Solved Examples and Worksheet for Adding and Subtracting Fractions-Unlike Denominators
Q1
Find:
3
4
+
3
7
A
.
1
7
B
.
1
5
28
C
. 27
D
.
1
1
27
Solutions
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Step: 1
3
4
+
3
7
[Original expression.]
Step: 2
=
3
×
7
4
×
7
+
3
×
4
7
×
4
[Write the fractions with the same denominator using the LCD, 28.]
Step: 3
=
21
28
+
12
28
Step: 4
=
2
1
+
1
2
2
8
[Add the numerators.]
Step: 5
=
33
28
Step: 6
=
1
5
28
[Simplify.]
Correct Answer is :
1
5
28
Q2
Find the sum of
7
8
and
8
9
.
A
.
72
17
B
.
127
72
C
.
7
8
D
.
15
17
Solutions
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Step: 1
7
8
+
8
9
[Write the expression.]
Step: 2
The LCM of 8 and 9 is 72, so the LCD of
7
8
and
8
9
is 72.
Step: 3
7
8
+
8
9
= (
7
8
×
9
9
) + (
8
9
×
8
8
)
[Write equivalent fractions with a denominator of 72.]
Step: 4
= (
63
72
) + (
64
72
)
[Simplify.]
Step: 5
=
6
3
+
6
4
7
2
[Write the sum over the common denominator.]
Step: 6
=
127
72
[Simplify.]
Step: 7
The sum of
7
8
and
8
9
is
127
72
.
Correct Answer is :
127
72
Q3
Subtract the fraction
1
2
from the fraction
5
2
.
A
. 5
B
. 6
C
. 1
D
. 2
Solutions
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Step: 1
5
2
-
1
2
[Original expression.]
Step: 2
=
5
-
1
2
[Write the difference over the common denominator 2.]
Step: 3
=
4
2
[Subtract the numerators.]
Step: 4
=
2
1
= 2
[Cancel 4 and 2 with 2.]
Correct Answer is :
2
Q4
Subtract
2
5
from
13
10
.
A
.
10
10
B
.
17
10
C
.
11
5
D
.
9
10
Solutions
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Step: 1
13
10
-
2
5
[Original expression.]
Step: 2
=
13
10
-
2×2
5×2
[Multiply the numerator and the denominator of
2
5
by 2 to make the denominators of both the fractions equal.]
Step: 3
=
13-4
10
[Write the difference over the common denominator.]
Step: 4
=
9
10
[Subtract the numerators.]
Correct Answer is :
9
10
Q5
Subtract the fraction
11
8
from the fraction
5
2
.
A
.
9
8
B
.
10
9
C
. 1
D
.
11
9
Solutions
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Step: 1
5
2
-
11
8
[Original expression.]
Step: 2
The denominators in the two fractions are not the same. So, we change the fraction
5
2
to a fraction whose denominator is 8.
Step: 3
=
5
×
4
2
×
4
-
11
8
[Multiply the fraction
5
2
by
4
4
.]
Step: 4
2
0
-
1
1
8
[Subtract the numerators.]
Step: 5
=
9
8
[Simplify by dividing numerator and denominator with 2.]
Correct Answer is :
9
8
Q6
Find the sum of
4
15
and
2
3
.
A
.
1
15
B
.
15
14
C
.
14
15
D
.
1
14
Solutions
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Step: 1
4
15
+
2
3
[Write the expression.]
Step: 2
LCM of 15 and 3 is 15.
Step: 3
=
4
15
+
10
15
[Write the equivalent fraction of
2
3
with a denominator 15.]
Step: 4
=
14
15
[Add the fractions.]
Correct Answer is :
14
15
Q7
What is the sum of the fractions
3
2
and
2
3
?
A
.
13
6
B
.
15
6
C
.
23
6
D
.
22
6
Solutions
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Step: 1
Write the equivalent fractions with 6 as the denominator. Then we add.
Correct Answer is :
13
6
Q8
Subtract the fraction
7
9
from the fraction
5
3
.
A
.
8
9
B
.
1
3
C
.
9
8
D
.
1
8
Solutions
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Step: 1
5
3
-
7
9
[Original expression.]
Step: 2
The denominators in the two fractions are not the same. So, we change the fraction
5
3
to a fraction whose denominator is 9.
