﻿ Adding Fractions with Like Denominators Worksheet | Problems & Solutions

# Adding Fractions with Like Denominators Worksheet

Adding Fractions with Like Denominators Worksheet
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1.
What would you add to the fraction $\frac{1}{6}$ to get a sum of 1?
 a. $\frac{6}{5}$ b. $\frac{5}{6}$ c. 1 d. $\frac{1}{6}$

#### Solution:

Required fraction = 1 - 1 / 6
[Sum of the fraction and 1 / 6 is 1.]

= 6 / 6 - 1 / 6
[Write 1 as 6 / 6 so as to make denominators equal.]

6 - 1 = 5
[Denominators are equal. So, subtract the numerators.]

1 - 1 / 6 = 5 / 6

The fraction that should be added to 1 / 6 to get sum 1 is 5 / 6.

2.
What would you add to the fraction $\frac{3}{8}$ to get a sum of 1?
 a. $\frac{5}{8}$ b. $\frac{3}{8}$ c. $\frac{8}{5}$ d. 1

#### Solution:

Required fraction = 1 - 3 / 8
[Sum of the fraction and 3 / 8 is 1.]

= 8 / 8 - 3 / 8
[Write 1 as 8 / 8 so as to make denominators equal.]

8 - 3 = 5
[Denominators are equal. So, subtract the numerators.]

1 - 3 / 8 = 5 / 8

The fraction that should be added to 3 / 8 to get sum 1 is 5 / 8.

3.
What would you add to the fraction $\frac{7}{10}$ to get a sum of 1?
 a. $\frac{3}{7}$ b. $\frac{10}{3}$ c. 10 d. $\frac{3}{10}$

#### Solution:

Required fraction = 1 - 7 / 10
[Sum of the fraction and 7 / 10 is 1.]

= 10 / 10 - 7 / 10
[Write 1 as 10 / 10 so as to make denominators equal.]

10 - 7 = 3
[Denominators are equal. So, subtract the numerators.]

1 - 7 / 10 = 3 / 10

The fraction that should be added to 7 / 10 to get sum 1 is 3 / 10.

4.
What would you add to the fraction $\frac{4}{9}$ to get a sum of 1?
 a. $\frac{5}{4}$ b. $\frac{9}{4}$ c. $\frac{5}{9}$ d. $\frac{9}{5}$

#### Solution:

Required fraction = 1 - 4 / 9
[Sum of the fraction and 4 / 9 is 1.]

= 9 / 9 - 4 / 9
[Write 1 as 9 / 9 so as to make denominators equal.]

9 - 4 = 5
[Denominators are equal. So, subtract the numerators.]

1 - 4 / 9 = 5 / 9

The fraction that should be added to 4 / 9 to get sum 1 is 5 / 9.

5.
What would you add to the fraction $\frac{1}{3}$ to get a sum of 1?
 a. $\frac{1}{4}$ b. 3 c. $\frac{2}{3}$ d. $\frac{1}{3}$

#### Solution:

Required fraction = 1 - 1 / 3
[Sum of the fraction and 1 / 3 is 1.]

= 3 / 3 - 1 / 3
[Write 1 as 3 / 3 so as to make denominators equal.]

3 - 1 = 2
[Denominators are equal. So, subtract the numerators.]

1 - 1 / 3 = 2 / 3

The fraction that should be added to 1 / 3 to get sum 1 is 2 / 3.

6.
Which of the choices correctly represents the sum of the two fractions $\frac{2}{9}$ and $\frac{3}{9}$?

#### Solution:

29 + 39
[Given fraction.]

= 2+39
[Add the numerators over the common denominators.]

= 59

The fraction 5 / 9 means: 5 stars are shaded out of 9 stars.

From the choices, Choice A represents the fraction 5 / 9 correctly.

7.
Find the sum.
$\frac{3}{4}$ + $\frac{1}{4}$
 a. $\frac{1}{2}$ b. 2 c. 1 d. $\frac{1}{3}$

8.
A tap fills $\frac{2}{5}$of a tank in the first two hours and $\frac{1}{5}$of the tank in the next two hours. What portion of the tank is filled in four hours?
 a. $\frac{1}{3}$ b. $\frac{1}{5}$ c. $\frac{3}{5}$ d. $\frac{1}{8}$

#### Solution:

The portion of the tank filled by the tap in two hours = 2 / 5

The portion of the tank filled in the next two hours = 1 / 5

The portion of the tank filled in the four hours = 2 / 5 + 1 / 5

25 + 15 = 35
[Add the numerators and keep the denominator same.]

The portion of the tank filled in four hours = 3 / 5

9.
A person has done $\frac{5}{12}$ of a job in one week. In the next week, he is only able to complete $\frac{1}{12}$ of the job. Find the fraction of work he has completed in the two weeks.
 a. $\frac{1}{5}$ b. $\frac{1}{2}$ c. $\frac{1}{3}$ d. $\frac{1}{4}$

#### Solution:

Work done by the person in the first week = 5 / 12

Work done by the person in the second week = 1 / 12

Total work done by the person in the past two weeks = 5 / 12 + 1 / 12

5 + 1 = 6
[Denominators are equal. So, add the numerators.]

512 + 112 = 612

612 = 12
[Divide.]

The work done by the person during the two weeks = 1 / 2.

10.
Jim spent $\frac{3}{7}$ of his salary in the first two weeks of January and $\frac{2}{7}$ in the next two weeks. What fraction of his salary did he spend in the month of January?
 a. $\frac{1}{2}$ b. $\frac{5}{7}$ c. $\frac{1}{5}$ d. $\frac{1}{7}$

#### Solution:

Salary spent in the first two weeks = 3 / 7

Salary spent in the next two weeks = 2 / 7

The total part of salary spent in the month = 3 / 7 + 2 / 7

= 3 + 27 = 57
[Denominators are equal. So, add the numerators.]

Jim spent 5 / 7 of the total part of salary in the month.