ARRANGING FRACTIONS IN ASCENDING AND DESCENDING ORDER

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

Problem 9 :

Tell which letter shows the graph of the number.

1)  2/5        2)  45.2%      3)  0.435     4)  4/9

Solution :

By observing the number line, every quantity is represented as decimal. Then we convert everything as decimal.

1) 2/5

To convert 2/5, as decimal we have to multiply both numerator and denominator by 2.

= 2/5 x 2/2

= 4/10

Converting into decimal, we get 0.4

2) 45.2%

= 45.2/100

Moving the decimal two digits left.

= 0.452

3) 0.435 is already decimal.

4)  4/9

Since we have the denominator as 9, we cannot convert the denominator as 10, 100, ...........

Using long division, we get

= 0.444..........

2/5 or 0.4 ---> A

0.435 ---> B

4/9 or 0.444...... ---> C

45.2% or 0.452 ---> D

Problem 10 :

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 x (1/100)

= 5.5/100

Moving the decimal two digits to the left, we get

= 0.055

Stage 7 :

0.444

Stage 8 :

6/125

To convert the denominator 6/125 as 10, 100, 1000, ............ we should multiply both numerator and denominator by 8.

= (6/125) x 8/8

= 48/1000

= 0.48

Stage 17 :

0.06

Stage 21 :

= 4%

= 4/100

Moving the decimal two digits left.

= 0.04

0.055, 0.44, 0.48, 0.06, 0.04

0.04, 0.055, 0.06, 0.44, 0.48

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

Problem 11 :

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

Solution :

Brazil  :

3% = 3/100

Moving the decimal two digits left, we get 0.03

China  :

1/5

To convert the denominator as 10, we should multiply both numerator and denominator by 2.

= 1/5 x 2/2

= 2/10

= 0.2

Japan  :

= 1/50

To convert the denominator as 100, we should multiply both numerator and denominator by 2.

= 1/50 x 2/2

= 2/100

= 0.02

United States  :

0.046

0.03, 0.2, 0.02, 0.046

Arranging from least to greatest :

0.02, 0.03, 0.046, 0.2

Arranging the countries from least to greatest :

Japan, Brazil, United States, China