Math worksheet with ten fraction operations problems for practice.

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

1. $\frac{2}{11} + \frac{1}{17} + \frac{2}{3}$
* Find a common denominator for 11, 17, and 3. Since they are all prime numbers, multiply them: $11 \times 17 \times 3 = 561$.
* Convert fractions:
* $\frac{2 \times 51}{561} = \frac{102}{561}$
* $\frac{1 \times 33}{561} = \frac{33}{561}$
* $\frac{2 \times 187}{561} = \frac{374}{561}$
* Add numerators: $102 + 33 + 374 = 509$.
* Result: $\frac{509}{561}$ (This cannot be simplified further).

2. $\frac{21}{5} + \frac{11}{6} - \frac{5}{2}$
* Common denominator for 5, 6, and 2 is 30.
* Convert fractions:
* $\frac{21 \times 6}{30} = \frac{126}{30}$
* $\frac{11 \times 5}{30} = \frac{55}{30}$
* $\frac{5 \times 15}{30} = \frac{75}{30}$
* Calculate: $126 + 55 - 75 = 106$.
* Result: $\frac{106}{30}$. Simplify by dividing top and bottom by 2: $\frac{53}{15}$.

3. $\frac{28}{17} \times \frac{6}{19} \div \frac{3}{4}$
* Change division to multiplication by flipping the last fraction: $\frac{28}{17} \times \frac{6}{19} \times \frac{4}{3}$.
* Simplify before multiplying: The 6 on top and 3 on bottom cancel out ($6 \div 3 = 2$).
* New equation: $\frac{28}{17} \times \frac{2}{19} \times \frac{4}{1}$.
* Multiply tops: $28 \times 2 \times 4 = 224$.
* Multiply bottoms: $17 \times 19 \times 1 = 323$.
* Result: $\frac{224}{323}$.

4. $\frac{12}{5} - \frac{18}{17} + \frac{1}{2}$
* Common denominator for 5, 17, and 2 is $5 \times 17 \times 2 = 170$.
* Convert fractions:
* $\frac{12 \times 34}{170} = \frac{408}{170}$
* $\frac{18 \times 10}{170} = \frac{180}{170}$
* $\frac{1 \times 85}{170} = \frac{85}{170}$
* Calculate: $408 - 180 + 85 = 313$.
* Result: $\frac{313}{170}$.

5. $\frac{31}{12} + \frac{1}{2} + \frac{7}{3}$
* Common denominator for 12, 2, and 3 is 12.
* Convert fractions:
* $\frac{31}{12}$ stays same.
* $\frac{1 \times 6}{12} = \frac{6}{12}$
* $\frac{7 \times 4}{12} = \frac{28}{12}$
* Add numerators: $31 + 6 + 28 = 65$.
* Result: $\frac{65}{12}$.

6. $\frac{6}{5} \div \frac{5}{6} \times \frac{7}{16}$
* Flip the divided fraction: $\frac{6}{5} \times \frac{6}{5} \times \frac{7}{16}$.
* Simplify: The two 6s on top make 36. We can divide 36 and 16 by 4.
* $36 \div 4 = 9$
* $16 \div 4 = 4$
* New equation: $\frac{9}{5} \times \frac{1}{5} \times \frac{7}{4}$.
* Multiply tops: $9 \times 1 \times 7 = 63$.
* Multiply bottoms: $5 \times 5 \times 4 = 100$.
* Result: $\frac{63}{100}$.

7. $\frac{16}{3} - \frac{4}{3} - \frac{7}{6}$
* First part has same denominator: $\frac{16 - 4}{3} = \frac{12}{3} = 4$.
* Now subtract the last part: $4 - \frac{7}{6}$.
* Turn 4 into a fraction with denominator 6: $\frac{24}{6}$.
* Calculate: $\frac{24}{6} - \frac{7}{6} = \frac{17}{6}$.
* Result: $\frac{17}{6}$.

8. $\frac{7}{3} \div \frac{3}{4} \times \frac{26}{17}$
* Flip the divided fraction: $\frac{7}{3} \times \frac{4}{3} \times \frac{26}{17}$.
* Multiply tops: $7 \times 4 \times 26 = 728$.
* Multiply bottoms: $3 \times 3 \times 17 = 153$.
* Result: $\frac{728}{153}$.

9. $\frac{46}{9} - \frac{28}{11} + \frac{7}{6}$
* Common denominator for 9, 11, and 6.
* Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99...
* 99 is divisible by 9. Is it divisible by 6? No.
* Next multiple: $11 \times 18 = 198$.
* 198 is divisible by 9 ($22 \times 9$) and 6 ($33 \times 6$). So, LCD is 198.
* Convert fractions:
* $\frac{46 \times 22}{198} = \frac{1012}{198}$
* $\frac{28 \times 18}{198} = \frac{504}{198}$
* $\frac{7 \times 33}{198} = \frac{231}{198}$
* Calculate: $1012 - 504 + 231 = 739$.
* Result: $\frac{739}{198}$.

10. $\frac{5}{3} \times \frac{5}{4} \div \frac{5}{2}$
* Flip the divided fraction: $\frac{5}{3} \times \frac{5}{4} \times \frac{2}{5}$.
* Simplify: There is a 5 on top and a 5 on bottom. They cancel out.
* Also, there is a 2 on top and a 4 on bottom. $2 \div 2 = 1$ and $4 \div 2 = 2$.
* Remaining numbers: Top is $5 \times 1 = 5$. Bottom is $3 \times 2 = 6$.
* Result: $\frac{5}{6}$.

Final Answer:
1. 509/561
2. 53/15
3. 224/323
4. 313/170
5. 65/12
6. 63/100
7. 17/6
8. 728/153
9. 739/198
10. 5/6