﻿ Comparing Fractions with Like Denominators Worksheet | Problems & Solutions Comparing Fractions with Like Denominators Worksheet

Comparing Fractions with Like Denominators Worksheet
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1.
Bob and David have two oranges of the same size. Bob's orange is cut into 6 equal slices. David's orange is cut into 8 equal slices. Bob eats 5 slices and David eats 3 slices. Which orange has larger slices? a. We cannot compare b. Both have same size slices c. David′s orange d. Bob′s orange

Solution:

The orange that has less number of slices will have larger slices, because the sizes of the oranges are the same.

Since Bob's orange has less slices (6), it has larger slices.

2.
Choose an appropriate symbol to compare the fractions.
$\frac{4}{7}$  $\begin{array}{|c|}\hline \\ \hline\end{array}$  $\frac{6}{7}$ a. = b. + c. < d. >

Solution:

As the denominators are same on both sides, compare the numerators.
The fraction having greater numerator is the greater fraction.

So, 4 / 7 < 6 / 7.

3.
State which one of the comparisons of the fractions is true. a. $\frac{4}{5}$ > $\frac{5}{5}$ b. $\frac{1}{4}$ = $\frac{3}{4}$ c. $\frac{2}{7}$ < $\frac{5}{7}$ d. $\frac{5}{7}$ < $\frac{4}{7}$

Solution:

As the denominators are same on both sides, compare the numerators.
The fraction having greater numerator is the greater fraction.

So, 2 / 7 < 5 / 7.

4.
Choose an appropriate symbol to compare the fractions.
$\frac{7}{11}$  $\begin{array}{|c|}\hline \\ \hline\end{array}$  $\frac{3}{11}$ a. = b. > c. ÷ d. <

Solution:

As the denominators are same on both sides, compare the numerators.
The fraction having greater numerator is the greater fraction.

So, 7 / 11 > 3 / 11.

5.
Choose the figure where the shaded portion represents less than $\frac{3}{6}$ .  a. Figure 1 b. Figure 4 c. Figure 2 d. Figure 3

Solution:

Figure 1 represents 1 / 6.
1 / 6 < 3 / 6

Figure 2 represents 4 / 6.
4 / 6 > 3 / 6

Figure 3 represents 3 / 6.
3 / 6 = 3 / 6

Figure 4 represents 5 / 6.
5 / 6 > 3 / 6

So, Figure 1 represents the fraction smaller than 3 / 6.

6.
$\frac{3}{5}$ + $\frac{4}{5}$ a. $1\frac{3}{5}$ b. $1\frac{2}{5}$ c. $\frac{8}{5}$ d. $2\frac{1}{5}$

Solution:

3 / 5 + 4 / 5

= 3 + 45

= 7 / 5

= 12 / 5
[7 / 5 = 5 / 5 + 2 / 5 = 1 + 2 / 5 = 12 / 5.]

7.
What is the sum of $\frac{3}{5}$ and $\frac{2}{5}$? a. 4 b. 2 c. 3 d. 1

Solution:

3 / 5 + 2 / 5 = 3 + 25
[Denominators are equal. So, add the numerators.]

= 5 / 5 = 1

8.
What is the sum of $\frac{8}{9}$ and $\frac{2}{9}$? a. $\frac{10}{9}$ b. $\frac{10}{81}$ c. $\frac{9}{10}$ d. $\frac{6}{9}$

Solution:

8 / 9 + 2 / 9 = 8 + 29
[Denominators are equal. So, add the numerators.]

= 10 / 9

9.
Choose an appropriate symbol to compare the fractions.
$\frac{7}{3}$   $\begin{array}{|c|}\hline \\ \hline\end{array}$  $\frac{4}{3}$ a. < b. = c. + d. >

Solution:

7 / 3, 4 / 3
[Given fractions.]

Since the denominators are same, compare the numerators.

As 7 > 4, 7 / 3 > 4 / 3 .

10.
Which of the symbols is used to compare the given fractions?
$\frac{8}{7}$  $\begin{array}{|c|}\hline \\ \hline\end{array}$  $\frac{9}{7}$ a. < b. + c. = d. >

Solution:

8 / 7, 9 / 7
[Given fractions.]

Since the denominators are same, compare the numerators.

As 8 < 9, 8 / 7 < 9 / 7 .