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Comparing Fractions with Unlike Denominators Worksheet

Comparing Fractions with Unlike Denominators Worksheet
  • Page 1
 1.  
Jonathan ate 3 8 of a pizza and Terry ate 1 4 of another pizza. Identify the appropriate symbol to compare the fractions.


a.
<
b.
=
c.
>
d.
×


Answer: (c)


Correct answer : (3)
 2.  
Joanna bought 18 peaches. She gave 1 3 of them to Cris and 1 2 of the them to Hal. Which symbol would you put inside the circle to compare the fractions rightly?


a.
=
b.
<
c.
×
d.
>


Solution:

1 / 3, 1 / 2
[Original fractions.]

Since the numerator for all the fractions is same, compare the denominators.

The fraction with the greatest denominator will have the least value.

As 3 > 2, 1 / 3 < 1 / 2

So, 1 / 3 < 1 / 2.


Correct answer : (2)
 3.  
Choose an appropriate symbol to compare the fractions.

1 4  1 2

a.
<
b.
+
c.
=
d.
>


Solution:

The strip representing 1 / 4 covers half of the strip representing 1 / 2 .

This shows that, one strip representing 1 / 2 equals two strips of 1 / 4 .

So, 1 / 4 < 1 / 2.


Correct answer : (1)
 4.  
Choose an appropriate symbol to compare the fractions.


a.
<
b.
>
c.
+
d.
=


Solution:

The strip representing 1 / 6 covers half of the strip representing 1 / 3.

This shows that, one strip representing 1 / 3 equals two strips of 1 / 6.

1 / 3 > 1 / 6


Correct answer : (2)
 5.  
Order the fractions from least to greatest.


a.
125, 115, 15
b.
125, 215, 15
c.
15, 115, 125
d.
15, 115, 115, 125


Solution:

From the figure, 1 / 25 < 1 / 15 .
[The fraction strip representing 1 / 25 is smaller than the fraction strip representing 1 / 15.]

From the figure, 1 / 15 < 1 / 5 .
[Each fraction strip representing 1 / 15is smaller than the fraction strip representing 1 / 5.]

As 125 <115 and 115 <15, 125 <115 <15.

So, the fractions ordered from least to greatest are 1 / 25 , 1 / 15 , 1 / 5 .


Correct answer : (1)
 6.  
Order the fractions from the greatest to the least.

a.
12 , 35 , 15
b.
12 , 15 , 13
c.
225 , 215 , 13
d.
12 , 25 , 13


Solution:

From the figure, 1 / 2 > 2 / 5 .
[The fraction strip representing 1 / 2 is larger than the two fraction strips representing 1 / 5 each.]

From the figure, 2 / 5 > 1 / 3 .
[The strip combining the two fraction strips representing 1 / 5 each, is larger than the strip representing 1 / 3 .]

As 1 / 2 > 2 / 5 and 2 / 5 > 1 / 3 , 1 / 2 > 2 / 5 > 1 / 3 .

So, the fractions ordered from greatest to least are 1 / 2 , 2 / 5 , 1 / 3 .


Correct answer : (4)
 7.  
Order the fractions from the least to the greatest.

a.
18, 14, 12
b.
16, 14, 48
c.
16, 14, 18
d.
16, 48, 18


Solution:

From the figure, 1 / 6 < 1 / 4.
[The fraction strip representing 1 / 6 is smaller than the fraction strip representing 1 / 4.]

From the figure, 1 / 4 < 4 / 8 .
[The fraction strip representing 1 / 4 is smaller than the strip combining the four fraction strips representing 1 / 8 each.]

As 1 / 6 < 1 / 4 and 1 / 4 < 4 / 8, 1 / 6 < 1 / 4 < 4 / 8.

So, the fractions ordered from least to greatest are 1 / 6, 1 / 4, 4 / 8.


Correct answer : (2)
 8.  
A child spends 1 2 of a day in sleeping, 1 10 of the day in eating, 1 9 of the day in playing and the rest 1 5 of the day in doing other activities, like bathing, etc. Arrange these fractions from the least to the greatest.
a.
110>19<15>12
b.
110>19>15>12
c.
110>19<15<12
d.
110<19<15<12


Solution:

1 / 2, 1 / 10, 1 / 9, 1 / 5
[Original fractions.]

Since the numerator for all the fractions is same, compare the denominators.

The fraction with the greatest denominator will have the least value.

As 10 > 9 > 5 > 2, 1 / 10 < 1 / 9 < 1 / 5 < 1 / 2

The order of the fractions from least to greatest is 1 / 10 < 1 / 9 < 1 / 5 < 1 / 2 .


Correct answer : (4)
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