Dividing Fractions Sheet 3 - A math worksheet with 18 fraction division problems, designed for practice and learning.

To solve the problems on the "Dividing Fractions Sheet 3," we need to use the rule for dividing fractions:

\[
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \cdot d}{b \cdot c}
\]

This means we multiply the first fraction by the reciprocal of the second fraction. After performing the multiplication, we simplify the resulting fraction if possible.

Let's solve each problem step by step.

---

Problem 1:

\[
\frac{2}{3} \div \frac{1}{5}
\]
- Reciprocal of \(\frac{1}{5}\) is \(\frac{5}{1}\).
- Multiply:
\[
\frac{2}{3} \times \frac{5}{1} = \frac{2 \cdot 5}{3 \cdot 1} = \frac{10}{3}
\]
- Simplify (already in simplest form):
\[
\boxed{\frac{10}{3}}
\]

---

Problem 2:

\[
\frac{3}{8} \div \frac{2}{7}
\]
- Reciprocal of \(\frac{2}{7}\) is \(\frac{7}{2}\).
- Multiply:
\[
\frac{3}{8} \times \frac{7}{2} = \frac{3 \cdot 7}{8 \cdot 2} = \frac{21}{16}
\]
- Simplify (already in simplest form):
\[
\boxed{\frac{21}{16}}
\]

---

Problem 3:

\[
\frac{3}{2} \div \frac{4}{9}
\]
- Reciprocal of \(\frac{4}{9}\) is \(\frac{9}{4}\).
- Multiply:
\[
\frac{3}{2} \times \frac{9}{4} = \frac{3 \cdot 9}{2 \cdot 4} = \frac{27}{8}
\]
- Simplify (already in simplest form):
\[
\boxed{\frac{27}{8}}
\]

---

Problem 4:

\[
\frac{2}{7} \div \frac{5}{3}
\]
- Reciprocal of \(\frac{5}{3}\) is \(\frac{3}{5}\).
- Multiply:
\[
\frac{2}{7} \times \frac{3}{5} = \frac{2 \cdot 3}{7 \cdot 5} = \frac{6}{35}
\]
- Simplify (already in simplest form):
\[
\boxed{\frac{6}{35}}
\]

---

Problem 5:

\[
\frac{5}{8} \div \frac{3}{7}
\]
- Reciprocal of \(\frac{3}{7}\) is \(\frac{7}{3}\).
- Multiply:
\[
\frac{5}{8} \times \frac{7}{3} = \frac{5 \cdot 7}{8 \cdot 3} = \frac{35}{24}
\]
- Simplify (already in simplest form):
\[
\boxed{\frac{35}{24}}
\]

---

Problem 6:

\[
\frac{1}{6} \div \frac{4}{15}
\]
- Reciprocal of \(\frac{4}{15}\) is \(\frac{15}{4}\).
- Multiply:
\[
\frac{1}{6} \times \frac{15}{4} = \frac{1 \cdot 15}{6 \cdot 4} = \frac{15}{24}
\]
- Simplify:
\[
\frac{15}{24} = \frac{5}{8}
\]
- Final answer:
\[
\boxed{\frac{5}{8}}
\]

---

Problem 7:

\[
\frac{3}{5} \div \frac{10}{4}
\]
- Reciprocal of \(\frac{10}{4}\) is \(\frac{4}{10}\).
- Multiply:
\[
\frac{3}{5} \times \frac{4}{10} = \frac{3 \cdot 4}{5 \cdot 10} = \frac{12}{50}
\]
- Simplify:
\[
\frac{12}{50} = \frac{6}{25}
\]
- Final answer:
\[
\boxed{\frac{6}{25}}
\]

---

Problem 8:

\[
\frac{5}{7} \div \frac{8}{3}
\]
- Reciprocal of \(\frac{8}{3}\) is \(\frac{3}{8}\).
- Multiply:
\[
\frac{5}{7} \times \frac{3}{8} = \frac{5 \cdot 3}{7 \cdot 8} = \frac{15}{56}
\]
- Simplify (already in simplest form):
\[
\boxed{\frac{15}{56}}
\]

---

Problem 9:

\[
\frac{4}{11} \div \frac{2}{9}
\]
- Reciprocal of \(\frac{2}{9}\) is \(\frac{9}{2}\).
- Multiply:
\[
\frac{4}{11} \times \frac{9}{2} = \frac{4 \cdot 9}{11 \cdot 2} = \frac{36}{22}
\]
- Simplify:
\[
\frac{36}{22} = \frac{18}{11}
\]
- Final answer:
\[
\boxed{\frac{18}{11}}
\]

---

Problem 10:

\[
\frac{7}{4} \div \frac{5}{12}
\]
- Reciprocal of \(\frac{5}{12}\) is \(\frac{12}{5}\).
- Multiply:
\[
\frac{7}{4} \times \frac{12}{5} = \frac{7 \cdot 12}{4 \cdot 5} = \frac{84}{20}
\]
- Simplify:
\[
\frac{84}{20} = \frac{21}{5}
\]
- Final answer:
\[
\boxed{\frac{21}{5}}
\]

