Math worksheet for practicing adding and subtracting two fractions, featuring ten problems with varying denominators.

Here are the step-by-step solutions for each problem on the worksheet.

1. $\frac{8}{6} - \frac{2}{19}$
* First, find a common denominator for 6 and 19. Since they don't share factors, multiply them: $6 \times 19 = 114$.
* Convert the fractions:
* $\frac{8 \times 19}{6 \times 19} = \frac{152}{114}$
* $\frac{2 \times 6}{19 \times 6} = \frac{12}{114}$
* Subtract the numerators: $152 - 12 = 140$.
* Result: $\frac{140}{114}$.
* Simplify by dividing top and bottom by 2: $\frac{70}{57}$.

2. $\frac{14}{3} - \frac{1}{8}$
* Common denominator for 3 and 8 is 24 ($3 \times 8$).
* Convert the fractions:
* $\frac{14 \times 8}{3 \times 8} = \frac{112}{24}$
* $\frac{1 \times 3}{8 \times 3} = \frac{3}{24}$
* Subtract: $112 - 3 = 109$.
* Result: $\frac{109}{24}$ (This cannot be simplified further).

3. $\frac{38}{9} - \frac{6}{11}$
* Common denominator for 9 and 11 is 99 ($9 \times 11$).
* Convert the fractions:
* $\frac{38 \times 11}{9 \times 11} = \frac{418}{99}$
* $\frac{6 \times 9}{11 \times 9} = \frac{54}{99}$
* Subtract: $418 - 54 = 364$.
* Result: $\frac{364}{99}$ (This cannot be simplified further).

4. $\frac{12}{5} - \frac{5}{8}$
* Common denominator for 5 and 8 is 40 ($5 \times 8$).
* Convert the fractions:
* $\frac{12 \times 8}{5 \times 8} = \frac{96}{40}$
* $\frac{5 \times 5}{8 \times 5} = \frac{25}{40}$
* Subtract: $96 - 25 = 71$.
* Result: $\frac{71}{40}$ (This cannot be simplified further).

5. $\frac{41}{9} - \frac{2}{5}$
* Common denominator for 9 and 5 is 45 ($9 \times 5$).
* Convert the fractions:
* $\frac{41 \times 5}{9 \times 5} = \frac{205}{45}$
* $\frac{2 \times 9}{5 \times 9} = \frac{18}{45}$
* Subtract: $205 - 18 = 187$.
* Result: $\frac{187}{45}$ (This cannot be simplified further).

6. $\frac{37}{8} + \frac{10}{17}$
* Common denominator for 8 and 17 is 136 ($8 \times 17$).
* Convert the fractions:
* $\frac{37 \times 17}{8 \times 17} = \frac{629}{136}$
* $\frac{10 \times 8}{17 \times 8} = \frac{80}{136}$
* Add: $629 + 80 = 709$.
* Result: $\frac{709}{136}$ (This cannot be simplified further).

7. $\frac{44}{8} + \frac{1}{11}$
* *Tip:* You can simplify $\frac{44}{8}$ first to $\frac{11}{2}$, but let's stick to the standard method to be safe.
* Common denominator for 8 and 11 is 88 ($8 \times 11$).
* Convert the fractions:
* $\frac{44 \times 11}{8 \times 11} = \frac{484}{88}$
* $\frac{1 \times 8}{11 \times 8} = \frac{8}{88}$
* Add: $484 + 8 = 492$.
* Result: $\frac{492}{88}$.
* Simplify: Both are divisible by 4.
* $492 \div 4 = 123$
* $88 \div 4 = 22$
* Final Result: $\frac{123}{22}$.

8. $\frac{5}{3} + \frac{18}{20}$
* *Tip:* Simplify $\frac{18}{20}$ to $\frac{9}{10}$ first. It makes the numbers smaller.
* New problem: $\frac{5}{3} + \frac{9}{10}$.
* Common denominator for 3 and 10 is 30.
* Convert the fractions:
* $\frac{5 \times 10}{3 \times 10} = \frac{50}{30}$
* $\frac{9 \times 3}{10 \times 3} = \frac{27}{30}$
* Add: $50 + 27 = 77$.
* Result: $\frac{77}{30}$ (This cannot be simplified further).

9. $\frac{3}{2} + \frac{5}{17}$
* Common denominator for 2 and 17 is 34 ($2 \times 17$).
* Convert the fractions:
* $\frac{3 \times 17}{2 \times 17} = \frac{51}{34}$
* $\frac{5 \times 2}{17 \times 2} = \frac{10}{34}$
* Add: $51 + 10 = 61$.
* Result: $\frac{61}{34}$ (This cannot be simplified further).

10. $\frac{17}{3} + \frac{4}{14}$
* *Tip:* Simplify $\frac{4}{14}$ to $\frac{2}{7}$ first.
* New problem: $\frac{17}{3} + \frac{2}{7}$.
* Common denominator for 3 and 7 is 21.
* Convert the fractions:
* $\frac{17 \times 7}{3 \times 7} = \frac{119}{21}$
* $\frac{2 \times 3}{7 \times 3} = \frac{6}{21}$
* Add: $119 + 6 = 125$.
* Result: $\frac{125}{21}$ (This cannot be simplified further).

Final Answer:
1. $\frac{70}{57}$
2. $\frac{109}{24}$
3. $\frac{364}{99}$
4. $\frac{71}{40}$
5. $\frac{187}{45}$
6. $\frac{709}{136}$
7. $\frac{123}{22}$
8. $\frac{77}{30}$
9. $\frac{61}{34}$
10. $\frac{125}{21}$