Solved Activity 5) Dividing Fractions | Visual Models Divide ... - Free Printable

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!