﻿ Comparing and Ordering Fractions Worksheets | Problems & Solutions Comparing and Ordering Fractions Worksheets

Comparing and Ordering Fractions Worksheets
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1.
Order the $\frac{2}{5}$, $2\frac{2}{8}$, 0.07, and 70% in descending order. a. $2\frac{2}{8}$, 70%, $\frac{2}{5}$, 0.07 b. $2\frac{2}{8}$, $\frac{2}{5}$, 0.07, 70% c. $\frac{2}{5}$, 70%, $2\frac{2}{8}$, 0.07 d. 0.07, $\frac{2}{5}$, 70%, $2\frac{2}{8}$

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.

2.
Which of the following set is arranged from the least to the greatest? a. b. c. d.

3.
Which of the following set is arranged from the least to the greatest? a. b. c. d.

4.
Which of the following set is arranged from the least to the greatest? a. b. c. d.

5.
Which of the following set is arranged from the least to the greatest? a. b. c. d.

6.
Which of the following set is arranged from the least to the greatest? a. b. c. d.

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.

8.
Pick the appropriate symbol to compare the fractions.
$\frac{15}{7}$ ____ $\frac{9}{19}$ 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.

9.
Kelsey gave $3\frac{6}{7}$ pints of milk to Ursula and $\frac{25}{8}$ 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.

10.
Which group orders the fractions $\frac{6}{13}$, $\frac{12}{13}$, and $\frac{11}{13}$ from the greatest to the least? a. $\frac{12}{13}$, $\frac{11}{13}$, and $\frac{6}{13}$ b. $\frac{11}{13}$, $\frac{6}{13}$, and $\frac{12}{13}$ c. $\frac{12}{13}$, $\frac{6}{13}$, and $\frac{11}{13}$ d. $\frac{6}{13}$, $\frac{12}{13}$, and $\frac{11}{13}$

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.