Addition of Fractions: In combination with other operations

Using fractionsMultiplication of signed numbersNumber of termsWorded problemsOne of the denominators is the common denominator in visual displayMore than two fractionsComplete the missing numbersVisual display of fractions with like denominatorsFractions with common denominatorsThe common denominator is smaller than the product of the denominatorsFinding a Common Denominator by Multiplying the DenominatorsOne of the denominators is the common denominator
Question 1

\( \frac{2}{3}+\frac{2}{15}-\frac{4}{5}= \)

Question 2

\( \frac{1}{3}+\frac{7}{15}-\frac{2}{5}= \)

Question 3

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

Question 4

\( \frac{3}{5}+\frac{1}{5}-\frac{3}{15}= \)

Question 5

\( \frac{3}{5}-\frac{1}{5}+\frac{3}{15}= \)

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

Exercise #1

23+215−45= \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+2×115×1−4×35×3=1015+215−1215 \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+2−1215=12−1215=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+715−25= \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+7×115×1−2×35×3=515+715−615 \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+7−615=12−615=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

(14+74−54−14)⋅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 #4

35+15−315= \frac{3}{5}+\frac{1}{5}-\frac{3}{15}=

Video Solution

Answer

35 \frac{3}{5}

Exercise #5

35−15+315= \frac{3}{5}-\frac{1}{5}+\frac{3}{15}=

Video Solution

Answer

35 \frac{3}{5}

Question 1

\( \frac{3}{6}-\frac{2}{4}+\frac{1}{12}= \)

Question 2

\( \frac{3}{6}+\frac{2}{4}-\frac{1}{12}= \)

Question 3

\( \frac{1}{4}-\frac{3}{4}+\frac{1}{2}+\frac{5}{10}= \)

Question 4

Solve the following exercise:

\( \frac{6}{7}-\frac{1}{2}+\frac{3}{14}=\text{?} \)

Question 5

Solve the following exercise:

\( \frac{2}{7}+\frac{1}{2}-\frac{7}{14}=\text{?} \)

Exercise #6

36−24+112= \frac{3}{6}-\frac{2}{4}+\frac{1}{12}=

Video Solution

Answer

112 \frac{1}{12}

Exercise #7

36+24−112= \frac{3}{6}+\frac{2}{4}-\frac{1}{12}=

Video Solution

Answer

1112 \frac{11}{12}

Exercise #8

14−34+12+510= \frac{1}{4}-\frac{3}{4}+\frac{1}{2}+\frac{5}{10}=

Video Solution

Answer

12 \frac{1}{2}

Exercise #9

Solve the following exercise:

67−12+314=? \frac{6}{7}-\frac{1}{2}+\frac{3}{14}=\text{?}

Video Solution

Answer

814 \frac{8}{14}

Exercise #10

Solve the following exercise:

27+12−714=? \frac{2}{7}+\frac{1}{2}-\frac{7}{14}=\text{?}

Video Solution

Answer

414 \frac{4}{14}

Question 1

Solve the following exercise:

\( \frac{2}{5}+\frac{1}{2}-\frac{1}{3}=\text{?} \)

Question 2

Solve the following exercise:

\( \frac{9}{10}-\frac{4}{5}+\frac{1}{2}=\text{?} \)

Question 3

Solve the following exercise:

\( \frac{4}{10}+\frac{1}{5}-\frac{1}{2}=\text{?} \)

Question 4

Solve the following exercise:

\( \frac{3}{8}+\frac{1}{2}-\frac{1}{4}=\text{?} \)

Question 5

\( \frac{1}{4}+\frac{3}{4}+\frac{3}{20}-\frac{5}{10}= \)

Exercise #11

Solve the following exercise:

25+12−13=? \frac{2}{5}+\frac{1}{2}-\frac{1}{3}=\text{?}

Video Solution

Answer

1730 \frac{17}{30}

Exercise #12

Solve the following exercise:

910−45+12=? \frac{9}{10}-\frac{4}{5}+\frac{1}{2}=\text{?}

Video Solution

Answer

610 \frac{6}{10}

Exercise #13

Solve the following exercise:

410+15−12=? \frac{4}{10}+\frac{1}{5}-\frac{1}{2}=\text{?}

Video Solution

Answer

110 \frac{1}{10}

Exercise #14

Solve the following exercise:

38+12−14=? \frac{3}{8}+\frac{1}{2}-\frac{1}{4}=\text{?}

Video Solution

Answer

58 \frac{5}{8}

Exercise #15

14+34+320−510= \frac{1}{4}+\frac{3}{4}+\frac{3}{20}-\frac{5}{10}=

Video Solution

Answer

1320 \frac{13}{20}

Question 1

\( \frac{1}{4}-\frac{3}{4}+\frac{1}{2}-\frac{5}{10}= \)

Exercise #16

14−34+12−510= \frac{1}{4}-\frac{3}{4}+\frac{1}{2}-\frac{5}{10}=

Video Solution

Answer

−12 -\frac{1}{2}