Adding and Subtracting Fractions Worksheet

Adding and Subtracting Fractions Worksheet
  • Page 1
 1.  
Which model represents the product of the fractions 3 2 and 4 14 ?

a.
Figure 4
b.
Figure 3
c.
Figure 2
d.
Figure 1


Solution:

3 / 2 × 4 / 14
[Original expression.]

3 / 2 × 2 / 7
[Simplify.]

= 3×22×7
[Multiply numerators and denominators separately.]

= 3 / 7
[Simplify.]

The fraction 3 / 7 has 3 colored parts out of 7 parts on the whole.

So, Figure 4 is the model representing the product of the fractions 3 / 2 and 4 / 14 .


Correct answer : (1)
 2.  
Write the product statement of the numbers represented by the letters C, G and B on the number line.


a.
0.4 × 0.8 × 0.2
b.
0.8 × 1.2 × 0.2
c.
0.4 × 1.2 × 0.2
d.
0.2 × 0.6 × 0.4


Solution:

From the number line, the value of C = 0.4, G = 1.2 and B = 0.2

So, the product statement of the numbers represented by the given letters is 0.4 × 1.2 × 0.2.


Correct answer : (3)
 3.  
The difference between Jones' height and John's height is 22.6 cm. Identify the expression that tells you Jones' height, if John's height is 157.3 cm.
a.
157.3 22.6 cm
b.
157.3 - 22.6 cm
c.
157.3 + 22.6 cm
d.
( 157.3) × (22.6) cm


Solution:

Let the John's height be h cm.

Jones' height - John's height = 22.6
[Original expression.]

h - 157.3 = 22.6
[Substitute the values.]

h - 157.3 + 157.3 = 22.6 + 157.3
[Add 157.3 to each side.]

So, Jones' height is 157.3 + 22.6 cm.


Correct answer : (3)
 4.  
Subtract:
924 - 827
a.
178
b.
17216
c.
1
d.
179


Solution:

9 / 24 - 8 / 27 = 9 × 924 × 9 - 8 × 827 × 8
[Use LCD 216 to write equivalent fractions.]

= 81 / 216- 64 / 216
[Simplify.]

= 81 - 64216
[Since the denominators are equal, subtract the numerators.]

= 17 / 216


Correct answer : (2)
 5.  
Katie ate 1 4 of a burger. How much more of the burger should she eat to complete 5 8 of the burger?
a.
3 8
b.
4 9
c.
1 2
d.
6 11


Solution:

5 / 8 - 1 / 4

= 5 / 8 - 2 / 8
[Use LCD 8 to write equivalent fractions.]

= 5 - 28
[Since the denominators are equal, subtract the numerators.]

= 3 / 8

She has to eat 3 / 8 more of the burger to complete 5 / 8 of the burger.


Correct answer : (1)
 6.  
Find the sum of - 7 9 and 8 9.
a.
1 5
b.
3 11
c.
1 3
d.
1 9


Solution:

- 79 + 89
[Original expression.]

= - 7+89
[Since the denominators are equal, add the numerators.]

= 19

The sum of - 7 / 9 and 8 / 9 is 1 / 9.


Correct answer : (4)
 7.  
Christina and Lydia are plucking oranges in an orchard. Christina has plucked 3 7 of the oranges and Lydia has plucked 3 10 of the oranges. What fraction of oranges did Christina and Lydia pluck together?
a.
26 35
b.
5 7
c.
51 71
d.
51 70


Solution:

3 / 7 + 3 / 10
[Original expression.]

3 × 107 × 10 + 3 × 710 × 7
[Use LCD 70 to write equivalent fractions.]

= 3070 + 2170

= 30 + 2170
[Since the denominators are equal, add the numerators.]

= 5170

Christina and Lydia plucked 51 / 70 of the oranges.


Correct answer : (4)
 8.  
Find: 8 9 - 5 6
a.
3 20
b.
1 19
c.
1 18
d.
2 19


Solution:

8 / 9 - 5 / 6
[Original expression.]

= 8 × 29 × 2 - 5 × 36 × 3
[Use LCD 18 to write equivalent fractions.]

= 16 / 18 - 15 / 18
[Simplify.]

= 16 - 1518
[Since the denominators are equal, subtract the numerators.]

= 1 / 18
[Simplify.]


Correct answer : (3)
 9.  
Charlie and Jeff are picking up trash along the highway. Together they have picked up 10 11 of the trash. Jeff has picked up 9 22 of the trash. Find the fraction of trash picked up by Charlie.
a.
1 2
b.
9 22
c.
1 4
d.
9 11


Solution:

1011 - 922
[Original e×pression.]

= 2 × 102 × 11 - 922
[Write the fractions with the same denominator using their LCD, 22.]

= 2022 - 922
[Simplify.]

= 20 - 922
[Subtract the numerators.]

= 1122 = 12
[Simplify.]

Charlie picked up 1 / 2 of the trash.


Correct answer : (1)
 10.  
A survey taken reported that 9 / 19th of the population listened to the President's speech. If the margin for error is plus or minus 4 / 38, then what are the maximum and minimum values for the actual number of people who listened the speech?
a.
3 5 and 5 13
b.
23 39 and 5 13
c.
11 19 and 7 19
d.
None of the above


Solution:

The actual population more than the estimated value = 9 / 19 + 4 / 38

(9×2) / (19×2) + 4 / 38
[The LCD is 38.]

= 18 / 38 + 4 / 38
[Write the equivalent fractions with a denominator of 38.]

= (18+4) / 38
[Add the numerators.]

= 22 / 38 = 11 / 19
[Simplify.]

The actual population less than the estimated value = 9 / 19 - 4 / 38

(9×2) / (19×2) - 4 / 38
[The LCD is 38.]

= 18 / 38 - 4 / 38
[Write the equivalent fractions with a denominator of 38.]

= (18-4)38

[Subtract the numerators.]

= 1438 = 719
[Simplify.]

The possible values for the actual population could be 11 / 19 and 7 / 19.


Correct answer : (3)

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