ARRANGING FRACTIONS IN ASCENDING AND DESCENDING ORDER

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.

Arrange the fractions from least to greatest.

Problem 1 :

11/9, 7/6, 1 1/3

Solution :

Converting the mixed fraction as improper fraction, we get

1 1/3 = (3 + 1)/3 ==> 4/3

11/9, 7/6, 4/3

Taking the LCM and make the denominators same:

LCM (6, 9, 3) = 18

(11/9) x (2/2) ==> 22/18

(7/6) x (3/3) ==> 21/18

(4/3) x (6/6) ==> 24/18

Least to greatest :

21/18 < 22/18 < 24/18

7/6 < 11/9 < 4/3

Order the numbers from least to greatest.

Problem 2 :

27/8, 13/4, 3 1/2

Solution :

Converting the mixed fraction as improper fraction, we get

3 1/2 = (6 + 1)/2 ==> 7/2

27/8, 13/4, 7/2

Taking the LCM and make the denominators same:

LCM (4, 2, 8) = 8

(27/8) x (1/1) ==> 27/8

(13/4) x (2/2) ==> 26/8

(7/2) x (4/4) ==> 28/8

Least to greatest :

26/8 < 27/8 < 28/8

13/4 < 27/8 < 7/2

Problem 3 :

1/5, 8/15,  3/10

Solution :

Taking the LCM and make the denominators same:

LCM (15, 5, 10) = 30

(1/5) x (6/6) ==> 6/30

(8/15) x (2/2) ==> 16/30

(3/10) x (3/3) ==> 9/30

Least to greatest :

6/30 < 9/30 < 16/30

1/5 < 3/10 < 8/15

Problem 4 :

14/33, 5/11, 9/22

Solution :

Taking the LCM and make the denominators same:

LCM (11, 33, 22) = 66

(14/33) x (2/2) ==> 28/66

(5/11) x (6/6) ==> 30/66

(9/22) x (3/3) ==> 27/66

Least to greatest:

27/66 < 28/66 < 30/66

9/22 < 14/33 < 5/11

Problem 5 :

4/9, 3/4, 7/15

Solution :

Taking the LCM and make the denominators same:

LCM (4, 9, 15) = 180

(4/9) x (20/20) ==> 80/180

(3/4) x (45/45) ==> 135/180

(7/15) x (12/12) ==> 84/180

Least to greatest :

80/180 < 84/180 < 135/180

4/9 < 7/15 < 3/4

Problem 6 :

11/15, 5/6, 7/10,

Solution :

Taking the LCM and make the denominators same:

LCM (6, 10, 15) = 30

(11/15) x (2/2) ==> 22/30

(5/6) x (5/5) ==> 25/30

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

Least to greatest:

21/30 < 22/30 < 25/30

7/10 < 11/15 < 5/6

Problem 7 :

2 5/12, 12/5, 43/18

Solution :

Converting the mixed fraction as improper fraction, we get

2  5/12 = (24 + 5)/12 ==> 29/12

29/12, 12/5, 43/18

Taking the LCM and make the denominators same:

LCM (5, 12, 18) = 180

(29/12) x (15/15) ==> 435/180

(12/5) x (36/36) ==> 432/180

(43/18) x (10/10) ==> 430/180

Least to greatest :

430/180 < 432/180 < 435/180

43/18 < 12/5 < 29/12

Problem 8 :

1 13/33, 1 1/3, 10/7

Solution :

Converting the mixed fraction as improper fraction, we get

1 1/3 = (3 + 1)/3 ==> 4/3

1 13/33 = (33 + 13)/33 ==> 46/33

46/33, 4/3, 10/7

Taking the LCM and make the denominators same:

LCM (3, 7, 33) = 231

(46/33) x (7/7) ==> 322/231

(4/3) x (77/77) ==> 308/231

(10/7) x (33/33) ==> 330/231

Least to greatest :

308/231 < 322/231 < 330/231

4/3 < 46/33 < 10/7

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