ORDERING FRACTIONS

Example 2 :

Order the numbers

3  4/15, 33/10, 19/6

from greatest to least.

Solution :

Converting the mixed fraction as improper fraction. We get

3  4/15  =  (45 + 4)/15 ==>  49/15

49/15, 33/10, 19/6

Taking the LCM and make the denominators same :

LCM (15, 10, 6) = 30

(49/15) x (2/2) ==> 98/30

(33/10) x (3/3) ==> 99/30

(19/6) x (5/5) ==> 95/30

Greatest to least :

99/30 > 98/30 > 95/30

33/10 > 49/15 > 19/6

Example 3 :

Order the numbers

7/6, 11/9, 1  1 1/3

from least to greatest.

Solution :

Converting the mixed fraction as improper fraction. We get

1  1/3  =  (3 + 1)/3 ==>  4/3

7/6, 11/9, 4/3

Taking the LCM and make the denominators same :

LCM (6, 9, 3) = 18

(7/6) x (3/3) ==> 21/18

(11/9) x (2/2) ==> 22/18

(4/3) x (6/6) ==> 24/18

Least to greatest :

21/18 < 22/18 < 24/18

7/6 < 11/9 < 4/3

Example 4 :

Last year, a winter resort had 144,000 visitors, including 45,000 snowboarders. This year, the resort had 160,000 visitors, including 56,000 snowboarders. In which year was the fraction of snowboarders greater?

Solution :

Total number of visitors = 144, 000

Number of visitors including snowboarders = 45,000

Last year :

= Number of snowboarders / Total number of visitors

= 45000/144000

= 45/144

By simplification, we get

= 5/16

Total number of visitors = 166, 000

Number of visitors including snowboarders = 56,000

This year :

= Number of snowboarders / Total number of visitors

= 56000/166000

= 56/166

By simplification, we get

= 7/20

Comparing fractions 5/16 and 7/20.

LCM(16, 20) = 80

= (5/16) x (5/5) ==>  25/80

= (7/20) x (4/4) ==>  28/80

28/80 > 25/80

7/20 > 5/16

This year > Last year

The fraction of snowboarders was greater this year.