9/25) x (4/4) ==> 36/100

Now we can compare the fractions 35/100 and 36/100 since the denominators are same.

36/100 > 35/100

9/25 > 7/20

Problem 7 :

5/18, 8/21

Solution :

By considering the denominator (18 and 21), they are not same. So, we will take the least common multiple.

LCD (18, 21) = 126

= (5/18) x (7/7) ==> 35/126

= (8/21) x (6/6) ==> 48/126

Now we can compare the fractions 35/126 and 48/126 since the denominators are same.

48/126 > 35/126

8/21 > 5/18

Problem 8 :

11/42, 20/63

Solution :

By considering the denominator (42 and 63), they are not same. So, we will take the least common multiple.

LCD (42, 63) = 126

(11/42) x (3/3) ==> 33/126

(20/63) x (2/2) ==> 40/126

Now we can compare the fractions 33/126 and 40/126 since the denominators are same.

40/126 > 33/126

20/63 > 11/42

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