Adding and Subtracting Fractions Worksheets

Adding and Subtracting Fractions Worksheets
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 1.  
Tanya takes half an hour to reach the dance class. She practices dance for 1 4 of an hour in the morning and 1 3 of an hour in the evening. What is the time spent on dance practice?
a.
7 12 of an hour
b.
2 3 of an hour
c.
1 12 of an hour
d.
3 5 of an hour


Solution:

Time spent on dance practice = 1 / 4 + 1 / 3
[Time spent in the morning + Time spent in the evening]

= 3 / 12 + 4 / 12
[Write equivalent fractions using the LCD, 12.]

= 7 / 12
[Since the denominators are same, add the numerators.]

Tanya spent 7 / 12 of an hour on dance practice.


Correct answer : (1)
 2.  
At a bakery, each cake was cut into 8 equal pieces. Andrew sold 5 pieces of a cake, Amy sold 4 pieces of another, and Sarah sold 7 pieces of another. Which expression can be used to find the total number of cakes sold by these 3 people?
a.
85 + 84 + 87
b.
1 - 78 - 58 - 48
c.
58 + 48 + 78
d.
1 + 58 + 48 + 78


Solution:

Andrew sold 58 of a cake.

Amy sold 48 of a cake.

Sarah sold 78 of a cake.

So, the expression that represents the total number of cakes sold by these 3 people = 58 + 48 + 78.


Correct answer : (3)
 3.  
Steve bought 23 5 pounds of grapes, 12 5 pounds of nuts, and 34 5 pounds of apples. Which expression can be used to find the total weight of all the three items that Steve bought?
a.
235 + 125 + 345
b.
235 + 125
c.
1 + 235 + 125 + 345
d.
1 - 235 + 125 + 345


Solution:

Steve bought 23 / 5 pounds of grapes, 12 / 5 pounds of nuts, and 34 / 5 pounds of apples.

So, the expression that can be used to find the total weight of all the three items that Steve bought = 235 + 125 + 345.


Correct answer : (1)
 4.  
Tim ate 3 5 of a pie. Sunny ate 1 5 of a pie. Carlos ate 12 10 pies. Which expression can be used to find the total number of pies consumed by these 3 boys?
a.
1 - 35 + 15 + 1210
b.
35 + 15 + 1210
c.
35 + 15 + 210
d.
1 + 35 + 15 + 1210


Solution:

Tim ate 3 / 5 of a pie.

Sunny ate 1 / 5 of a pie.

Carlos ate 12 / 10 pies.

So, the expression that represents the total number of pies consumed by these 3 boys = 35 + 15 + 1210.


Correct answer : (2)
 5.  
Which statement leads you through to estimate mentally the quotient of 11750 to the nearest tenth?
I. Use a calculator.
II. Check for numbers that multiply with 50 to give 117.
III. The fraction is easily convertible to a fraction with a denominator of 100.
a.
III
b.
I and II
c.
II
d.
I


Solution:

Statement I is ruled out, as we need to estimate the quotient mentally.

Statement II is about trial and error method. You keep trying different numbers until you find the relevant one, and sometimes you may not find one.

As suggested in statement III, we shall convert the fraction 11750 into 234100 just by multiplying its numerator and denominator by 2.

234100 = 2.34 2.3, to the nearest tenth.

Among the statements given, statement III would lead us through the estimation.


Correct answer : (1)
 6.  
Estimate using compatible numbers the sum of 6421 and 55112 to the nearest tenth.
a.
3.0
b.
3.5
c.
4.5
d.
4.0


Solution:

6421 6321 = 3
[64 is close to 63 and is compatible with 21.]

55112 55110 = 1 / 2 = 0.5
[112 is close to 110 and is compatible with 55.]

So, 6421 + 55112 3 + 0.5 = 3.5 to the nearest tenth.


Correct answer : (2)
 7.  
Annie had a board 21 3 ft long. She bought another board 11 5 ft long and attached it to the first one. Estimate the total length of the board.
a.
6 ft
b.
3 ft
c.
2 ft
d.
5 ft


Solution:

Length of the board initally = 21 / 3 ft

21 / 3 = 2 + 1 / 3 2 + 0 = 2
[1 / 3 = 0.33333. . . 0.]

Length of the board attached = 11 / 5

11 / 5 = 1 + 1 / 5 1 + 0 = 1
[1 / 5 = 0.2 0.]

Therefore, the total length of the board = 21 / 3 + 11 / 5 2 + 1 = 3 ft


Correct answer : (2)
 8.  
A container holds 101 9 pints of liquid. If 1 5 of it is juice, estimate the quantity of juice in the container.
a.
4 pints
b.
6 pints
c.
8 pints
d.
2 pints


Solution:

Quantity of liquid container holds = 101 / 9

1019 = 10 + 19 10 + 0 = 10
[1 / 9 = 0.111111. . . 0.]

Quantity of juice in the container 1 / 5 × 10 = 2 pints

Quantity of juice in the container is 2 pints.


Correct answer : (4)
 9.  
Andrew bought a cake. He gave 1 4 of it to his brother, 1 6 of it to his sister, and 1 2 of it to his friend. What fraction of the cake did he distribute?
a.
7 12
b.
1 12
c.
5 12
d.
11 12


Solution:

The fraction of cake Andrew distributed = Fraction of cake he gave to his brother + Fraction of cake he gave to his sister + Fraction of cake he gave to his friend

= 1 / 4 + 1 / 6 + 1 / 2

= 3 + 2 + 612 = 1112
[Take LCD and add.]

The fraction of cake he distributed is 11 / 12.


Correct answer : (4)
 10.  
Lauren ate 1 5 of a pizza and Zelma ate 1 4 of it. Which operation would help you to find the fraction of pizza that Lauren and Zelma ate in all?
a.
addition
b.
division
c.
multiplication
d.
subtraction


Solution:

Fraction of pizza that Lauren and Zelma ate = Fraction of pizza that Lauren ate + Fraction of pizza that Zelma ate

The fraction of pizza that Lauren and Zelma ate is found using the operation additon.


Correct answer : (1)

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