Math worksheet titled 'Operations with Fractions (A)' containing ten practice problems for students to solve.

Problem: Solve the given operations with fractions.

We will solve each problem step by step, ensuring clarity in each calculation. Let's go through them one by one.

---

#### 1. \( \frac{2}{11} + \frac{1}{17} + \frac{2}{3} \)

To add these fractions, we need a common denominator. The denominators are 11, 17, and 3. The least common multiple (LCM) of 11, 17, and 3 is \( 11 \times 17 \times 3 = 561 \).

- Convert each fraction to have the denominator 561:
\[
\frac{2}{11} = \frac{2 \times 51}{11 \times 51} = \frac{102}{561}
\]
\[
\frac{1}{17} = \frac{1 \times 33}{17 \times 33} = \frac{33}{561}
\]
\[
\frac{2}{3} = \frac{2 \times 187}{3 \times 187} = \frac{374}{561}
\]

- Add the fractions:
\[
\frac{102}{561} + \frac{33}{561} + \frac{374}{561} = \frac{102 + 33 + 374}{561} = \frac{509}{561}
\]

Answer:
\[
\boxed{\frac{509}{561}}
\]

---

#### 2. \( \frac{21}{5} + \frac{11}{6} - \frac{5}{2} \)

The denominators are 5, 6, and 2. The LCM of 5, 6, and 2 is \( 30 \).

- Convert each fraction to have the denominator 30:
\[
\frac{21}{5} = \frac{21 \times 6}{5 \times 6} = \frac{126}{30}
\]
\[
\frac{11}{6} = \frac{11 \times 5}{6 \times 5} = \frac{55}{30}
\]
\[
\frac{5}{2} = \frac{5 \times 15}{2 \times 15} = \frac{75}{30}
\]

- Perform the addition and subtraction:
\[
\frac{126}{30} + \frac{55}{30} - \frac{75}{30} = \frac{126 + 55 - 75}{30} = \frac{106}{30}
\]

- Simplify the fraction:
\[
\frac{106}{30} = \frac{53}{15}
\]

Answer:
\[
\boxed{\frac{53}{15}}
\]

---

#### 3. \( \frac{28}{17} \times \frac{6}{19} \div \frac{3}{4} \)

First, perform the multiplication:
\[
\frac{28}{17} \times \frac{6}{19} = \frac{28 \times 6}{17 \times 19} = \frac{168}{323}
\]

Next, divide by \( \frac{3}{4} \). Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
\frac{168}{323} \div \frac{3}{4} = \frac{168}{323} \times \frac{4}{3} = \frac{168 \times 4}{323 \times 3} = \frac{672}{969}
\]

Simplify the fraction:
\[
\frac{672}{969} = \frac{224}{323} \quad (\text{both numerator and denominator divided by 3})
\]

Answer:
\[
\boxed{\frac{224}{323}}
\]

---

#### 4. \( \frac{12}{5} - \frac{18}{17} + \frac{1}{2} \)

The denominators are 5, 17, and 2. The LCM of 5, 17, and 2 is \( 170 \).

- Convert each fraction to have the denominator 170:
\[
\frac{12}{5} = \frac{12 \times 34}{5 \times 34} = \frac{408}{170}
\]
\[
\frac{18}{17} = \frac{18 \times 10}{17 \times 10} = \frac{180}{170}
\]
\[
\frac{1}{2} = \frac{1 \times 85}{2 \times 85} = \frac{85}{170}
\]

- Perform the operations:
\[
\frac{408}{170} - \frac{180}{170} + \frac{85}{170} = \frac{408 - 180 + 85}{170} = \frac{313}{170}
\]

Answer:
\[
\boxed{\frac{313}{170}}
\]

---

#### 5. \( \frac{31}{12} + \frac{1}{2} + \frac{7}{3} \)

The denominators are 12, 2, and 3. The LCM of 12, 2, and 3 is \( 12 \).

