﻿ Comparing Fractions with Unlike Denominators Worksheet | Problems & Solutions

# Comparing Fractions with Unlike Denominators Worksheet

Comparing Fractions with Unlike Denominators Worksheet
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1.
Jonathan ate $\frac{3}{8}$ of a pizza and Terry ate $\frac{1}{4}$ of another pizza. Identify the appropriate symbol to compare the fractions.

 a. < b. = c. > d. ×

2.
Joanna bought 18 peaches. She gave $\frac{1}{3}$ of them to Cris and $\frac{1}{2}$ 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.

3.
Choose an appropriate symbol to compare the fractions.

$\frac{1}{4}$ $\begin{array}{|c|}\hline \\ \hline\end{array}$ $\frac{1}{2}$

 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.

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

5.
Order the fractions from least to greatest.

 a. $\frac{1}{25}$, $\frac{1}{15}$, $\frac{1}{5}$ b. $\frac{1}{25}$, $\frac{2}{15}$, $\frac{1}{5}$ c. $\frac{1}{5}$, $\frac{1}{15}$, $\frac{1}{25}$ d. $\frac{1}{5}$, $\frac{1}{15}$, $\frac{1}{15}$, $\frac{1}{25}$

#### 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 .

6.
Order the fractions from the greatest to the least.

 a. $\frac{1}{2}$ , $\frac{3}{5}$ , $\frac{1}{5}$ b. $\frac{1}{2}$ , $\frac{1}{5}$ , $\frac{1}{3}$ c. $\frac{2}{25}$ , $\frac{2}{15}$ , $\frac{1}{3}$ d. $\frac{1}{2}$ , $\frac{2}{5}$ , $\frac{1}{3}$

#### 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 .

7.
Order the fractions from the least to the greatest.

 a. $\frac{1}{8}$, $\frac{1}{4}$, $\frac{1}{2}$ b. $\frac{1}{6}$, $\frac{1}{4}$, $\frac{4}{8}$ c. $\frac{1}{6}$, $\frac{1}{4}$, $\frac{1}{8}$ d. $\frac{1}{6}$, $\frac{4}{8}$, $\frac{1}{8}$

#### 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.

8.
A child spends $\frac{1}{2}$ of a day in sleeping, $\frac{1}{10}$ of the day in eating, $\frac{1}{9}$ of the day in playing and the rest $\frac{1}{5}$ of the day in doing other activities, like bathing, etc. Arrange these fractions from the least to the greatest.
 a. $\frac{1}{10}>\frac{1}{9}<\frac{1}{5}>\frac{1}{2}$ b. $\frac{1}{10}>\frac{1}{9}>\frac{1}{5}>\frac{1}{2}$ c. $\frac{1}{10}>\frac{1}{9}<\frac{1}{5}<\frac{1}{2}$ d. $\frac{1}{10}<\frac{1}{9}<\frac{1}{5}<\frac{1}{2}$

#### 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 .