#### Solved Examples and Worksheet for Adding Rational Numbers

Q1Find 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.
Q2Find the sum.
313 + 415

A. 11315
B. 11516
C. 11416
D. 11415

Step: 1
313 + 415
[Original expression.]
Step: 2
= 103 + 215
[Rewrite the mixed fractions as improper fractions.]
Step: 3
The LCM of 3 and 5 is 15, so the LCD of 103 and 215 is 15.
Step: 4
103 + 215 = 5015 + 6315
[Write equivalent fractions with a denominator of 15.]
Step: 5
= 50+6315
[Write the sum over the common Denominator.]
Step: 6
= 11315.
[Simplify.]
Q3Find the sum.
513 + 615

A. 17315
B. -1316
C. 18815
D. 15815

Step: 1
513 + 615
[Original expression.]
Step: 2
= 163 + 315
[Rewrite the mixed fractions as improper fractions.]
Step: 3
The LCM of 3 and 5 is 15, so the LCD of 163 and 315 is 15.
Step: 4
163 + 315 = 8015 + 9315
[Write equivalent fractions with a denominator of 15.]
Step: 5
= (80+93)(15)
[Write the sum over the common Denominator.]
Step: 6
= 17315
[Simplify.]
Q4Find the sum.
83 5 + 1021 22

A. 835
B. 102122
C. 1961110
D. 2061110

Step: 1
83 5 + ( 1021 22)
[Write the expression.]
Step: 2
= 435 + 24122
[Rewrite the mixed fractions as improper fractions.]
Step: 3
The LCM of 5 and 22 is 110, so the LCD of 435 and 24122 is 110.
Step: 4
= [( 435) × ( 2222)] + [( 24122) × (55)]
[Write equivalent fractions with a denominator of 110 .]
Step: 5
= ( 946110) + ( 1205110)
[Multiply inside the grouping symbols..]
Step: 6
=  946+ ( 1205)110
[Write the sum over the common denominator.]
Step: 7
= 2151110
[Simplify]
Step: 8
= 1961110
[Convert the proper fraction to a mixed fraction.]
Step: 9
The sum of 83 5 and 1021 22 is 1961110 .
Q5Marissa and Rachel pluck apples in an orchard. Marissa plucked 47 of the apples and Rachel plucked 49 of the apples this morning. Identify the fraction that shows the fraction of apples they plucked together.
A. 6463
B. 863
C. 421
D. 6364

Step: 1
47 + 49
[Original expression.]
Step: 2
= 4 × 97 × 9 + 4 × 79 × 7
[Use LCD 63 to write equivalent fractions.]
Step: 3
= 3663 + 2863
Step: 4
= 36 + 2863