Math worksheet for practicing operations with fractions, featuring 12 problems that include adding, subtracting, multiplying, and dividing fractions.

Let's solve each problem step by step. The problems involve adding, subtracting, multiplying, and dividing fractions. We'll go through each one systematically.

---

Problem 1: $\frac{17}{3} + \frac{3}{17}$

To add these fractions, we need a common denominator. The least common denominator (LCD) of 3 and 17 is $3 \times 17 = 51$.

\[
\frac{17}{3} = \frac{17 \times 17}{3 \times 17} = \frac{289}{51}
\]
\[
\frac{3}{17} = \frac{3 \times 3}{17 \times 3} = \frac{9}{51}
\]

Now add the fractions:

\[
\frac{289}{51} + \frac{9}{51} = \frac{289 + 9}{51} = \frac{298}{51}
\]

So, the answer is:

\[
\boxed{\frac{298}{51}}
\]

---

Problem 2: $\frac{7}{2} + \frac{11}{13}$

The LCD of 2 and 13 is $2 \times 13 = 26$.

\[
\frac{7}{2} = \frac{7 \times 13}{2 \times 13} = \frac{91}{26}
\]
\[
\frac{11}{13} = \frac{11 \times 2}{13 \times 2} = \frac{22}{26}
\]

Now add the fractions:

\[
\frac{91}{26} + \frac{22}{26} = \frac{91 + 22}{26} = \frac{113}{26}
\]

So, the answer is:

\[
\boxed{\frac{113}{26}}
\]

---

Problem 3: $\frac{3}{2} + \frac{20}{3}$

The LCD of 2 and 3 is $2 \times 3 = 6$.

\[
\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}
\]
\[
\frac{20}{3} = \frac{20 \times 2}{3 \times 2} = \frac{40}{6}
\]

Now add the fractions:

\[
\frac{9}{6} + \frac{40}{6} = \frac{9 + 40}{6} = \frac{49}{6}
\]

So, the answer is:

\[
\boxed{\frac{49}{6}}
\]

---

Problem 4: $\frac{13}{14} - \frac{12}{22}$

First, simplify $\frac{12}{22}$:

\[
\frac{12}{22} = \frac{6}{11}
\]

The LCD of 14 and 11 is $14 \times 11 = 154$.

\[
\frac{13}{14} = \frac{13 \times 11}{14 \times 11} = \frac{143}{154}
\]
\[
\frac{6}{11} = \frac{6 \times 14}{11 \times 14} = \frac{84}{154}
\]

Now subtract the fractions:

\[
\frac{143}{154} - \frac{84}{154} = \frac{143 - 84}{154} = \frac{59}{154}
\]

So, the answer is:

\[
\boxed{\frac{59}{154}}
\]

---

Problem 5: $\frac{9}{10} - \frac{3}{15}$

First, simplify $\frac{3}{15}$:

\[
\frac{3}{15} = \frac{1}{5}
\]

The LCD of 10 and 5 is 10.

\[
\frac{9}{10} = \frac{9}{10}
\]
\[
\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}
\]

Now subtract the fractions:

\[
\frac{9}{10} - \frac{2}{10} = \frac{9 - 2}{10} = \frac{7}{10}
\]

So, the answer is:

\[
\boxed{\frac{7}{10}}
\]

---

Problem 6: $\frac{18}{19} - \frac{5}{6}$

The LCD of 19 and 6 is $19 \times 6 = 114$.

\[
\frac{18}{19} = \frac{18 \times 6}{19 \times 6} = \frac{108}{114}
\]
\[
\frac{5}{6} = \frac{5 \times 19}{6 \times 19} = \frac{95}{114}
\]

Now subtract the fractions:

\[
\frac{108}{114} - \frac{95}{114} = \frac{108 - 95}{114} = \frac{13}{114}
\]

So, the answer is:

\[
\boxed{\frac{13}{114}}
\]

