Math worksheet for practicing multiplication and division of fractions with ten problems.

To solve the problems involving multiplication and division of fractions, we will follow these steps:

1. Multiplication of Fractions: Multiply the numerators together and the denominators together.
2. Division of Fractions: Convert division into multiplication by taking the reciprocal of the divisor.

Let's solve each problem step by step.

---

Problem ①:

\[
\frac{11}{3} \times \frac{9}{13} \div \frac{4}{6}
\]

#### Step 1: Convert division to multiplication
\[
\frac{11}{3} \times \frac{9}{13} \times \frac{6}{4}
\]

#### Step 2: Simplify the fractions
\[
\frac{11}{3} \times \frac{9}{13} \times \frac{3}{2}
\]
- Simplify \(\frac{6}{4}\) to \(\frac{3}{2}\).

#### Step 3: Multiply the numerators and denominators
\[
\frac{11 \times 9 \times 3}{3 \times 13 \times 2} = \frac{297}{78}
\]

#### Step 4: Simplify the result
\[
\frac{297}{78} = \frac{99}{26}
\]

Answer:
\[
\boxed{\frac{99}{26}}
\]

---

Problem ②:

\[
\frac{7}{4} \div \frac{8}{3} \div \frac{9}{14}
\]

#### Step 1: Convert divisions to multiplications
\[
\frac{7}{4} \times \frac{3}{8} \times \frac{14}{9}
\]

#### Step 2: Multiply the numerators and denominators
\[
\frac{7 \times 3 \times 14}{4 \times 8 \times 9} = \frac{294}{288}
\]

#### Step 3: Simplify the result
\[
\frac{294}{288} = \frac{49}{48}
\]

Answer:
\[
\boxed{\frac{49}{48}}
\]

---

Problem ③:

\[
\frac{3}{5} \div \frac{17}{6} \times \frac{15}{9}
\]

#### Step 1: Convert division to multiplication
\[
\frac{3}{5} \times \frac{6}{17} \times \frac{15}{9}
\]

#### Step 2: Simplify the fractions
\[
\frac{3}{5} \times \frac{6}{17} \times \frac{5}{3}
\]
- Simplify \(\frac{15}{9}\) to \(\frac{5}{3}\).

#### Step 3: Multiply the numerators and denominators
\[
\frac{3 \times 6 \times 5}{5 \times 17 \times 3} = \frac{90}{255}
\]

#### Step 4: Simplify the result
\[
\frac{90}{255} = \frac{6}{17}
\]

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

---

Problem ④:

\[
\frac{16}{5} \times \frac{3}{11} \times \frac{10}{16}
\]

#### Step 1: Multiply the numerators and denominators
\[
\frac{16 \times 3 \times 10}{5 \times 11 \times 16} = \frac{480}{880}
\]

#### Step 2: Simplify the result
\[
\frac{480}{880} = \frac{6}{11}
\]

Answer:
\[
\boxed{\frac{6}{11}}
\]

---

Problem ⑤:

\[
\frac{20}{9} \times \frac{2}{6} \times \frac{12}{58}
\]

#### Step 1: Simplify the fractions
\[
\frac{20}{9} \times \frac{1}{3} \times \frac{6}{29}
\]
- Simplify \(\frac{2}{6}\) to \(\frac{1}{3}\).
- Simplify \(\frac{12}{58}\) to \(\frac{6}{29}\).

#### Step 2: Multiply the numerators and denominators
\[
\frac{20 \times 1 \times 6}{9 \times 3 \times 29} = \frac{120}{837}
\]

#### Step 3: Simplify the result
\[
\frac{120}{837} = \frac{40}{279}
\]

Answer:
\[
\boxed{\frac{40}{279}}
\]

---

Problem ⑥:

\[
\frac{19}{9} \div \frac{13}{6} \times \frac{24}{76}
\]

#### Step 1: Convert division to multiplication
\[
\frac{19}{9} \times \frac{6}{13} \times \frac{24}{76}
\]

#### Step 2: Simplify the fractions
\[
\frac{19}{9} \times \frac{6}{13} \times \frac{6}{19}
\]
- Simplify \(\frac{24}{76}\) to \(\frac{6}{19}\).

