Math worksheet featuring fraction division problems.

You're given a set of 10 fraction division problems. To solve them, we use the rule:

> Dividing by a fraction is the same as multiplying by its reciprocal.

That is:
\[
a \div \frac{b}{c} = a \times \frac{c}{b}
\]

Also, when dividing by a whole number (like 8, 15, etc.), you can think of it as dividing by that number over 1:
\[
a \div n = a \div \frac{n}{1} = a \times \frac{1}{n}
\]

Let’s solve each one step-by-step.

---

a) \(6 \div \frac{1}{4}\)

→ Multiply by reciprocal of \(\frac{1}{4}\), which is 4:
\[
6 \times 4 = 24
\]
✔ Answer: 24

---

b) \(\frac{1}{5} \div 8\)

→ 8 = \(\frac{8}{1}\), so reciprocal is \(\frac{1}{8}\):
\[
\frac{1}{5} \times \frac{1}{8} = \frac{1}{40}
\]
✔ Answer: \(\frac{1}{40}\)

---

c) \(7 \div \frac{2}{3}\)

→ Reciprocal of \(\frac{2}{3}\) is \(\frac{3}{2}\):
\[
7 \times \frac{3}{2} = \frac{21}{2} = 10\frac{1}{2}
\]
✔ Answer: \(\frac{21}{2}\) or \(10\frac{1}{2}\)

---

d) \(5 \div \frac{2}{5}\)

→ Reciprocal of \(\frac{2}{5}\) is \(\frac{5}{2}\):
\[
5 \times \frac{5}{2} = \frac{25}{2} = 12\frac{1}{2}
\]
✔ Answer: \(\frac{25}{2}\) or \(12\frac{1}{2}\)

---

e) \(\frac{3}{4} \div 15\)

→ 15 = \(\frac{15}{1}\), reciprocal is \(\frac{1}{15}\):
\[
\frac{3}{4} \times \frac{1}{15} = \frac{3}{60} = \frac{1}{20}
\]
✔ Answer: \(\frac{1}{20}\)

---

f) \(\frac{6}{7} \div 12\)

→ 12 = \(\frac{12}{1}\), reciprocal is \(\frac{1}{12}\):
\[
\frac{6}{7} \times \frac{1}{12} = \frac{6}{84} = \frac{1}{14}
\]
✔ Answer: \(\frac{1}{14}\)

---

g) \(\frac{5}{6} \div 5\)

→ 5 = \(\frac{5}{1}\), reciprocal is \(\frac{1}{5}\):
\[
\frac{5}{6} \times \frac{1}{5} = \frac{5}{30} = \frac{1}{6}
\]
✔ Answer: \(\frac{1}{6}\)

---

h) \(4 \div \frac{2}{5}\)

→ Reciprocal of \(\frac{2}{5}\) is \(\frac{5}{2}\):
\[
4 \times \frac{5}{2} = \frac{20}{2} = 10
\]
✔ Answer: 10

---

i) \(\frac{2}{7} \div 7\)

→ 7 = \(\frac{7}{1}\), reciprocal is \(\frac{1}{7}\):
\[
\frac{2}{7} \times \frac{1}{7} = \frac{2}{49}
\]
✔ Answer: \(\frac{2}{49}\)

---

j) \(10 \div \frac{3}{4}\)

→ Reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\):
\[
10 \times \frac{4}{3} = \frac{40}{3} = 13\frac{1}{3}
\]
✔ Answer: \(\frac{40}{3}\) or \(13\frac{1}{3}\)

---

## ✔ Final Answers:

a) 24
b) \(\frac{1}{40}\)
c) \(\frac{21}{2}\) or \(10\frac{1}{2}\)
d) \(\frac{25}{2}\) or \(12\frac{1}{2}\)
e) \(\frac{1}{20}\)
f) \(\frac{1}{14}\)
g) \(\frac{1}{6}\)
h) 10
i) \(\frac{2}{49}\)
j) \(\frac{40}{3}\) or \(13\frac{1}{3}\)

Let me know if you’d like to see any steps visualized or explained further!