---

Problem 7: $\frac{12}{15} \times \frac{6}{20}$

First, simplify the fractions:

\[
\frac{12}{15} = \frac{4}{5}, \quad \frac{6}{20} = \frac{3}{10}
\]

Now multiply the simplified fractions:

\[
\frac{4}{5} \times \frac{3}{10} = \frac{4 \times 3}{5 \times 10} = \frac{12}{50}
\]

Simplify $\frac{12}{50}$:

\[
\frac{12}{50} = \frac{6}{25}
\]

So, the answer is:

\[
\boxed{\frac{6}{25}}
\]

---

Problem 8: $\frac{23}{18} \times \frac{16}{21}$

Multiply the fractions directly:

\[
\frac{23}{18} \times \frac{16}{21} = \frac{23 \times 16}{18 \times 21} = \frac{368}{378}
\]

Simplify $\frac{368}{378}$ by finding the greatest common divisor (GCD) of 368 and 378, which is 2:

\[
\frac{368}{378} = \frac{184}{189}
\]

So, the answer is:

\[
\boxed{\frac{184}{189}}
\]

---

Problem 9: $\frac{9}{14} \times \frac{22}{24}$

First, simplify $\frac{22}{24}$:

\[
\frac{22}{24} = \frac{11}{12}
\]

Now multiply the fractions:

\[
\frac{9}{14} \times \frac{11}{12} = \frac{9 \times 11}{14 \times 12} = \frac{99}{168}
\]

Simplify $\frac{99}{168}$ by finding the GCD of 99 and 168, which is 3:

\[
\frac{99}{168} = \frac{33}{56}
\]

So, the answer is:

\[
\boxed{\frac{33}{56}}
\]

---

Problem 10: $\frac{26}{52} \div \frac{12}{13}$

First, simplify $\frac{26}{52}$:

\[
\frac{26}{52} = \frac{1}{2}
\]

Now divide the fractions by multiplying by the reciprocal of $\frac{12}{13}$:

\[
\frac{1}{2} \div \frac{12}{13} = \frac{1}{2} \times \frac{13}{12} = \frac{1 \times 13}{2 \times 12} = \frac{13}{24}
\]

So, the answer is:

\[
\boxed{\frac{13}{24}}
\]

---

Problem 11: $\frac{5}{96} \div \frac{3}{64}$

Divide the fractions by multiplying by the reciprocal of $\frac{3}{64}$:

\[
\frac{5}{96} \div \frac{3}{64} = \frac{5}{96} \times \frac{64}{3} = \frac{5 \times 64}{96 \times 3} = \frac{320}{288}
\]

Simplify $\frac{320}{288}$ by finding the GCD of 320 and 288, which is 32:

\[
\frac{320}{288} = \frac{10}{9}
\]

So, the answer is:

\[
\boxed{\frac{10}{9}}
\]

---

Problem 12: $\frac{27}{21} \div \frac{44}{14}$

First, simplify $\frac{27}{21}$ and $\frac{44}{14}$:

\[
\frac{27}{21} = \frac{9}{7}, \quad \frac{44}{14} = \frac{22}{7}
\]

Now divide the fractions by multiplying by the reciprocal of $\frac{22}{7}$:

\[
\frac{9}{7} \div \frac{22}{7} = \frac{9}{7} \times \frac{7}{22} = \frac{9 \times 7}{7 \times 22} = \frac{9}{22}
\]

So, the answer is:

\[
\boxed{\frac{9}{22}}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{lll}
1. & \frac{298}{51} & 2. & \frac{113}{26} & 3. & \frac{49}{6} \\
4. & \frac{59}{154} & 5. & \frac{7}{10} & 6. & \frac{13}{114} \\
7. & \frac{6}{25} & 8. & \frac{184}{189} & 9. & \frac{33}{56} \\
10. & \frac{13}{24} & 11. & \frac{10}{9} & 12. & \frac{9}{22}
\end{array}
}
\]