ARRANGING FRACTIONS FROM LEAST TO GREATEST

Order the numbers from least to greatest.

Problem 1 :

4/25, 2/9, 1/6

Solution :

By comparing the denominators of the fractions, they are not same.

LCM (9, 6, 25) = 450

(4/25) x (18/18) ==> 72/450

(2/9) x (50/50) ==> 100/450

(1/6) x (75/75) ==> 75/450

Comparing the fractions 100/450, 75/450 and 72/450 the denominators are same now.

Least to greatest :

72/450 < 75/450 < 100/450

4/25 < 1/6 < 2/9

Problem 2 :

11/24, 3/7, 9/21

Solution :

LCM (7, 24, 21) = 168

(11/24) x (7/7) ==> 77/168

(3/7) x (24/24) ==> 72/168

(9/21) x (8/8) ==> 72/168

Comparing the fractions 72/168, 77/168 and 72/168 the denominators are same.

Least to greatest:

72/168 = 72/168 < 77/168

3/7 = 9/21 < 11/24

Problem 3 :

7/20, 5/12, 3/8

Solution :

LCM (20, 8, 12) = 120

(7/20) x (6/6) ==> 42/120

(5/12) x (10/10) ==> 50/120

(3/8) x (15/15) ==> 45/120

Comparing the fractions 42/120, 45/120 and 50/120 the denominators are same.

Least to greatest:

42/120 < 45/120 < 50/120

7/20 < 3/8 < 5/12

Problem 4 :

19/40, 2/5, 21/45

Solution :

LCM (5, 40, 45) = 360

(19/40) x (9/9) ==> 171/360

(2/5) x (72/72) ==> 144/360

(21/45) x (8/8) ==> 168/360

Comparing the fractions 144/360, 171/360 and 168/360 the denominators are same.

Least to greatest:

144/360 < 168/360 < 171/360

2/5 < 21/45 < 19/40