- Convert each fraction to have the denominator 12:
\[
\frac{31}{12} = \frac{31}{12}
\]
\[
\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}
\]
\[
\frac{7}{3} = \frac{7 \times 4}{3 \times 4} = \frac{28}{12}
\]

- Add the fractions:
\[
\frac{31}{12} + \frac{6}{12} + \frac{28}{12} = \frac{31 + 6 + 28}{12} = \frac{65}{12}
\]

Answer:
\[
\boxed{\frac{65}{12}}
\]

---

#### 6. \( \frac{6}{5} \div \frac{5}{6} \times \frac{7}{16} \)

First, divide \( \frac{6}{5} \) by \( \frac{5}{6} \):
\[
\frac{6}{5} \div \frac{5}{6} = \frac{6}{5} \times \frac{6}{5} = \frac{6 \times 6}{5 \times 5} = \frac{36}{25}
\]

Next, multiply by \( \frac{7}{16} \):
\[
\frac{36}{25} \times \frac{7}{16} = \frac{36 \times 7}{25 \times 16} = \frac{252}{400}
\]

Simplify the fraction:
\[
\frac{252}{400} = \frac{63}{100} \quad (\text{both numerator and denominator divided by 4})
\]

Answer:
\[
\boxed{\frac{63}{100}}
\]

---

#### 7. \( \frac{16}{3} - \frac{4}{3} - \frac{7}{6} \)

The denominators are 3 and 6. The LCM of 3 and 6 is \( 6 \).

- Convert each fraction to have the denominator 6:
\[
\frac{16}{3} = \frac{16 \times 2}{3 \times 2} = \frac{32}{6}
\]
\[
\frac{4}{3} = \frac{4 \times 2}{3 \times 2} = \frac{8}{6}
\]
\[
\frac{7}{6} = \frac{7}{6}
\]

- Perform the operations:
\[
\frac{32}{6} - \frac{8}{6} - \frac{7}{6} = \frac{32 - 8 - 7}{6} = \frac{17}{6}
\]

Answer:
\[
\boxed{\frac{17}{6}}
\]

---

#### 8. \( \frac{7}{3} \div \frac{3}{4} \times \frac{26}{17} \)

First, divide \( \frac{7}{3} \) by \( \frac{3}{4} \):
\[
\frac{7}{3} \div \frac{3}{4} = \frac{7}{3} \times \frac{4}{3} = \frac{7 \times 4}{3 \times 3} = \frac{28}{9}
\]

Next, multiply by \( \frac{26}{17} \):
\[
\frac{28}{9} \times \frac{26}{17} = \frac{28 \times 26}{9 \times 17} = \frac{728}{153}
\]

The fraction \( \frac{728}{153} \) is already in simplest form.

Answer:
\[
\boxed{\frac{728}{153}}
\]

---

#### 9. \( \frac{46}{9} - \frac{28}{11} + \frac{7}{6} \)

The denominators are 9, 11, and 6. The LCM of 9, 11, and 6 is \( 198 \).

- Convert each fraction to have the denominator 198:
\[
\frac{46}{9} = \frac{46 \times 22}{9 \times 22} = \frac{1012}{198}
\]
\[
\frac{28}{11} = \frac{28 \times 18}{11 \times 18} = \frac{504}{198}
\]
\[
\frac{7}{6} = \frac{7 \times 33}{6 \times 33} = \frac{231}{198}
\]

- Perform the operations:
\[
\frac{1012}{198} - \frac{504}{198} + \frac{231}{198} = \frac{1012 - 504 + 231}{198} = \frac{739}{198}
\]

Answer:
\[
\boxed{\frac{739}{198}}
\]

---

#### 10. \( \frac{5}{3} \times \frac{5}{4} \div \frac{5}{2} \)

First, multiply \( \frac{5}{3} \) and \( \frac{5}{4} \):
\[
\frac{5}{3} \times \frac{5}{4} = \frac{5 \times 5}{3 \times 4} = \frac{25}{12}
\]

Next, divide by \( \frac{5}{2} \):
\[
\frac{25}{12} \div \frac{5}{2} = \frac{25}{12} \times \frac{2}{5} = \frac{25 \times 2}{12 \times 5} = \frac{50}{60}
\]

Simplify the fraction:
\[
\frac{50}{60} = \frac{5}{6} \quad (\text{both numerator and denominator divided by 10})
\]

Answer:
\[
\boxed{\frac{5}{6}}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \frac{509}{561} \\
2. & \frac{53}{15} \\
3. & \frac{224}{323} \\
4. & \frac{313}{170} \\
5. & \frac{65}{12} \\
6. & \frac{63}{100} \\
7. & \frac{17}{6} \\
8. & \frac{728}{153} \\
9. & \frac{739}{198} \\
10. & \frac{5}{6}
\end{array}
}
\]