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.

Example 5 :

A football team wins 3/8 of their matches in a season The same team loses 1/3 of their matches. Show that the team win more matches than they lose.

Solution :

Team wins = 3/8 of the matches

Team loses = 1/3 of the matches.

To compare these two fraction, we have to find teh least common multiple and make the denominators same.

LCM of 3 and 8 = 24

3/8 x (3/3) = 9/24

1/3 x (8/8) = 8/24

9/24 > 8/24

3/8 > 1/3

So, number of matches won in greater than number of matches lose.

Example 6 :

The table shows the portions of the day that several animals sleep.

Order the animals by sleep time from least to greatest.

Solution :

Observing the table above, some quantities are decimals some quanttiies are fraction and some quantities are percentage. To compare all we make it as one unit. Making it as decimal.

Dolphin = 0.433

Lion = 56.3% = 56.3/100 ==> 0.563

Rabbit = 19/40 ==> (19/4) x 1/10

= 4.75/10

= 0.475

Squirrel = 31/50 ==> 31/50 x 2/2

= 62/100

= 0.62

Tiger = 65.8% ==> 65.8/100

= 0.658

Ordering from least to greatest :

0.433, 0.475, 0.563, 0.62, 0.658

Example 7 :

The Tour de France is a bicycle road race. The whole race is made up of 21 small races called stages. The table shows how several stages compare to the whole Tour de France. Order the stages from shortest to longest

Solution :

Stage 1 :

11/200 ==> (11/2) x (1/100)

= 5.5/100

= 0.055

Stage 7 :

= 0.044

Stage 8 :

= 6/125

Converting the denominator as multiple of 10

= 6/125 x (8/8)

= 48/1000

= 0.048

Stage 17 :

0.06

Stage 21 :

= 4%

= 4/100

= 0.04

Arranging from shortest to longest :

0.04, 0.044, 0.048, 0.055, 0.06

Arranging the stages from least to greatest :

Stage 21, Stage 7, Stage 8, Stage 1, Stage 17

Example 8 :

The table shows the portions of the world population that live in four countries. Order the countries by population from least to greatest.

Solution :

Portion of world population of Brazil :

= 3%

= 3/100

= 0.03

Portion of world population of China :

= 1/5

= 1/5 x (2/2)

= 2/10

= 0.2

Portion of world population of Japan :

= 1/50

= 1/50 x (2/2)

= 2/100

= 0.02

Portion of world population of United States :

= 0.046

From least to greatest :

0.02, 0.03, 0.046, 0.2

Ordering countries from least to greatest :

Japan, Brazil, United States, China

Example 9 :

You make 75% of your shots, your sister makes 13/20 of her shots, and your friend makes 0.7 of his shots. Who made the most shots?

Solution :

Number of shots you make = 75%

= 75/100

Number of shots your sister make = 13/20

Number of shots your friend make :

= 0.7

= 7/10

Least common multiple of 10, 20 and 100 = 100

13/20 = 13/20 x 5/5

= 65/100

7/10 = 7/10 x 10/10

= 70/100

Comparing 75/100, 65/100 and 70/100

75/100 is greater. So, you made more shots.