Examples with solutions for Addition of Fractions: More than two fractions

Exercise #1

Solve the following exercise:

310+15+410=? \frac{3}{10}+\frac{1}{5}+\frac{4}{10}=\text{?}

Video Solution

Step-by-Step Solution

When we have a fraction addition exercise with more than one fraction, we make sure all the denominators of the fractions are identical.

Let's find the common denominator of the fractions' denominators: 10 10 and 5 5

The common denominator is 10 10 .

Now we'll multiply both numerator and denominator of the fraction 15 \frac{1}{5} by 2 2 and create a fraction addition exercise where all denominators are 10 10 :

310+1×25×2+410=310+210+410 \frac{3}{10}+\frac{1\times2}{5\times2}+\frac{4}{10}=\frac{3}{10}+\frac{2}{10}+\frac{4}{10}

Finally, we'll add all the numerators of the fractions:

310+210+410=3+2+410=910 \frac{3}{10}+\frac{2}{10}+\frac{4}{10}=\frac{3+2+4}{10}=\frac{9}{10}

Answer

910 \frac{9}{10}

Exercise #2

56x+78x+24x= \frac{5}{6}x+\frac{7}{8}x+\frac{2}{4}x=

Video Solution

Step-by-Step Solution

First, let's find a common denominator for 4, 8, and 6: it's 24.

Now, we'll multiply each fraction by the appropriate number to get:

5×46×4x+7×38×3x+2×64×6x= \frac{5\times4}{6\times4}x+\frac{7\times3}{8\times3}x+\frac{2\times6}{4\times6}x=

Let's solve the multiplication exercises in the numerator and denominator:

2024x+2124x+1224x= \frac{20}{24}x+\frac{21}{24}x+\frac{12}{24}x=

We'll connect all the numerators:

20+21+1224x=41+1224x=5324x \frac{20+21+12}{24}x=\frac{41+12}{24}x=\frac{53}{24}x

Let's break down the numerator into a smaller addition exercise:

48+524=4824+524=2+524=2524x \frac{48+5}{24}=\frac{48}{24}+\frac{5}{24}=2+\frac{5}{24}=2\frac{5}{24}x

Answer

2524x 2\frac{5}{24}x

Exercise #3

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 #4

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 #5

25+16+430= \frac{2}{5}+\frac{1}{6}+\frac{4}{30}=

Video Solution

Answer

2130 \frac{21}{30}

Exercise #6

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

Video Solution

Answer

32 \frac{3}{2}

Exercise #7

310+15+46= \frac{3}{10}+\frac{1}{5}+\frac{4}{6}=

Video Solution

Answer

76 \frac{7}{6}

Exercise #8

12+34+68= \frac{1}{2}+\frac{3}{4}+\frac{6}{8}=

Video Solution

Answer

2 2

Exercise #9

35+13+215= \frac{3}{5}+\frac{1}{3}+\frac{2}{15}=

Video Solution

Answer

1615 \frac{16}{15}

Exercise #10

Solve the following exercise:

412+13+16=? \frac{4}{12}+\frac{1}{3}+\frac{1}{6}=\text{?}

Video Solution

Answer

1012 \frac{10}{12}

Exercise #11

Solve the following exercise:

15+310+25=? \frac{1}{5}+\frac{3}{10}+\frac{2}{5}=\text{?}

Video Solution

Answer

910 \frac{9}{10}

Exercise #12

Solve the following exercise:

16+13+212=? \frac{1}{6}+\frac{1}{3}+\frac{2}{12}=\text{?}

Video Solution

Answer

812 \frac{8}{12}

Exercise #13

Solve the following exercise:

12+18+14=? \frac{1}{2}+\frac{1}{8}+\frac{1}{4}=\text{?}

Video Solution

Answer

78 \frac{7}{8}

Exercise #14

Solve the following exercise:

15+315+13=? \frac{1}{5}+\frac{3}{15}+\frac{1}{3}=\text{?}

Video Solution

Answer

1115 \frac{11}{15}

Exercise #15

Solve the following exercise:

12+16+312=? \frac{1}{2}+\frac{1}{6}+\frac{3}{12}=\text{?}

Video Solution

Answer

1112 \frac{11}{12}

Exercise #16

Solve the following exercise:

26+14+212=? \frac{2}{6}+\frac{1}{4}+\frac{2}{12}=\text{?}

Video Solution

Answer

912 \frac{9}{12}

Exercise #17

37+514+13= \frac{3}{7}+\frac{5}{14}+\frac{1}{3}=

Video Solution

Answer

4742 \frac{47}{42}

Exercise #18

12+34+25= \frac{1}{2}+\frac{3}{4}+\frac{2}{5}=

Video Solution

Answer

3320 \frac{33}{20}

Exercise #19

23+14+56+112= \frac{2}{3}+\frac{1}{4}+\frac{5}{6}+\frac{1}{12}=

Video Solution

Answer

116 \frac{11}{6}