Activity 5: Dividing Fractions using Visual Models - Practice dividing whole numbers by unit fractions with shaded fraction bars and rectangles.

Let's solve each problem step by step using the visual models provided. The task is to divide whole numbers by unit fractions and explain what the operation means.

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🔷 Understanding the Concept:

Dividing a whole number by a unit fraction (like $ \frac{1}{5}, \frac{1}{4}, \frac{1}{2} $, etc.) means:
> "How many parts of size $ \frac{1}{n} $ fit into the whole number?"

For example:
$ 6 \div \frac{1}{5} $ means: *How many $ \frac{1}{5} $-sized pieces are in 6 wholes?*

Each whole is divided into 5 equal parts (fifths), so we count how many fifths are in 6 wholes.

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## ✔ Problem 1: $ 6 \div \frac{1}{5} $

Visual Model:
- 6 wholes, each divided into 5 parts → each part is $ \frac{1}{5} $
- Total number of $ \frac{1}{5} $ pieces = $ 6 \times 5 = 30 $

✔ So:
$$
6 \div \frac{1}{5} = 30
$$

Means:
There are 30 fifths in 6 wholes.
So, dividing 6 by $ \frac{1}{5} $ tells us how many $ \frac{1}{5} $-sized pieces fit into 6.

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## ✔ Problem 2: $ 7 \div \frac{1}{4} $

Visual Model:
- 7 wholes, each divided into 4 parts → each part is $ \frac{1}{4} $
- Total number of $ \frac{1}{4} $ pieces = $ 7 \times 4 = 28 $

✔ So:
$$
7 \div \frac{1}{4} = 28
$$

Means:
There are 28 fourths in 7 wholes.
This means you can fit 28 pieces of size $ \frac{1}{4} $ into 7 wholes.

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## ✔ Problem 3: $ 9 \div \frac{1}{2} $

Visual Model:
- 9 wholes, each divided into 2 parts → each part is $ \frac{1}{2} $
- Total number of $ \frac{1}{2} $ pieces = $ 9 \times 2 = 18 $

✔ So:
$$
9 \div \frac{1}{2} = 18
$$

Means:
There are 18 halves in 9 wholes.
Each whole has 2 halves, so 9 wholes have 18 halves.

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## ✔ Problem 4: $ 2 \div \frac{1}{7} $

Visual Model:
- 2 wholes, each divided into 7 parts → each part is $ \frac{1}{7} $
- Total number of $ \frac{1}{7} $ pieces = $ 2 \times 7 = 14 $

✔ So:
$$
2 \div \frac{1}{7} = 14
$$

Means:
There are 14 sevenths in 2 wholes.
You can fit 14 pieces of size $ \frac{1}{7} $ into 2 wholes.

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## ✔ Problem 5: $ 5 \div \frac{1}{3} $

Visual Model:
- 5 wholes, each divided into 3 parts → each part is $ \frac{1}{3} $
- Total number of $ \frac{1}{3} $ pieces = $ 5 \times 3 = 15 $

✔ So:
$$
5 \div \frac{1}{3} = 15
$$

Means:
There are 15 thirds in 5 wholes.
Each whole has 3 thirds, so 5 wholes have 15 thirds.

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🟩 Final Answers:

| Problem | Expression | Answer | Meaning |
|--------|------------|--------|---------|
| 1 | $ 6 \div \frac{1}{5} $ | 30 | There are 30 fifths in 6 wholes. |
| 2 | $ 7 \div \frac{1}{4} $ | 28 | There are 28 fourths in 7 wholes. |
| 3 | $ 9 \div \frac{1}{2} $ | 18 | There are 18 halves in 9 wholes. |
| 4 | $ 2 \div \frac{1}{7} $ | 14 | There are 14 sevenths in 2 wholes. |
| 5 | $ 5 \div \frac{1}{3} $ | 15 | There are 15 thirds in 5 wholes. |

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🔍 General Rule:

$$
\text{Whole number} \div \frac{1}{n} = \text{Whole number} \times n
$$
Because dividing by $ \frac{1}{n} $ is the same as multiplying by $ n $.

✔ Example: $ 6 \div \frac{1}{5} = 6 \times 5 = 30 $

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Let me know if you'd like these answers filled into the worksheet format!