#### Solved Examples and Worksheet for Adding and Subtracting Fractions-Unlike Denominators

Q1Find: 34 + 37

A. 17
B. 1528
C. 27
D. 1127

Step: 1
34 + 37
[Original expression.]
Step: 2
= 3 × 74 × 7 + 3 × 47×4
[Write the fractions with the same denominator using the LCD, 28.]
Step: 3
= 2128 + 1228

Step: 4
= 21 + 1228
Step: 5
= 3328

Step: 6
= 1528
[Simplify.]
Q2Find the sum of 78 and 89.
A. 7217
B. 12772
C. 78
D. 1517

Step: 1
78 + 89
[Write the expression.]
Step: 2
The LCM of 8 and 9 is 72, so the LCD of 78 and 89 is 72.
Step: 3
78 + 89= (78 × 99) + (89 × 88)
[Write equivalent fractions with a denominator of 72.]
Step: 4
= (6372) + (6472)
[Simplify.]
Step: 5
= 63 + 6472
[Write the sum over the common denominator.]
Step: 6
= 12772
[Simplify.]
Step: 7
The sum of 78 and 89 is 12772.
Q3Subtract the fraction 12 from the fraction 52 .

A. 5
B. 6
C. 1
D. 2

Step: 1
52 - 12
[Original expression.]
Step: 2
= 5 - 12
[Write the difference over the common denominator 2.]
Step: 3
= 42
[Subtract the numerators.]
Step: 4
= 21 = 2
[Cancel 4 and 2 with 2.]
Q4Subtract 25 from 1310.
A. 1010
B. 1710
C. 115
D. 910

Step: 1
1310- 25
[Original expression.]
Step: 2
= 1310 - 2×25×2
[Multiply the numerator and the denominator of 25 by 2 to make the denominators of both the fractions equal.]
Step: 3
= 13-410
[Write the difference over the common denominator.]
Step: 4
= 910
[Subtract the numerators.]
Q5Subtract the fraction 118 from the fraction 52.

A. 98
B. 109
C. 1
D. 119

Step: 1
52 - 118
[Original expression.]
Step: 2
The denominators in the two fractions are not the same. So, we change the fraction 52 to a fraction whose denominator is 8.
Step: 3
= 5 × 42 × 4 - 118
[Multiply the fraction 52 by 44.]
Step: 4
20 - 118
[Subtract the numerators.]
Step: 5
= 98
[Simplify by dividing numerator and denominator with 2.]
Q6Find the sum of 415 and 23.
A. 115
B. 1514
C. 1415
D. 114

Step: 1
415 + 23
[Write the expression.]
Step: 2
LCM of 15 and 3 is 15.
Step: 3
= 415 + 1015
[Write the equivalent fraction of 23 with a denominator 15.]
Step: 4
= 1415
Q7What is the sum of the fractions 32 and 23?
A. 136
B. 156
C. 236
D. 226

Step: 1
Write the equivalent fractions with 6 as the denominator. Then we add.
Q8Subtract the fraction 79 from the fraction 53.
A. 89
B. 13
C. 98
D. 18

Step: 1
53 - 79
[Original expression.]
Step: 2
The denominators in the two fractions are not the same. So, we change the fraction 53 to a fraction whose denominator is 9.
Step: 3
= 5 × 33 × 3 - 79
[Multiply the fraction 53 by 33.]
Step: 4
= 15 - 79
[Subtract the numerators.]
Step: 5
= 89
[Simplify.]
Q9Subtract.
49 - 25

A. 3845
B. 245
C. 2045
D. 1845

Step: 1
Write the equivalent fractions with 45 as the denominator. Then we subtract.
Q10Subtract the fraction 1112 from the fraction 43.

A. 713
B. 613
C. 512

Step: 1
43 - 1112
[Original expression.]
Step: 2
The denominators in the two fractions are not the same. So, we change the fraction 43 to a fraction whose denominator is 12.
Step: 3
= 4 × 43 × 4 - 1112
[Multiply the fraction 43 by 44.]
Step: 4
16 - 1112
[Subtract the numerators.]
Step: 5
= 512
[Simplify by dividing numerator and denominator with 3.]
Q11Subtract the fraction 14 from the fraction 78.

A. 57
B. 58
C. 38
D. 37

Step: 1
78 - 14
[Given.]
Step: 2
The denominators are different. So we need to make them the same.
Step: 3
78 - 1×24×2
[Find the equivalent fraction for 14.]
Step: 4
= 78 - 28
[14 is equivalent to 28.]
Step: 5
= 7 - 28
[Subtract the numerators as the denominators are same.]
Step: 6
= 58
[Subtract 2 from 7.]
Step: 7
78 - 14 = 58
Q12Find:
23 + 25

A. 1115
B. 1114
C. 14
D. 15

Step: 1
23 + 25

Step: 2
= 2 × 53 × 5 + 2 × 35 × 3
[Write the fractions with the same denominator using the LCM, 15.]
Step: 3
= 1015 + 615

Step: 4
= 10 + 615
[Add the numerators as the denominators are equal.]
Step: 5
= 1615

Step: 6
= 1115
[Convert improper fraction to mixed number.]
Q13 34 + 37 = ?
A. 17
B. 27
C. 1528
D. 1127

Step: 1
34 + 37

Step: 2
= 3 × 74 × 7 + 3 × 47 × 4
[Write the fractions with the same denominator using the LCM, 28.]
Step: 3
= 2128 + 1228

Step: 4
= 21 + 1228
[Add the numerators as the denominators are equal.]
Step: 5
= 3328

Step: 6
= 1528
[Convert improper fraction to mixed number.]
Q14Simplify : 115 - 13= ?

A. 1328
B. 2815
C. 1528
D. 1315

Step: 1
The LCM of 5 and 3 is 15.
Step: 2
115 - 13 = 11 × 35 × 3 - 1 × 53 × 5
Step: 3
= 3315 - 515 = 2815
Q15Find the sum of 37 and 92 .

A. 6714
B. 9614
C. 694
D. 6914

Step: 1
L. C. M. of 7 and 2 = 7 × 2 = 14.
Step: 2
37 + 92 = 3 × 27 × 2 + 9 × 72 × 7
Step: 3
= 614 + 6314= 6 + 6314 = 6914
Step: 4
Therefore, the sum of 37 and 92 is 6914.