Step: 3
=
5
×
3
3
×
3
-
7
9
[Multiply the fraction
5
3
by
3
3
.]
Step: 4
=
1
5
-
7
9
[Subtract the numerators.]
Step: 5
=
8
9
[Simplify.]
Correct Answer is :
8
9
Q9
Subtract.
4
9
-
2
5
A
.
38
45
B
.
2
45
C
.
20
45
D
.
18
45
Solutions
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Step: 1
Write the equivalent fractions with 45 as the denominator. Then we subtract.
Correct Answer is :
2
45
Q10
Subtract the fraction
11
12
from the fraction
4
3
.
A
.
7
13
B
.
6
13
C
.
5
12
Solutions
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Step: 1
4
3
-
11
12
[Original expression.]
Step: 2
The denominators in the two fractions are not the same. So, we change the fraction
4
3
to a fraction whose denominator is 12.
Step: 3
=
4
×
4
3
×
4
-
11
12
[Multiply the fraction
4
3
by
4
4
.]
Step: 4
1
6
-
1
1
1
2
[Subtract the numerators.]
Step: 5
=
5
12
[Simplify by dividing numerator and denominator with 3.]
Correct Answer is :
5
12
Q11
Subtract the fraction
1
4
from the fraction
7
8
.
A
.
5
7
B
.
5
8
C
.
3
8
D
.
3
7
Solutions
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Step: 1
7
8
-
1
4
[Given.]
Step: 2
The denominators are different. So we need to make them the same.
Step: 3
7
8
-
1
×
2
4
×
2
[Find the equivalent fraction for
1
4
.]
Step: 4
=
7
8
-
2
8
[
1
4
is equivalent to
2
8
.]
Step: 5
=
7
-
2
8
[Subtract the numerators as the denominators are same.]
Step: 6
=
5
8
[Subtract 2 from 7.]
Step: 7
7
8
-
1
4
=
5
8
Correct Answer is :
5
8
Q12
Find:
2
3
+
2
5
A
.
1
1
15
B
.
1
1
14
C
. 14
D
.
1
5
Solutions
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Step: 1
2
3
+
2
5
Step: 2
=
2
×
5
3
×
5
+
2
×
3
5
×
3
[Write the fractions with the same denominator using the LCM, 15.]
Step: 3
=
10
15
+
6
15
Step: 4
=
1
0
+
6
1
5
[Add the numerators as the denominators are equal.]
Step: 5
=
16
15
Step: 6
=
1
1
15
[Convert improper fraction to mixed number.]
Correct Answer is :
1
1
15
Q13
3
4
+
3
7
= ?
A
.
1
7
B
. 27
C
.
1
5
28
D
.
1
1
27
Solutions
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Step: 1
3
4
+
3
7
Step: 2
=
3
×
7
4
×
7
+
3
×
4
7
×
4
[Write the fractions with the same denominator using the LCM, 28.]
Step: 3
=
21
28
+
12
28
Step: 4
=
2
1
+
1
2
2
8
[Add the numerators as the denominators are equal.]
Step: 5
=
33
28
Step: 6
=
1
5
28
[Convert improper fraction to mixed number.]
Correct Answer is :
1
5
28
Q14
Simplify :
11
5
-
1
3
= ?
A
.
13
28
B
.
28
15
C
.
15
28
D
.
13
15
Solutions
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Step: 1
The LCM of 5 and 3 is 15.
Step: 2
11
5
-
1
3
=
1
1
×
3
5
×
3
-
1
×
5
3
×
5
Step: 3
=
33
15
-
5
15
=
28
15
Correct Answer is :
28
15
Q15
Find the sum of
3
7
and
9
2
.
A
.
67
14
B
.
96
14
C
.
69
4
D
.
69
14
Solutions
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Step: 1
L. C. M. of 7 and 2 = 7 × 2 = 14.
Step: 2
3
7
+
9
2
=
3
×
2
7
×
2
+
9
×
7
2
×
7
Step: 3
=
6
14
+
63
14
=
6
+
6
3
1
4
=
69
14
Step: 4
Therefore, the sum of
3
7
and
9
2
is
69
14
.
Correct Answer is :
69
14
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Related Topic
Fraction
HighSchool Math
Grade 3
Grade 4
Grade 5