Dividing Fractions | Visual Models worksheet with fraction bars and equations.

The task involves solving fraction division problems using visual models. Let's break down each problem step by step.

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Problem 1:

$$
\frac{3}{4} \div \frac{1}{2}
$$

#### Visual Representation:
- The first fraction, $\frac{3}{4}$, is represented as a rectangle divided into 4 equal parts, with 3 parts shaded.
- The second fraction, $\frac{1}{2}$, represents how many times the shaded portion of $\frac{1}{2}$ fits into $\frac{3}{4}$.

#### Solution:
1. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
$$
\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1}
$$
2. Multiply the numerators and denominators:
$$
\frac{3 \times 2}{4 \times 1} = \frac{6}{4}
$$
3. Simplify the fraction:
$$
\frac{6}{4} = \frac{3}{2} = 1 \frac{1}{2}
$$

#### Answer:
$$
\boxed{1 \frac{1}{2}}
$$

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Problem 2:

$$
\frac{2}{3} \div \frac{1}{3}
$$

#### Visual Representation:
- The first fraction, $\frac{2}{3}$, is represented as a rectangle divided into 3 equal parts, with 2 parts shaded.
- The second fraction, $\frac{1}{3}$, represents how many times the shaded portion of $\frac{1}{3}$ fits into $\frac{2}{3}$.

#### Solution:
1. Divide the fractions by multiplying the first fraction by the reciprocal of the second fraction:
$$
\frac{2}{3} \div \frac{1}{3} = \frac{2}{3} \times \frac{3}{1}
$$
2. Multiply the numerators and denominators:
$$
\frac{2 \times 3}{3 \times 1} = \frac{6}{3}
$$
3. Simplify the fraction:
$$
\frac{6}{3} = 2
$$

#### Answer:
$$
\boxed{2}
$$

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Problem 3:

$$
\frac{5}{6} \div \frac{1}{3}
$$

#### Visual Representation:
- The first fraction, $\frac{5}{6}$, is represented as a rectangle divided into 6 equal parts, with 5 parts shaded.
- The second fraction, $\frac{1}{3}$, represents how many times the shaded portion of $\frac{1}{3}$ fits into $\frac{5}{6}$.

#### Solution:
1. Divide the fractions by multiplying the first fraction by the reciprocal of the second fraction:
$$
\frac{5}{6} \div \frac{1}{3} = \frac{5}{6} \times \frac{3}{1}
$$
2. Multiply the numerators and denominators:
$$
\frac{5 \times 3}{6 \times 1} = \frac{15}{6}
$$
3. Simplify the fraction:
$$
\frac{15}{6} = \frac{5}{2} = 2 \frac{1}{2}
$$

#### Answer:
$$
\boxed{2 \frac{1}{2}}
$$

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Problem 4:

$$
\frac{4}{5} \div \frac{2}{5}
$$

#### Visual Representation:
- The first fraction, $\frac{4}{5}$, is represented as a rectangle divided into 5 equal parts, with 4 parts shaded.
- The second fraction, $\frac{2}{5}$, represents how many times the shaded portion of $\frac{2}{5}$ fits into $\frac{4}{5}$.

#### Solution:
1. Divide the fractions by multiplying the first fraction by the reciprocal of the second fraction:
$$
\frac{4}{5} \div \frac{2}{5} = \frac{4}{5} \times \frac{5}{2}
$$
2. Multiply the numerators and denominators:
$$
\frac{4 \times 5}{5 \times 2} = \frac{20}{10}
$$
3. Simplify the fraction:
$$
\frac{20}{10} = 2
$$

#### Answer:
$$
\boxed{2}
$$

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Final Answers:

1. $\frac{3}{4} \div \frac{1}{2} = \boxed{1 \frac{1}{2}}$
2. $\frac{2}{3} \div \frac{1}{3} = \boxed{2}$
3. $\frac{5}{6} \div \frac{1}{3} = \boxed{2 \frac{1}{2}}$
4. $\frac{4}{5} \div \frac{2}{5} = \boxed{2}$

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Thus, the final boxed answers are:
$$
\boxed{1 \frac{1}{2}, 2, 2 \frac{1}{2}, 2}
$$