ORDERING FRACTIONS WITH DIFFERENT DENOMINATORS WORKSHEET

Order each set of fractions from least to greatest : 

1)  3/4, 5/8, 11/12

2)  3/4, 2/5, 1/8, 7/10

3)  11/15, 9/10, 7/12, 17/20

4)  -1/6, -5/12, -8/9, -7/18

Order each set of fractions from greatest to  least : 

5)  3/4, 2/5, 5/8, 1/2

6)  1/6, 1/3, 3/14, 2/7

7)  5/6, 11/5, 9/16, 3/4

8)  -5/6, -1/3, -7/12, -3/4

9)  Dennis used 3⁄8 of a bucket of paint, and Jackson used 5⁄8 of an identical bucket of paint. Who used more paint? They used the same amount of paint. Dennis Jackson

10)  Four-sevenths of the annual visitors at an amusement park are between the ages of 18 and 26, and 4⁄10 of the visitors are under the age of 18. Which age group comes to the amusement park more often? 18 to 26 Both age groups visit the park equally often. Under 18

1. Answer :

3/4, 5/8, 11/12

Least common multiple of (4, 8, 12) = 24.

3/4 = (3 ⋅ 6)/(4 ⋅ 6) = 18/24

5/8 = (5 ⋅ 3)/(8 ⋅ 3) = 15/24

11/12 = (11 ⋅ 2)/(12 ⋅ 2) = 22/24

Compare the numerators of like fractions above and order them from least to greatest. 

15/24, 18/24, 22/24

Substitute the corresponding original fractions. 

5/8, 3/4, 11/12

2. Answer :

3/4, 2/5, 1/8, 7/10

Least common multiple of (4, 5, 8, 10) = 40.

3/4 = (3 ⋅ 10)/(4 ⋅ 10) = 30/40

2/5 = (2 ⋅ 8)/(5 ⋅ 8) = 16/40

1/8 = (1 ⋅ 5)/(8 ⋅ 5) = 5/40

7/10 = (7 ⋅ 4)/(10 ⋅ 4) = 28/40

Compare the numerators of like fractions above and order them from least to greatest. 

5/40, 16/40, 28/40, 30/40

Substitute the corresponding original fractions. 

1/8, 2/5, 7/10, 3/4

3. Answer :

11/15, 9/10, 7/12, 17/20

Least common multiple of (15, 12, 20) = 60.

11/15 = (11 ⋅ 4)/(15 ⋅ 4) = 44/60

9/10 = (9 ⋅ 6)/(10 ⋅ 6) = 54/60

7/12 = (7 ⋅ 5)/(12 ⋅ 5) = 35/60

17/20 = (17 ⋅ 3)/(20 ⋅ 3) = 51/60

Compare the numerators of like fractions above and order them from least to greatest. 

35/60, 44/60, 51/60, 54/60

Substitute the corresponding original fractions. 

7/12, 11/15, 17/20, 9/10 

4. Answer :

-1/6, -5/12, -8/9, -7/18

Least common multiple of (6, 12, 18) = 36.

-1/6 = (-1 ⋅ 6)/(6 ⋅ 6) = -6/36

-5/12 = (-5 ⋅ 3)/(12 ⋅ 3) = -15/36

-8/9 = (-8 ⋅ 4)/(9 ⋅ 4) = -32/36

-7/18 = (-7 ⋅ 2)/(18 ⋅ 2) = -14/36

Compare the numerators of like fractions above and order them from least to greatest. 

-32/36, -15/36, -14/36, -6/36

Substitute the corresponding original fractions. 

-8/9, -5/12, -7/18, -1/6

5. Answer :

3/4, 2/5, 5/8, 1/2

Least common multiple of (4, 5, 8, 2) = 40.

3/4 = (3 ⋅ 10)/(4 ⋅ 10) = 30/40

2/5 = (2 ⋅ 8)/(5 ⋅ 8) = 16/40

5/8 = (5 ⋅ 5)/(8 ⋅ 5) = 25/40

1/2 = (1 ⋅ 20)/(2 ⋅ 20) = 20/40

Compare the numerators of like fractions above and order them from greatest to least. 

30/40, 25/40, 20/40, 16/40

Substitute the corresponding original fractions. 

3/4, 5/8, 1/2, 2/5

6. Answer :

1/6, 1/3, 3/14, 2/7

Least common multiple of (6, 3, 14, 7) = 42.

1/6 = (1 ⋅ 7)/(6 ⋅ 7) = 7/42

1/3 = (1 ⋅ 14)/(3 ⋅ 14) = 14/42

3/14 = (3 ⋅ 3)/(14 ⋅ 3) = 9/42

2/7 = (2 ⋅ 6)/(7 ⋅ 6) = 12/42

Compare the numerators of like fractions above and order them from greatest to least. 

14/42, 12/42, 9/42, 7/42

Substitute the corresponding original fractions. 

1/3, 2/7, 3/14, 1/6

7. Answer :

5/6, 11/5, 9/16, 3/4

Least common multiple of (6, 5, 16, 4) = 240.

5/6 = (5 ⋅ 40)/(6 ⋅ 40) = 200/240 

11/5 = (11 ⋅ 48)/(5 ⋅ 48) = 528/240

9/16 = (9 ⋅ 15)/(6 ⋅ 16) = 135/240

3/4 = (3 ⋅ 60)/(4 ⋅ 60) = 180/240

Compare the numerators of like fractions above and order them from greatest to least. 

528/240, 200/240, 180/240, 135/240

Substitute the corresponding original fractions. 

11/5, 5/6, 3/4, 9/16

8. Answer :

-5/6, -1/3, -7/12, -3/4

Least common multiple of (6, 3, 12, 4) = 12.

-5/6 = (-5 ⋅ 2)/(6 ⋅ 2) = -10/12 

-1/3 = (-1 ⋅ 4)/(3 ⋅ 4) = -4/12

-7/12 = (-7 ⋅ 1)/(12 ⋅ 1) = -7/12

-3/4 = (-3 ⋅ 3)/(4 ⋅ 3) = -9/12

Compare the numerators of like fractions above and order them from greatest to least. 

-4/12, -7/12, -9/12, -10/12

Substitute the corresponding original fractions. 

-1/3, -7/12, -3/4, -5/6

9. Answer :

Quantity of paint Dennis used = 3⁄8

Quantity of paint Jackson used = 5⁄8

Since the denominators are same for these two fractions, it is ok to compare the numerators and decide which fraction is greater.

3/8 < 5/8

So, Jackson used more quantity of paint.

10. Answer :

Number of visitors at an amusement park are between the ages of 18 and 26

= 4/7

Number of visitors at an amusement park are at the age under 18

= 4/10

To compare these two fractions, we have to compare the denominators and make it same.

LCM(7, 10) = 70

= 4/7 x 10/10

= 40/70

= 4/10 x (7/7)

= 28/70

40/70 > 28/70

So, in between the ages 18 and 26 the number of visitors is more.

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