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Comparing and Ordering Fractions Worksheets

Comparing and Ordering Fractions Worksheets
  • Page 1
 1.  
Order the 2 5, 22 8, 0.07, and 70% in descending order.
a.
22 8, 70%, 2 5, 0.07
b.
22 8, 2 5, 0.07, 70%
c.
2 5, 70%, 22 8, 0.07
d.
0.07, 2 5, 70%, 22 8


Solution:

2 / 5, 22 / 8, 0.07, and 70%
[Original terms.]

Consider the first term 2 / 5:
2 / 5 = 0.4
[Convert the fraction to a decimal number.]

Consider the second term 22 / 8:
22 / 8 = 2.25.
[Convert the mixed fraction to a decimal number.]

The third term is 0.07.

Consider the fourth term 70%:
70% = 70 / 100 = 0.7.
[Convert the percent to a decimal number.]

2.25 > 0.7 > 0.4 > 0.05
[Compare the values.]

22 / 8> 70% > 2 / 5> 0.07
[Compare the original terms.]

The descending order of the terms 22 / 8> 70% > 2 / 5> 0.07.


Correct answer : (1)
 2.  
Which of the following set is arranged from the least to the greatest?
a.
23 <34 <38
b.
34 <38 <23
c.
38 <23 <34
d.
34 <23 <38


Answer: (c)


Correct answer : (3)
 3.  
Which of the following set is arranged from the least to the greatest?
a.
34 <23 <38
b.
23 <34 <38
c.
38 <23 <34
d.
34 <38 <23


Answer: (c)


Correct answer : (3)
 4.  
Which of the following set is arranged from the least to the greatest?
a.
34 <38 <23
b.
34 <23 <38
c.
23 <34 <38
d.
38 <23 <34


Answer: (d)


Correct answer : (4)
 5.  
Which of the following set is arranged from the least to the greatest?
a.
23 <34 <38
b.
34 <38 <23
c.
34 <23 <38
d.
38 <23 <34


Answer: (d)


Correct answer : (4)
 6.  
Which of the following set is arranged from the least to the greatest?
a.
34 <23 <38
b.
34 <38 <23
c.
23 <34 <38
d.
38 <23 <34


Answer: (d)


Correct answer : (4)
 7.  
Which of the models is the greater fraction?

a.
Figure 1
b.
Figure 2


Solution:

Fraction modeled by Figure 1 is 3 / 6
[3 out of 6 parts are shaded.]

Fraction modeled by Figure 2 is 4 / 6
[4 out of 6 parts are shaded.]

4 is greater than 3
[Compare the numerators of 3 / 6 and 4 / 6.]

4 / 6 is greater than 3 / 6.

So, model in Figure 2 is greater fraction.


Correct answer : (2)
 8.  
Pick the appropriate symbol to compare the fractions.
15 7 ____ 9 19
a.
<
b.
=
c.
+
d.
>


Solution:

9 / 19 is a proper fraction and 15 / 7 is an improper fraction.

An improper fraction is always greater than a proper fraction.

15 / 7 is greater than 9 / 19.


Correct answer : (4)
 9.  
Kelsey gave 36 7 pints of milk to Ursula and 25 8 pints of milk to Jason. Who got more milk, Ursula or Jason?
a.
Jason
b.
Ursula


Solution:

25 / 8 = 31 / 8
[Convert improper fraction into mixed number.]

Compare 6 / 7 and 1 / 8.
[Since the whole numbers are equal.]

LCD = LCM of the denominators = 7 × 8 = 56
[Find LCM to find LCD.]

6 / 7 = (6×8) / (7×8) = 48 / 56
[Multiply both numerator and denominator with 8 to get LCD in the denominator.]

1 / 8 = (1×7) / (8×7) = 7 / 56
[Multiply both numerator and denominator with 7 to get LCD in the denominator.]

48 > 7
[Compare the numerators of 48 / 56 and 7 / 56 .]

Since 48 / 56 > 7 / 56, 6 / 7 > 1 / 8

36 / 7 is greater than 31 / 8.

36 / 7 is greater than 25 / 8.

So, Ursula got more milk than Jason.


Correct answer : (2)
 10.  
Which group orders the fractions 6 13, 12 13, and 11 13 from the greatest to the least?
a.
12 13, 11 13, and 613
b.
11 13, 6 13, and 1213
c.
12 13, 6 13, and 1113
d.
6 13, 12 13, and 1113


Solution:

12 > 11 > 6
[Since the denominators are equal, arrange the numerators in the decreasing order.]

So, the order of the fractions from greatest to least is 12 / 13, 11 / 13, and 6 / 13.


Correct answer : (1)

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