Examples with solutions for Addition of Fractions: Using fractions

Exercise #1

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 #2

x(13+12)= x(\frac{1}{3}+\frac{1}{2})=

Video Solution

Answer

56x \frac{5}{6}x

Exercise #3

(13+911)×33= (\frac{1}{3}+\frac{9}{11})\times33=

Video Solution

Answer

38 38

Exercise #4

(13+512)×24= (\frac{1}{3}+\frac{5}{12})\times24=

Video Solution

Answer

18 18

Exercise #5

9(13+14)= 9(\frac{1}{3}+\frac{1}{4})=

Video Solution

Answer

514 5\frac{1}{4}

Exercise #6

3+(12)+(38)+58= -3+(-\frac{1}{2})+(\frac{3}{8})+\frac{5}{8}=

Video Solution

Answer

52 -\frac{5}{2}

Exercise #7

12+34+15+(45)= -\frac{1}{2}+\frac{3}{4}+-\frac{1}{5}+(-\frac{4}{5})=

Video Solution

Answer

34 -\frac{3}{4}

Exercise #8

49+5+(2)+59= -\frac{4}{9}+5+(-2)+\frac{5}{9}=

Video Solution

Answer

289 \frac{28}{9}

Exercise #9

5+12+10+(34)= -5+-\frac{1}{2}+10+(-\frac{3}{4})=

Video Solution

Answer

154 \frac{15}{4}

Exercise #10

38(58)(12)= -\frac{3}{8}-(-\frac{5}{8})-(-\frac{1}{2})=

Video Solution

Answer

34 \frac{3}{4}

Exercise #11

147+(3)12(14)= -\frac{14}{7}+(-3)-\frac{1}{2}-(-\frac{1}{4})=

Video Solution

Answer

214 -\frac{21}{4}

Exercise #12

Solve:

416(38)+28+(14)= -\frac{4}{16}-(-\frac{3}{8})+\frac{2}{8}+(-\frac{1}{4})=

Video Solution

Answer

18 \frac{1}{8}

Exercise #13

(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}