Dividing Fractions worksheet with visual fraction models and word problems.

Problem Overview:

The task involves interpreting visual models of fractions and writing division problems based on those models. Then, the division problems are to be solved by multiplying by the reciprocal of the divisor. Let's solve each part step by step.

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Part (a)

#### Visual Model:
- The model shows a rectangle divided into 3 equal parts, where each part represents \( \frac{1}{3} \).
- One of these parts is further divided into 9 smaller equal parts, where each smaller part represents \( \frac{1}{9} \).

#### Division Problem:
The model suggests dividing \( \frac{1}{3} \) by \( \frac{1}{9} \). This can be written as:
\[
\frac{1}{3} \div \frac{1}{9}
\]

#### Solution:
To solve this, we multiply by the reciprocal of the divisor:
\[
\frac{1}{3} \div \frac{1}{9} = \frac{1}{3} \times \frac{9}{1} = \frac{1 \times 9}{3 \times 1} = \frac{9}{3} = 3
\]

#### Final Answer for (a):
\[
\boxed{\frac{1}{3} \div \frac{1}{9} = 3}
\]

---

Part (b)

#### Visual Model:
- The model shows a rectangle divided into 2 equal parts, where each part represents \( \frac{1}{2} \).
- One of these parts is further divided into 6 smaller equal parts, where each smaller part represents \( \frac{1}{6} \).

#### Division Problem:
The model suggests dividing \( \frac{1}{2} \) by \( \frac{1}{6} \). This can be written as:
\[
\frac{1}{2} \div \frac{1}{6}
\]

#### Solution:
To solve this, we multiply by the reciprocal of the divisor:
\[
\frac{1}{2} \div \frac{1}{6} = \frac{1}{2} \times \frac{6}{1} = \frac{1 \times 6}{2 \times 1} = \frac{6}{2} = 3
\]

#### Final Answer for (b):
\[
\boxed{\frac{1}{2} \div \frac{1}{6} = 3}
\]

---

Part (c)

#### Visual Model:
- The model shows a rectangle divided into 5 equal parts, where each part represents \( \frac{1}{5} \).
- One of these parts is further divided into 3 smaller equal parts, where each smaller part represents \( \frac{1}{15} \).

#### Division Problem:
The model suggests dividing \( \frac{1}{5} \) by \( \frac{1}{15} \). This can be written as:
\[
\frac{1}{5} \div \frac{1}{15}
\]

#### Solution:
To solve this, we multiply by the reciprocal of the divisor:
\[
\frac{1}{5} \div \frac{1}{15} = \frac{1}{5} \times \frac{15}{1} = \frac{1 \times 15}{5 \times 1} = \frac{15}{5} = 3
\]

#### Final Answer for (c):
\[
\boxed{\frac{1}{5} \div \frac{1}{15} = 3}
\]

---

Part (d)

#### Visual Model:
- The model shows a rectangle divided into 4 equal parts, where each part represents \( \frac{1}{4} \).
- One of these parts is further divided into 2 smaller equal parts, where each smaller part represents \( \frac{1}{8} \).

#### Division Problem:
The model suggests dividing \( \frac{1}{4} \) by \( \frac{1}{8} \). This can be written as:
\[
\frac{1}{4} \div \frac{1}{8}
\]

#### Solution:
To solve this, we multiply by the reciprocal of the divisor:
\[
\frac{1}{4} \div \frac{1}{8} = \frac{1}{4} \times \frac{8}{1} = \frac{1 \times 8}{4 \times 1} = \frac{8}{4} = 2
\]

#### Final Answer for (d):
\[
\boxed{\frac{1}{4} \div \frac{1}{8} = 2}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
&\text{(a)} \quad \frac{1}{3} \div \frac{1}{9} = 3 \\
&\text{(b)} \quad \frac{1}{2} \div \frac{1}{6} = 3 \\
&\text{(c)} \quad \frac{1}{5} \div \frac{1}{15} = 3 \\
&\text{(d)} \quad \frac{1}{4} \div \frac{1}{8} = 2
\end{aligned}
}
\]