---

Problem 11:

\[
\frac{6}{15} \div \frac{3}{10}
\]
- Reciprocal of \(\frac{3}{10}\) is \(\frac{10}{3}\).
- Multiply:
\[
\frac{6}{15} \times \frac{10}{3} = \frac{6 \cdot 10}{15 \cdot 3} = \frac{60}{45}
\]
- Simplify:
\[
\frac{60}{45} = \frac{4}{3}
\]
- Final answer:
\[
\boxed{\frac{4}{3}}
\]

---

Problem 12:

\[
\frac{7}{9} \div \frac{8}{5}
\]
- Reciprocal of \(\frac{8}{5}\) is \(\frac{5}{8}\).
- Multiply:
\[
\frac{7}{9} \times \frac{5}{8} = \frac{7 \cdot 5}{9 \cdot 8} = \frac{35}{72}
\]
- Simplify (already in simplest form):
\[
\boxed{\frac{35}{72}}
\]

---

Problem 13:

\[
\frac{2}{15} \div \frac{4}{7}
\]
- Reciprocal of \(\frac{4}{7}\) is \(\frac{7}{4}\).
- Multiply:
\[
\frac{2}{15} \times \frac{7}{4} = \frac{2 \cdot 7}{15 \cdot 4} = \frac{14}{60}
\]
- Simplify:
\[
\frac{14}{60} = \frac{7}{30}
\]
- Final answer:
\[
\boxed{\frac{7}{30}}
\]

---

Problem 14:

\[
\frac{5}{12} \div \frac{3}{8}
\]
- Reciprocal of \(\frac{3}{8}\) is \(\frac{8}{3}\).
- Multiply:
\[
\frac{5}{12} \times \frac{8}{3} = \frac{5 \cdot 8}{12 \cdot 3} = \frac{40}{36}
\]
- Simplify:
\[
\frac{40}{36} = \frac{10}{9}
\]
- Final answer:
\[
\boxed{\frac{10}{9}}
\]

---

Problem 15:

\[
\frac{3}{5} \div \frac{12}{7}
\]
- Reciprocal of \(\frac{12}{7}\) is \(\frac{7}{12}\).
- Multiply:
\[
\frac{3}{5} \times \frac{7}{12} = \frac{3 \cdot 7}{5 \cdot 12} = \frac{21}{60}
\]
- Simplify:
\[
\frac{21}{60} = \frac{7}{20}
\]
- Final answer:
\[
\boxed{\frac{7}{20}}
\]

---

Problem 16:

\[
\frac{7}{10} \div \frac{5}{12}
\]
- Reciprocal of \(\frac{5}{12}\) is \(\frac{12}{5}\).
- Multiply:
\[
\frac{7}{10} \times \frac{12}{5} = \frac{7 \cdot 12}{10 \cdot 5} = \frac{84}{50}
\]
- Simplify:
\[
\frac{84}{50} = \frac{42}{25}
\]
- Final answer:
\[
\boxed{\frac{42}{25}}
\]

---

Problem 17:

\[
\frac{10}{11} \div \frac{5}{8}
\]
- Reciprocal of \(\frac{5}{8}\) is \(\frac{8}{5}\).
- Multiply:
\[
\frac{10}{11} \times \frac{8}{5} = \frac{10 \cdot 8}{11 \cdot 5} = \frac{80}{55}
\]
- Simplify:
\[
\frac{80}{55} = \frac{16}{11}
\]
- Final answer:
\[
\boxed{\frac{16}{11}}
\]

---

Problem 18:

\[
\frac{4}{13} \div \frac{5}{14}
\]
- Reciprocal of \(\frac{5}{14}\) is \(\frac{14}{5}\).
- Multiply:
\[
\frac{4}{13} \times \frac{14}{5} = \frac{4 \cdot 14}{13 \cdot 5} = \frac{56}{65}
\]
- Simplify (already in simplest form):
\[
\boxed{\frac{56}{65}}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & \frac{10}{3} \\
2) & \frac{21}{16} \\
3) & \frac{27}{8} \\
4) & \frac{6}{35} \\
5) & \frac{35}{24} \\
6) & \frac{5}{8} \\
7) & \frac{6}{25} \\
8) & \frac{15}{56} \\
9) & \frac{18}{11} \\
10) & \frac{21}{5} \\
11) & \frac{4}{3} \\
12) & \frac{35}{72} \\
13) & \frac{7}{30} \\
14) & \frac{10}{9} \\
15) & \frac{7}{20} \\
16) & \frac{42}{25} \\
17) & \frac{16}{11} \\
18) & \frac{56}{65} \\
\end{array}
}
\]