# Adding and Subtracting Fractions Worksheet

• Page 1
1.
Which model represents the product of the fractions $\frac{3}{2}$ and $\frac{4}{14}$ ?

 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 .

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.

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. $\frac{157.3}{22.6}$ 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

So, Jones' height is 157.3 + 22.6 cm.

4.
Subtract:
$\frac{9}{\mathrm{24}}$ - $\frac{8}{\mathrm{27}}$
 a. $\frac{\mathrm{17}}{8}$ b. $\frac{\mathrm{17}}{\mathrm{216}}$ c. 1 d. $\frac{\mathrm{17}}{9}$

#### 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

5.
Katie ate $\frac{1}{4}$ of a burger. How much more of the burger should she eat to complete $\frac{5}{8}$ of the burger?
 a. $\frac{3}{8}$ b. $\frac{4}{9}$ c. $\frac{1}{2}$ d. $\frac{6}{11}$

#### 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.

6.
Find the sum of - $\frac{7}{9}$ and $\frac{8}{9}$.
 a. $\frac{1}{5}$ b. $\frac{3}{11}$ c. $\frac{1}{3}$ d. $\frac{1}{9}$

#### 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.

7.
Christina and Lydia are plucking oranges in an orchard. Christina has plucked $\frac{3}{7}$ of the oranges and Lydia has plucked $\frac{3}{10}$ of the oranges. What fraction of oranges did Christina and Lydia pluck together?
 a. $\frac{26}{35}$ b. $\frac{5}{7}$ c. $\frac{51}{71}$ d. $\frac{51}{70}$

#### 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.

8.
Find: $\frac{8}{9}$ - $\frac{5}{6}$
 a. $\frac{3}{20}$ b. $\frac{1}{19}$ c. $\frac{1}{18}$ d. $\frac{2}{19}$

#### 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.]

9.
Charlie and Jeff are picking up trash along the highway. Together they have picked up $\frac{10}{11}$ of the trash. Jeff has picked up $\frac{9}{22}$ of the trash. Find the fraction of trash picked up by Charlie.
 a. $\frac{1}{2}$ b. $\frac{9}{22}$ c. $\frac{1}{4}$ d. $\frac{9}{11}$

#### 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.

10.
A survey taken reported that $\frac{9}{19}$th of the population listened to the President's speech. If the margin for error is plus or minus $\frac{4}{38}$, then what are the maximum and minimum values for the actual number of people who listened the speech?
 a. $\frac{3}{5}$ and $\frac{5}{13}$ b. $\frac{23}{39}$ and $\frac{5}{13}$ c. $\frac{11}{19}$ and $\frac{7}{19}$ 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

= 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.