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

Problem 5 :

Of the trees in the park, 3/8 were pines and 3/5 were spruce. Were there more pines or more spruce trees in the park ?

Solution :

Quantity of pines = 3/8

Quantity of spruce = 3/5

Comparing the fractions 3/8 and 3/5.

LCM of 5 and 8 = 40

Comparing the fractions 15/40 and 24/40, 24/40 is greater. So, number of spruce trees is greater.

Problem 6 :

Which is greater 3/20 or 16% ?

Solution :

3/20 and 16%

3/20 and 16/100

LCM of 20 and 100 is 100

To convert the decnominator of 3/20 as 100 we should multiply both numerator and denominator by 5.

= 3/20 x 5/5

= 15/100

16/100 is greater than 15/100. So, 16% is greater.

Problem 7 :

Which is greater 79% or 0.08 ?

Solution :

79% or 0.08

To convert 0.08 as fraction, we have to multiply both numerator and denominator by 100.

= 0.08 x (100/100)

= 8/100

Comparing the fractions 79/100 or 8/100, 79/100 is greater. So, 79% is greater.

Problem 8 :

Which is greater 25% or 7/25 ?

Solution :

25% or 7/25

25% = 25/100

LCM of 25 and 100 = 100

To convert the denoinator of 7/25 as 100, we should multiply both numerator and denominaor by 4.

= (7/25) x 4/4

= 28/100

Comparing the fractions 25/100 or 28/100, 28/100 is greater. So, 7/25 is greater.

Problem 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 :

Shots you make = 75%

= 75/100

Shots your sister make = 13/20

Shots your fried make = 0.7

= 7/10

Least common multiple of 10, 20 and 100.

Comparing the fractions 75/100, 65/100 and 70/100, 75/100 is greater. Then you make more shots.

Problem 10 :

You answer 21 out of 25 questions correctly on a test. Did you reach your goal of getting 80% or better?

Solution :

Your answer = 21/25

Your goal = 80% ==> 80/100

LCM of 25 and 100

= 21/25 x 4/4

= 84/100

Comparing the fractions 84/100 and 80/100, 84/100 is greater. Your score is better than your goal.

Order the numbers from least to greatest

Problem 11 :

2.62, 2  2/5, 26.8%, 2.26, 271%

Solution :

2.62, 2  2/5, 26.8%, 2.26, 271%

To arrage the given numbers from least to greatest, then we have to convert each quantity as same units.

2  2/5 = 12/5

= 2.4

26.8% = 26.8/100

Moving the decimal two digits left.

= 0.268

271% = 271/100

Moving the decimal 2 digits to the left,

= 2.71

2.62, 2.4, 0.268, 2.26, 2.71

Arranging from least to greatest,

0.268, 2.26, 2.4, 2.62, 2.71

26.8% , 2.26, 2  2/5, 2.62, 271%

Problem 12 :

87/100, 0.44, 43.7%, 21/50

Solution :

87/100, 0.44, 43.7%, 21/50

To arrage the given numbers from least to greatest, then we have to convert each quantity as same units.

87/100 = 0.87

43.7% = 43.7/100

= 0.437

21/50 = 21/50 x 2/2

= 42/100

= 0.42

0.87, 0.44, 0.437, 0.42

0.42, 0.437, 0.44, 0.87

The corresponding terms arranging from least to greatest,

21/50, 43.7%, 0.44, 87/100.