# Subtracting Fractions with Unlike Denominators Worksheet

Subtracting Fractions with Unlike Denominators Worksheet
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1.
Simplify the expression: $\frac{2}{5}$ - $\frac{1}{10}$
 a. $\frac{7}{10}$ b. $\frac{3}{10}$ c. $\frac{3}{5}$ d. $\frac{1}{25}$

#### Solution:

2 / 5 - 1 / 10
[Original expression.]

The denominators in the two fractions are not the same. So, change the fraction 2 / 5 to a fraction whose denominator is 10

= 2 × 25 × 2 - 1 / 10
[Multiply the fraction 2 / 5 by 2 / 2.]

= 4 - 110
[Subtract the numerators.]

= 3 / 10

2.
Simplify the expression: $\frac{9}{10}$ - $\frac{1}{2}$
 a. $\frac{3}{5}$ b. $\frac{2}{5}$ c. $\frac{4}{5}$ d. $\frac{1}{5}$

#### Solution:

9 / 10 - 1 / 2
[Original expression.]

The denominator of the two fractions are not the same. So, we change the fraction 1 / 2 to a fraction whose denominator is 10.

= 9 / 10 - 1 × 52 × 5
[Multiply the fraction 1 / 2 by 5 / 5.]

= 9 / 10 - 5 / 10
[Simplify.]

= 9 - 510 = 4 / 10
[Subtract the numerators.]

= 2 / 5
[Simplify.]

3.
Simplify the expression: $\frac{2}{5}$ - $\frac{1}{10}$
 a. $\frac{3}{5}$ b. $\frac{1}{25}$ c. $\frac{7}{10}$ d. $\frac{3}{10}$

#### Solution:

2 / 5 - 1 / 10
[Original expression.]

The denominators in the two fractions are not the same. So, change the fraction 2 / 5 to a fraction whose denominator is 10.

= 2 × 25 × 2 - 1 / 10
[Multiply the fraction 2 / 5 by 2 / 2.]

= 4 - 110
[Subtract the numerators.]

= 3 / 10

4.
Simplify the expression: $\frac{9}{10}$ - $\frac{1}{2}$
 a. $\frac{1}{5}$ b. $\frac{2}{5}$ c. $\frac{3}{5}$ d. $\frac{4}{5}$

#### Solution:

9 / 10 - 1 / 2
[Original expression.]

The denominator of the two fractions are not the same. So, we change the fraction 1 / 2 to a fraction whose denominator is 10.

= 9 / 10 - 1 × 52 × 5
[Multiply the fraction 1 / 2 by 5 / 5.]

= 9 / 10 - 5 / 10
[Simplify.]

= 9 - 510 = 4 / 10
[Subtract the numerators.]

= 2 / 5
[Simplify.]

5.
Charles and Ed together ate $\frac{5}{6}$ of a cake. If Charles ate $\frac{5}{11}$ of the cake, then how much did Ed eat?
 a. $\frac{5}{6}$ b. $\frac{5}{16}$ c. $\frac{10}{11}$ d. $\frac{25}{66}$

#### Solution:

The fraction of cake Ed ate = the difference between the fractions of cake they ate = 5 / 6 - 5 / 11

= 5566 - 3066
[Write equivalent fractions using the LCD, 66.]

= (55 - 30)66
[Since denominators are same, subtract numerators.]

= 2566

Ed ate 25 / 66 of the cake.

6.
Subtract:
$\frac{12}{5}$
- $\frac{7}{3}$
........
 a. $\frac{1}{15}$ b. 15 c. $\frac{5}{3}$ d. $\frac{3}{5}$

#### Solution:

To subtract unlike fractions, we must first convert them into like fractions.

Least Common Multiple of 5 and 3 is 15.

The equivalents of 12 / 5 and 7 / 3 with denominator 15 are 36 / 15 and 35 / 15.

7.
Simplify: $\frac{11}{5}$ - $\frac{1}{3}$
 a. $\frac{28}{15}$ b. $\frac{13}{15}$ c. $\frac{15}{28}$ d. $\frac{13}{28}$

#### Solution:

To subtract unlike fractions, we must first convert them into like fractions.

Least Common Multiple of 5 and 3 is 15.

The equivalents of 11 / 5 and 1 / 3 with denominator 15 are 33 / 15 and 5 / 15.

11 / 5 - 1 / 3 = 33 / 15 - 5 / 15

= 33-515 = 2815
[Group the numerators and subtract.]

8.
Simplify: $\frac{5}{4}$ - $\frac{1}{3}$
 a. $\frac{11}{12}$ b. $\frac{12}{11}$ c. $\frac{1}{12}$ d. $\frac{1}{11}$

#### Solution:

To subtract unlike fractions, we must first convert them into like fractions.

Least Common Multiple of 4 and 3 is 12.

The equivalents of 5 / 4 and 1 / 3 with denominator 12 are 15 / 12 and 4 / 12.

5 / 4 - 1 / 3 = 15 / 12 - 4 / 12

= (15-4)12 = 1112
[Group the numerators and subtract.]

9.
It takes $\frac{1}{2}$ hour on foot and $\frac{1}{4}$ hour on a bicycle for Tim to reach his home. How much time does Tim save by going on his bicycle?
 a. 25 minutes b. 15 minutes c. 20 minutes d. 10 minutes

#### Solution:

Time taken by Tim to reach his home on foot = 1 / 2 hour

Time taken by Tim to reach his home on bicycle = 1 / 4 hour

Time saved = 1 / 2 - 1 / 4
[time taken to reach his home on foot - time taken to reach his home on bicycle.]

12 hour = 30 minutes
[1 hour = 60 minutes, 1 / 2 hour = 60 / 2= 30 minutes.]

14 hour = 15 minutes
[1 hour = 60 minutes, 1 / 4 hour = 60 / 4 = 15 minutes.]

Time saved = 30 minutes - 15 minutes = 15 minutes
[Subtract.]

Tim saves 15 minutes by going on a bicycle.

10.
Subtract the fraction $\frac{7}{9}$ from the fraction $\frac{5}{3}$.
 a. $\frac{9}{10}$ b. 1 c. $\frac{9}{11}$ d. $\frac{8}{9}$

#### Solution:

5 / 3 - 7 / 9
[Original expression.]

The denominators in the two fractions are not the same. So, we change the fraction 5 / 3 to a fraction whose denominator is 9.

= 5 × 33 × 3 - 7 / 9
[Multiply the fraction 5 / 3 by 3 / 3.]

15 - 79
[Subtract the numerators.]

= 89
[Simplify by dividing numerator and denominator with 3.]