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Adding Fractions with Unlike Denominators Worksheet

Adding Fractions with Unlike Denominators Worksheet
  • Page 1
 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
[Add the numerators and simplify.]

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


Correct answer : (4)
 2.  
Find the sum of the fractions in the figure.

a.
3 4
b.
5 7
c.
7 12
d.
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
[Add the numerators.]

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


Correct answer : (3)
 3.  
Find the sum of the fractions in the figure.

a.
8 7
b.
7 12
c.
7 8
d.
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
[Add the numerators.]

= 712
[Simplify]


Correct answer : (2)
 4.  
Find the sum of the fractions in the figure.

a.
7 24
b.
1 8
c.
1 4
d.
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
[Add the numerators.]

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


Correct answer : (1)
 5.  
What is the sum of the fractions in the figure?

a.
3 4
b.
5 4
c.
1 4
d.
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
[Add the numerators.]

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


Correct answer : (1)
 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.


Correct answer : (1)
 7.  
What is the sum of the fractions in the figure?

a.
7 12
b.
1 12
c.
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
[Add the numerators.]

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


Correct answer : (1)
 8.  
What is the sum of the fractions in the figure?


a.
7 15
b.
8 15
c.
14 15
d.
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
[Add the numerators.]

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


Correct answer : (4)
 9.  
What is the sum of the fractions in the figure?


a.
8 15
b.
13 15
c.
11 15
d.
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
[Add the numerators.]


Correct answer : (2)
 10.  
Find the sum of the fractions in the figure.


a.
11 20
b.
11 13
c.
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
[Add the numerators.]

So, the sum of the fractions in the figure is 13 / 20 .


Correct answer : (3)

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