Solved Examples and Worksheet for Application of Adding Fractions-Unlike Denominators

Q1Chris bought 41 lb of sugar. He gave 56 of it to Andrew and 19 of it to Frank. What fraction of the sugar did he give them?
A. 1718
B. 118
C. 20554
D. 1318

Solutions
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Step: 1
The fraction of sugar Chris gave them = 56 + 19
Step: 2
= 1518 + 218
  [Write equivalent fractions using the LCD, 18.]
Step: 3
= 15 + 218
  [Since the denominators are same, add numerators.]
Step: 4
= 1718
  
Step: 5
Chris gave 1718 of the sugar to them.
Correct Answer is :   1718
Q2Olga and Lindsay picked oranges in an orchard. Olga picked 25 of the oranges and Lindsay picked 27 of the oranges. What fraction of oranges did Olga and Lindsay pick together?

A. 23
B. 57
C. 2435
D. 2335

Solutions
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Step: 1
25 + 27
  [Original expression.]
Step: 2
2 × 75 × 7 + 2 × 57 × 5
  [Use LCD 35 to write equivalent fractions.]
Step: 3
= 1435 + 1035
  
Step: 4
= 14 + 1035
  [Since the denominators are equal, add the numerators.]
Step: 5
= 2435
  
Step: 6
Olga and Lindsay picked 2435 of the oranges.
Correct Answer is :   2435
Q3Tony got 34 of the total points in a math test. Henry got 18 of the total point on the same math test. What is the fraction for the total points both Tony and Henry got?

A. 78
B. 18
C. 14
D. None of the above

Solutions
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Step: 1
34 + 18
  [Original expression.]
Step: 2
= 3×24×2 + 18
  [Write the fractions with the same denominator using the LCD, 8.]
Step: 3
= 68 + 18
  [Simplify.]
Step: 4
= 6+18
  [Add the numerators.]
Step: 5
= 78
  
Step: 6
The fraction of points scored by both Tony and Henry in the math test is 78.
Correct Answer is :   78
Q4Tommy needs 19 of an acre of land to grow strawberries and 16 of an acre to grow tomatoes. What fraction of land does Tommy need to grow both strawberries and tomatoes?

A. 718 of an acre
B. 518 of an acre
C. 13 of an acre
D. 29 of an acre

Solutions
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Step: 1
Land needed to grow strawberries and tomatoes = land needed to grow strawberries + land needed to grow tomatoes
Step: 2
= 19 + 16
  
Step: 3
= 1×29×2 + 1×36×3
  [Use LCD 18 to write the equivalent fractions.]
Step: 4
= 218 + 318
  [Simplify.]
Step: 5
= 2+318 = 518
  [Add the numerators.]
Step: 6
Tommy needs 518of an acre to grow both strawberries and tomatoes.
Correct Answer is :   518 of an acre
Q5Blue marbles occupy 511 of the area of a box and red marbles occupy 19 of the area. What fraction of the area do both occupy in total if neither color marbles overlap ?

A. 199
B. 5699
C. 4599
D. 1199

Solutions
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Step: 1
511+ 19
  [Write the sum of the fractions.]
Step: 2
LCD of the fractions = LCM of the denominators = 99.
Step: 3
= 4599 + 1199
  [Use LCD to write equivalent fractions.]
Step: 4
= 11+4599
  [Add the numerators.]
Step: 5
So, both red and blue marbles occupy 5699 of the area of box.
Correct Answer is :   5699
Q6Nathan bought 49 lb of sugar. He gave 56 parts of the sugar to Francis and 18 parts of the sugar to Jimmy. What fraction of the sugar did he give them?
A. 56
B. 2324
C. 19
D. 116

Solutions
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Step: 1
The fraction of sugar Nathan gave them = 56 + 18
Step: 2
= 2024 + 324
  [Write equivalent fractions using the LCD, 24.]
Step: 3
= 20 + 324
  [Since the denominators are same, add numerators.]
Step: 4
= 2324
  
Step: 5
Nathan gave 2324 of the sugar to them.
Correct Answer is :   2324
Q7Paula has some coins in her handbag. 17 of the coins are cents, 37 of the coins are quarters and the rest are nickels. What fraction of the coins are cents and quarters?

A. 23
B. 58
C. 47
D. 12

Solutions
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Step: 1
17 + 37
  [Sum of cents and quarters.]
Step: 2
= 17 + 37
  [Write equivalent fractions using the LCD, 7.]
Step: 3
= 1 + 37
  [Since the denominators are same, add the numerators.]
Step: 4
= 47
  [Simplify.]
Step: 5
47 of the coins are cents and quarters.
Correct Answer is :   47
Q8Nancy ate 12 an apple before leaving for school and 15 of the apple after coming back from school. How much of the apple did she eat?

A. 27
B. 17
C. 75
D. 710

Solutions
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Step: 1
The fraction of apple Nancy ate = The fraction of it she ate before leaving to school + The fraction of it she ate after coming back home.
Step: 2
= 12+ 15
  [Substitute the values.]
Step: 3

Step: 4
So, Nancy ate 710 of the apple.
Correct Answer is :   710
Q9Ed poured 45 qt of juice into a jug. Later, he added 315 qt of juice to it. How much juice is in the jug?
A. 4 qt
B. 2 qt
C. 1 qt
D. 3 qt

Solutions
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Step: 1
The quantity of juice in the jug = The quantity of that he poured first + The quantity he added later
Step: 2
= 45 + 315
  [Substitute the values.]
Step: 3

Step: 4
So, Ed poured 1 qt of juice into the jug.
Correct Answer is :   1 qt
Q10Francis bought two baskets of blackberries. 29 of them were stale in the first basket and 13 of them were stale in the second basket. What fraction of the blackberries were stale on the whole?

A. 95
B. 97
C. 19
D. 59

Solutions
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Step: 1
The fraction of stale blackberries in both the baskets = the fraction of stale blackberries in the first basket + the fraction of stale blackberries in the second basket.
Step: 2
= 29 + 13
  [Substitute the values.]
Step: 3

Step: 4
So, 59 of the blackberries were stale.
Correct Answer is :   59
Q11Katie has some coins in her handbag. 14 of the coins are dimes, 112 of the coins are pennies and the remaining coins are nickels. What fraction of the coins are dimes and pennies?
A. 412
B. 124
C. 216
D. 24

Solutions
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Step: 1
Total fraction coins that are dimes and pennies = 14 + 112
Step: 2
The equivalent fractions of 14 and 112 with common denominator 12 are 312 and 112
Step: 3
14 + 112 = 312 + 112
Step: 4
= 3 + 112 = 412
Step: 5
Therefore, the fraction coins that are dimes and pennies = 412
Correct Answer is :    412

HighSchool Math