﻿ Subtracting Fractions with Unlike Denominators Worksheet | Problems & Solutions 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.]