Fraction addition and subtraction worksheet for practice.

Here are the step-by-step solutions for each problem. Remember to find a common denominator when adding or subtracting fractions with different bottom numbers.

1) $(-\frac{5}{6}) - (-\frac{7}{8}) - (-\frac{4}{6})$
* Simplify signs: $-\frac{5}{6} + \frac{7}{8} + \frac{4}{6}$
* Combine the sixths: $-\frac{5}{6} + \frac{4}{6} = -\frac{1}{6}$
* Now solve: $-\frac{1}{6} + \frac{7}{8}$
* Common denominator for 6 and 8 is 24.
* $-\frac{1}{6} = -\frac{4}{24}$ and $\frac{7}{8} = \frac{21}{24}$
* $-\frac{4}{24} + \frac{21}{24} = \frac{17}{24}$

2) $\frac{8}{2} - \frac{3}{5}$
* Simplify $\frac{8}{2}$ to $4$.
* Problem becomes: $4 - \frac{3}{5}$
* Turn 4 into a fraction with denominator 5: $\frac{20}{5}$
* $\frac{20}{5} - \frac{3}{5} = \frac{17}{5}$

3) $\frac{9}{4} - (-\frac{7}{8})$
* Simplify signs: $\frac{9}{4} + \frac{7}{8}$
* Common denominator is 8. Convert $\frac{9}{4}$ to $\frac{18}{8}$.
* $\frac{18}{8} + \frac{7}{8} = \frac{25}{8}$

4) $(-\frac{4}{3}) + \frac{6}{7} + (-\frac{8}{3})$
* Group the thirds together: $-\frac{4}{3} - \frac{8}{3} = -\frac{12}{3}$
* Simplify $-\frac{12}{3}$ to $-4$.
* Now add the seventh: $-4 + \frac{6}{7}$
* Turn -4 into a fraction with denominator 7: $-\frac{28}{7}$
* $-\frac{28}{7} + \frac{6}{7} = -\frac{22}{7}$

5) $\frac{9}{7} + (-\frac{6}{3})$
* Simplify $-\frac{6}{3}$ to $-2$.
* Problem becomes: $\frac{9}{7} - 2$
* Turn 2 into a fraction with denominator 7: $\frac{14}{7}$
* $\frac{9}{7} - \frac{14}{7} = -\frac{5}{7}$

6) $(-\frac{2}{8}) + \frac{7}{4} + (-\frac{9}{8})$
* Group the eighths: $-\frac{2}{8} - \frac{9}{8} = -\frac{11}{8}$
* Now add the fourth: $-\frac{11}{8} + \frac{7}{4}$
* Convert $\frac{7}{4}$ to eighths: $\frac{14}{8}$
* $-\frac{11}{8} + \frac{14}{8} = \frac{3}{8}$

7) $\frac{8}{2} + (-\frac{6}{4})$
* Simplify $\frac{8}{2}$ to $4$.
* Simplify $-\frac{6}{4}$ to $-\frac{3}{2}$.
* Problem becomes: $4 - \frac{3}{2}$
* Turn 4 into halves: $\frac{8}{2}$
* $\frac{8}{2} - \frac{3}{2} = \frac{5}{2}$

8) $(-\frac{7}{3}) + (-\frac{6}{5}) + \frac{4}{3}$
* Group the thirds: $-\frac{7}{3} + \frac{4}{3} = -\frac{3}{3}$
* Simplify $-\frac{3}{3}$ to $-1$.
* Now subtract the fifth: $-1 - \frac{6}{5}$
* Turn -1 into fifths: $-\frac{5}{5}$
* $-\frac{5}{5} - \frac{6}{5} = -\frac{11}{5}$

9) $\frac{3}{4} - \frac{7}{2} - (-\frac{9}{4})$
* Simplify signs: $\frac{3}{4} - \frac{7}{2} + \frac{9}{4}$
* Group the fourths: $\frac{3}{4} + \frac{9}{4} = \frac{12}{4}$
* Simplify $\frac{12}{4}$ to $3$.
* Now subtract the half: $3 - \frac{7}{2}$
* Turn 3 into halves: $\frac{6}{2}$
* $\frac{6}{2} - \frac{7}{2} = -\frac{1}{2}$

10) $\frac{7}{5} + \frac{2}{9}$
* Common denominator for 5 and 9 is 45.
* $\frac{7 \times 9}{45} + \frac{2 \times 5}{45}$
* $\frac{63}{45} + \frac{10}{45} = \frac{73}{45}$

11) $(-\frac{7}{6}) + (-\frac{8}{3}) + (-\frac{4}{6})$
* Group the sixths: $-\frac{7}{6} - \frac{4}{6} = -\frac{11}{6}$
* Now add the third: $-\frac{11}{6} - \frac{8}{3}$
* Convert $\frac{8}{3}$ to sixths: $\frac{16}{6}$
* $-\frac{11}{6} - \frac{16}{6} = -\frac{27}{6}$
* Simplify by dividing top and bottom by 3: $-\frac{9}{2}$

12) $\frac{7}{3} - (-\frac{8}{9}) - (-\frac{2}{3})$
* Simplify signs: $\frac{7}{3} + \frac{8}{9} + \frac{2}{3}$
* Group the thirds: $\frac{7}{3} + \frac{2}{3} = \frac{9}{3}$
* Simplify $\frac{9}{3}$ to $3$.
* Now add the ninth: $3 + \frac{8}{9}$
* Turn 3 into ninths: $\frac{27}{9}$
* $\frac{27}{9} + \frac{8}{9} = \frac{35}{9}$

13) $(-\frac{7}{8}) + (-\frac{9}{6})$
* Simplify $-\frac{9}{6}$ to $-\frac{3}{2}$.
* Problem becomes: $-\frac{7}{8} - \frac{3}{2}$
* Convert $\frac{3}{2}$ to eighths: $\frac{12}{8}$
* $-\frac{7}{8} - \frac{12}{8} = -\frac{19}{8}$

14) $(-\frac{5}{8}) - \frac{9}{2} - \frac{3}{8}$
* Group the eighths: $-\frac{5}{8} - \frac{3}{8} = -\frac{8}{8}$
* Simplify $-\frac{8}{8}$ to $-1$.
* Now subtract the half: $-1 - \frac{9}{2}$
* Turn -1 into halves: $-\frac{2}{2}$
* $-\frac{2}{2} - \frac{9}{2} = -\frac{11}{2}$

Final Answer:
1) 17/24
2) 17/5
3) 25/8
4) -22/7
5) -5/7
6) 3/8
7) 5/2
8) -11/5
9) -1/2
10) 73/45
11) -9/2
12) 35/9
13) -19/8
14) -11/2