COMPARING UNLIKE FRACTIONS

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

Problem 9 :

Convert all the decimals into fraction and then find lowest value.

a) 0.82, 4/5

b) 0.2, 6/25

c) 0.4, 7/20

Solution :

a) 0.82, 4/5

Since we have two digits after the decimal in 0.82, we have to multiply both numerator and denominator by 100.

= 0.82 x 100/100

= 82/100

In 4/5, by multiplying both nuumerator and denominator by 2. We get

= 4/5 x 2/2

= 8/10

Least common multiple of 10 and 100 is 100.

= (8/10) x 10/10

= 80/100

80/100 is lesser than 82/100. Then 4/5 is lesser.

b) 0.2, 6/25

Since we have one digit after the decimal in 0.2, we have to multiply both numerator and denominator by 10.

= 0.2 x 10/10

= 2/10

In 6/25, by multiplying both nuumerator and denominator by 4. We get

= 6/25 x 4/4

= 24/100

Least common multiple of 10 and 100 is 100.

= (2/10) x 10/10

= 20/100

20/100 is lesser than 24/100. Then 0.2 is lesser.

c) 0.4, 7/20

Since we have one digit after the decimal in 0.4, we have to multiply both numerator and denominator by 10.

= 0.4 x 10/10

= 4/10

In 7/20, by multiplying both nuumerator and denominator by 5. We get

= 7/20 x 5/5

= 35/100

Least common multiple of 10 and 100 is 100.

= (4/10) x 10/10

= 40/100

35/100 is lesser than 40/100. Then 0.4 is lesser.

Problem 10 :

Convert these lists of numbers into decimals, and then place them on the number line

1.3, 0.2, 1.5, 3/4, 1, 4/5

Solution :

1.3, 0.2, 1.5, 3/4, 1, 4/5

Converting the fractions 3/4 and 4/5 as decimal, 

Arranging the decimals from least to greatest, we get

0.06, 0.2, 0.8, 1, 1.3, 1.5