#### Step 3: Multiply the numerators and denominators
\[
\frac{19 \times 6 \times 6}{9 \times 13 \times 19} = \frac{648}{2223}
\]

#### Step 4: Simplify the result
\[
\frac{648}{2223} = \frac{24}{83}
\]

Answer:
\[
\boxed{\frac{24}{83}}
\]

---

Problem ⑦:

\[
\frac{7}{6} \div \frac{15}{8} \times \frac{36}{35}
\]

#### Step 1: Convert division to multiplication
\[
\frac{7}{6} \times \frac{8}{15} \times \frac{36}{35}
\]

#### Step 2: Multiply the numerators and denominators
\[
\frac{7 \times 8 \times 36}{6 \times 15 \times 35} = \frac{2016}{3150}
\]

#### Step 3: Simplify the result
\[
\frac{2016}{3150} = \frac{16}{25}
\]

Answer:
\[
\boxed{\frac{16}{25}}
\]

---

Problem ⑧:

\[
\frac{13}{8} \times \frac{4}{3} \div \frac{26}{16}
\]

#### Step 1: Convert division to multiplication
\[
\frac{13}{8} \times \frac{4}{3} \times \frac{16}{26}
\]

#### Step 2: Simplify the fractions
\[
\frac{13}{8} \times \frac{4}{3} \times \frac{8}{13}
\]
- Simplify \(\frac{16}{26}\) to \(\frac{8}{13}\).

#### Step 3: Multiply the numerators and denominators
\[
\frac{13 \times 4 \times 8}{8 \times 3 \times 13} = \frac{416}{312}
\]

#### Step 4: Simplify the result
\[
\frac{416}{312} = \frac{4}{3}
\]

Answer:
\[
\boxed{\frac{4}{3}}
\]

---

Problem ⑨:

\[
\frac{3}{8} \times \frac{18}{42} \div \frac{12}{16}
\]

#### Step 1: Convert division to multiplication
\[
\frac{3}{8} \times \frac{18}{42} \times \frac{16}{12}
\]

#### Step 2: Simplify the fractions
\[
\frac{3}{8} \times \frac{3}{7} \times \frac{4}{3}
\]
- Simplify \(\frac{18}{42}\) to \(\frac{3}{7}\).
- Simplify \(\frac{16}{12}\) to \(\frac{4}{3}\).

#### Step 3: Multiply the numerators and denominators
\[
\frac{3 \times 3 \times 4}{8 \times 7 \times 3} = \frac{36}{168}
\]

#### Step 4: Simplify the result
\[
\frac{36}{168} = \frac{3}{14}
\]

Answer:
\[
\boxed{\frac{3}{14}}
\]

---

Problem ⑩:

\[
\frac{29}{10} \div \frac{7}{2} \times \frac{5}{58}
\]

#### Step 1: Convert division to multiplication
\[
\frac{29}{10} \times \frac{2}{7} \times \frac{5}{58}
\]

#### Step 2: Multiply the numerators and denominators
\[
\frac{29 \times 2 \times 5}{10 \times 7 \times 58} = \frac{290}{4060}
\]

#### Step 3: Simplify the result
\[
\frac{290}{4060} = \frac{1}{14}
\]

Answer:
\[
\boxed{\frac{1}{14}}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
① & \frac{99}{26} \\
② & \frac{49}{48} \\
③ & \frac{6}{17} \\
④ & \frac{6}{11} \\
⑤ & \frac{40}{279} \\
⑥ & \frac{24}{83} \\
⑦ & \frac{16}{25} \\
⑧ & \frac{4}{3} \\
⑨ & \frac{3}{14} \\
⑩ & \frac{1}{14}
\end{array}
}
\]