﻿ Adding Fractions with Unlike Denominators Worksheet | Problems & Solutions

# Adding Fractions with Unlike Denominators Worksheet

Adding Fractions with Unlike Denominators Worksheet
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1.
Find the sum of the fractions in the figure.

 a. 3 b. 4 c. 2 d. 1

#### Solution:

The two fractions are 2 / 4 and 6 / 12 .

To add unlike fractions, we must first convert them into like fractions.

To convert unlike fractions into like fractions, we must first find out the common denominator.

Common denominator = Least Common Multiple of the denominators = 12

The equivalents of 2 / 4 and 6 / 12 with 12 as denominator are 6 / 12 and 6 / 12.

24 + 612 = 612 + 612
[Substitute.]

= 6+612 = 1212 = 1

So, the sum of the fractions in the figure is 1.

2.
Find the sum of the fractions in the figure.

 a. $\frac{3}{4}$ b. $\frac{5}{7}$ c. $\frac{7}{12}$ d. $\frac{5}{12}$

#### Solution:

The two fractions are 1 / 4 and 1 / 3 .

To add unlike fractions, we must first convert them into like fractions.

To convert unlike fractions into like fractions, we must first find out the least common multiple of the denominators (LCM).

LCM of 3 and 4 is 12.

The equivalents of 1 / 4 and 1 / 3 with denominator 12 are 3 / 12 and 4 / 12.

14 + 13 = 312 + 412
[Substitute the fractions with their equivalent fractions.]

= (3+4)12 = 712

So, the sum of the fractions in the figure is 7 / 12 .

3.
Find the sum of the fractions in the figure.

 a. $\frac{8}{7}$ b. $\frac{7}{12}$ c. $\frac{7}{8}$ d. $\frac{1}{12}$

#### Solution:

The two fractions are 2 / 8 and 2 / 6 .

To add unlike fractions, we must first convert them into like fractions.

To convert unlike fractions into like fractions, find out the least common multiple of the denominators (LCM).

Least Common Multiple of 6 and 8 is 24.

The equivalents of 2 / 8 and 2 / 6 with denominator 24 are 6 / 24 and 8 / 24.

28 + 26 = 624 + 824
[Substitute the fractions with their equivalent fractions.]

= (6+8)24 = 1424

= 712
[Simplify]

4.
Find the sum of the fractions in the figure.

 a. $\frac{7}{24}$ b. $\frac{1}{8}$ c. $\frac{1}{4}$ d. $\frac{5}{24}$

#### Solution:

The two fractions are 1 / 8 and 1 / 6 .

To add unlike fractions, convert them into like fractions.

To convert unlike fractions into like fractions, we must first find the least common denominator.

Least common denominator = Least common multiple of denominators = 24

The equivalents of 1 / 8 and 1 / 6 with denominator 24 are 3 / 24 and 4 / 24.

18 + 16 = 324 + 424
[Substitute the fractions with their equivalent fractions.]

= 3+424 = 724

So, the sum of the fractions in the figure is 7 / 24 .

5.
What is the sum of the fractions in the figure?

 a. $\frac{3}{4}$ b. $\frac{5}{4}$ c. $\frac{1}{4}$ d. $\frac{4}{3}$

#### Solution:

The two fractions are 1 / 2 and 1 / 4 .

To add unlike fractions, we must first convert them into like fractions.

To convert unlike fractions into like fractions, we must first find out the least common multiple of the denominators (LCM).

Least Common Multiple of 2 and 4 is 4.

The equivalents of 1 / 2 and 1 / 4 with denominator 4 are 2 / 4 and 1 / 4.

12 + 14 = 24 + 14
[Substitute.]

= 2+14 = 34

So, the sum of the fractions in the figure is 3 / 4 .

6.
Which of the figures represents the unlike fractions?

 a. Figure 1 b. Figure 2 c. Figure 3 d. Figure 4

#### Solution:

The unlike fractions must have different denominators.

Choice A is correct.

7.
What is the sum of the fractions in the figure?

 a. $\frac{7}{12}$ b. $\frac{1}{12}$ c. $\frac{5}{12}$ d. None of the above

#### Solution:

The two fractions are 1 / 4 and 1 / 3 .

To add unlike fractions, we must first convert them into like fractions.

To convert unlike fractions into like fractions, we must first find out the least common multiple of the denominators (LCM).

Least Common Multiple of 4 and 3 is 12.

The equivalents of 1 / 4 and 1 / 3 with 12 as denominator are 3 / 12 and 4 / 12.

14 + 13 = 312 + 412
[Substitute.]

= 4+312 = 712

So, the sum of the fractions in the figure is 7 / 12 .

8.
What is the sum of the fractions in the figure?

 a. $\frac{7}{15}$ b. $\frac{8}{15}$ c. $\frac{14}{15}$ d. $\frac{11}{15}$

#### Solution:

The two fractions are 1 / 3 and 2 / 5 .

To add unlike fractions, we must first convert them into like fractions.

To convert unlike fractions into like fractions, we must first find out the least common multiple of denominators (LCM).

Least Common Multiple of 3 and 5 is 15.

The equivalents of 1 / 3 and 2 / 5 with 15 as denominator are 5 / 15 and 6 / 15.

13 + 25 = 515 + 615
[Substitute.]

= 5+615 = 1115

So, the sum of the fractions in the figure is 11 / 15 .

9.
What is the sum of the fractions in the figure?

 a. $\frac{8}{15}$ b. $\frac{13}{15}$ c. $\frac{11}{15}$ d. $\frac{17}{15}$

#### Solution:

The two fractions are 8 / 15 and 1 / 3 .

To add unlike fractions, we must first convert them into like fractions.

To convert unlike fractions into like fractions, we must first find out the least common multiple of the denominators.

Least Common multiple of 15 and 3 is 15.

The equivalents of 8 / 15 and 1 / 3 with 15 as denominator are 8 / 15 and 5 / 15 .

8 / 15 + 5 / 15 = 8 / 15 + 5 / 15
= (8+5) / 15 = 13 / 15

10.
Find the sum of the fractions in the figure.

 a. $\frac{11}{20}$ b. $\frac{11}{13}$ c. $\frac{13}{20}$ d. none of these

#### Solution:

The two fractions are 1 / 4 and 2 / 5 .

To add unlike fractions, we must first convert them into like fractions.

To convert unlike fractions into like fractions, we must first find out the common denominator.

Common denominator = Least Common Multiple of the denominators = 20

The equivalents of 1 / 4 and 2 / 5 with 20 as denominator are 5 / 20 and 8 / 20.

14 + 25 = 520 + 820
[Substitute.]

= 5+820 = 1320