Examples with solutions for Subtraction of Fractions: In combination with other operations

Exercise #1

23+21545= \frac{2}{3}+\frac{2}{15}-\frac{4}{5}=

Video Solution

Step-by-Step Solution

Let's try to find the lowest common denominator between 3, 15, and 5

To find the lowest common denominator, we need to find a number that is divisible by 3, 15, and 5

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 5

We'll multiply the second fraction by 1

We'll multiply the third fraction by 3

2×53×5+2×115×14×35×3=1015+2151215 \frac{2\times5}{3\times5}+\frac{2\times1}{15\times1}-\frac{4\times3}{5\times3}=\frac{10}{15}+\frac{2}{15}-\frac{12}{15}

Now we'll add and then subtract:

10+21215=121215=015 \frac{10+2-12}{15}=\frac{12-12}{15}=\frac{0}{15}

We'll divide both the numerator and denominator by 0 and get:

015=0 \frac{0}{15}=0

Answer

0 0

Exercise #2

13+71525= \frac{1}{3}+\frac{7}{15}-\frac{2}{5}=

Video Solution

Step-by-Step Solution

Let's try to find the lowest common denominator between 3, 15, and 5

To find the lowest common denominator, we need to find a number that is divisible by 3, 15, and 5

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 5

We'll multiply the second fraction by 1

We'll multiply the third fraction by 3

1×53×5+7×115×12×35×3=515+715615 \frac{1\times5}{3\times5}+\frac{7\times1}{15\times1}-\frac{2\times3}{5\times3}=\frac{5}{15}+\frac{7}{15}-\frac{6}{15}

Now we'll add and then subtract:

5+7615=12615=615 \frac{5+7-6}{15}=\frac{12-6}{15}=\frac{6}{15}

We'll divide both numerator and denominator by 3 and get:

6:315:3=25 \frac{6:3}{15:3}=\frac{2}{5}

Answer

25 \frac{2}{5}

Exercise #3

13(9234)= \frac{1}{3}(\frac{9}{2}-\frac{3}{4})=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we will first address the expression in parentheses.

The common denominator between the fractions is 4, so we will multiply each numerator by the number needed for its denominator to reach 4.

We will multiply the first fraction's numerator by 2 and the second fraction's numerator by 1:

(9234)=2×91×34=1834=154 (\frac{9}{2}-\frac{3}{4})=\frac{2\times9-1\times3}{4}=\frac{18-3}{4}=\frac{15}{4}

Now we have the expression:

13×154= \frac{1}{3}\times\frac{15}{4}=

Note that we can reduce 15 and 3:

11×54= \frac{1}{1}\times\frac{5}{4}=

Now we multiply numerator by numerator and denominator by denominator:

1×51×4=54=114 \frac{1\times5}{1\times4}=\frac{5}{4}=1\frac{1}{4}

Answer

114 1\frac{1}{4}

Exercise #4

14×(13+12)= \frac{1}{4}\times(\frac{1}{3}+\frac{1}{2})=

Video Solution

Step-by-Step Solution

According to the order of operations, we will first solve the expression in parentheses.

Note that since the denominators are not common, we will look for a number that is both divisible by 2 and 3. That is 6.

We will multiply one-third by 2 and one-half by 3, now we will get the expression:

14×(2+36)= \frac{1}{4}\times(\frac{2+3}{6})=

Let's solve the numerator of the fraction:

14×56= \frac{1}{4}\times\frac{5}{6}=

We will combine the fractions into a multiplication expression:

1×54×6=524 \frac{1\times5}{4\times6}=\frac{5}{24}

Answer

524 \frac{5}{24}

Exercise #5

(14+745414)10:7:5=? (\frac{1}{4}+\frac{7}{4}-\frac{5}{4}-\frac{1}{4})\cdot10:7:5=\text{?}

Video Solution

Answer

17 \frac{1}{7}

Exercise #6

Solve the following exercise:

110+3512=? \frac{1}{10}+\frac{3}{5}-\frac{1}{2}=\text{?}

Video Solution

Answer

15 \frac{1}{5}

Exercise #7

Solve the following exercise:

35+1213=? \frac{3}{5}+\frac{1}{2}-\frac{1}{3}=\text{?}

Video Solution

Answer

1330 \frac{13}{30}

Exercise #8

Solve the following exercise:

4712+414=? \frac{4}{7}-\frac{1}{2}+\frac{4}{14}=\text{?}

Video Solution

Answer

514 \frac{5}{14}

Exercise #9

Solve the following exercise:

111045+12=? \frac{11}{10}-\frac{4}{5}+\frac{1}{2}=\text{?}

Video Solution

Answer

45 \frac{4}{5}

Exercise #10

Solve the following exercise:

27+12714=? \frac{2}{7}+\frac{1}{2}-\frac{7}{14}=\text{?}

Video Solution

Answer

414 \frac{4}{14}

Exercise #11

Solve the following exercise:

58+1214=? \frac{5}{8}+\frac{1}{2}-\frac{1}{4}=\text{?}

Video Solution

Answer

78 \frac{7}{8}

Exercise #12

Solve the following exercise:

341214=? \frac{3}{4}\cdot\frac{1}{2}-\frac{1}{4}=\text{?}

Video Solution

Answer

18 \frac{1}{8}

Exercise #13

Solve the following exercise:

122514=? \frac{1}{2}\cdot\frac{2}{5}-\frac{1}{4}=\text{?}

Video Solution

Answer

110 \frac{1}{10}

Exercise #14

Solve the following exercise:

56121226=? \frac{5}{6}\cdot\frac{1}{2}-\frac{1}{2}\cdot\frac{2}{6}=\text{?}

Video Solution

Answer

14 \frac{1}{4}

Exercise #15

Solve the following exercise:

323512=? \frac{3}{2}\cdot\frac{3}{5}-\frac{1}{2}=\text{?}

Video Solution

Answer

25 \frac{2}{5}