Application worksheet for Grade 5 students focusing on division of whole numbers by unit fractions, using visual models for understanding.

Let's solve each problem step by step using the visual models provided. The task is to divide whole numbers by unit fractions (fractions with numerator 1), and the models help us see how many parts of the unit fraction fit into the whole number.

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🔷 Rule to Remember:

To divide a whole number by a unit fraction:
> $$
> \text{Whole Number} \div \frac{1}{n} = \text{Whole Number} \times n
> $$

This is because dividing by a fraction is the same as multiplying by its reciprocal.

But we’ll use the models to verify this visually.

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✔ Problem 1:

$ 4 \div \frac{1}{3} = ? $

- We have 4 whole units.
- Each whole is divided into thirds ($ \frac{1}{3} $).
- So, in one whole, there are 3 parts of $ \frac{1}{3} $.
- In 4 wholes: $ 4 \times 3 = 12 $ parts.

👉 So, $ 4 \div \frac{1}{3} = 12 $

✔ Answer: 12

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✔ Problem 2:

$ 8 \div \frac{1}{2} = ? $

- We have 8 whole units.
- Each whole is split into halves ($ \frac{1}{2} $).
- One whole has 2 halves.
- So, 8 wholes → $ 8 \times 2 = 16 $ halves.

👉 So, $ 8 \div \frac{1}{2} = 16 $

✔ Answer: 16

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✔ Problem 3:

$ 2 \div \frac{1}{6} = ? $

- We have 2 whole units.
- Each whole is split into sixths ($ \frac{1}{6} $).
- One whole has 6 parts of $ \frac{1}{6} $.
- So, 2 wholes → $ 2 \times 6 = 12 $ parts.

👉 So, $ 2 \div \frac{1}{6} = 12 $

✔ Answer: 12

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✔ Problem 4:

$ 7 \div \frac{1}{4} = ? $

- We have 7 whole units.
- Each whole is split into fourths ($ \frac{1}{4} $).
- One whole has 4 parts of $ \frac{1}{4} $.
- So, 7 wholes → $ 7 \times 4 = 28 $ parts.

👉 So, $ 7 \div \frac{1}{4} = 28 $

✔ Answer: 28

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✔ Problem 5:

$ 3 \div \frac{1}{9} = ? $

- We have 3 whole units.
- Each whole is split into ninths ($ \frac{1}{9} $).
- One whole has 9 parts of $ \frac{1}{9} $.
- So, 3 wholes → $ 3 \times 9 = 27 $ parts.

👉 So, $ 3 \div \frac{1}{9} = 27 $

✔ Answer: 27

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🟩 Final Answers:

1) $ 4 \div \frac{1}{3} = \boxed{12} $
2) $ 8 \div \frac{1}{2} = \boxed{16} $
3) $ 2 \div \frac{1}{6} = \boxed{12} $
4) $ 7 \div \frac{1}{4} = \boxed{28} $
5) $ 3 \div \frac{1}{9} = \boxed{27} $

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💡 Summary:

When you divide a whole number by a unit fraction $ \frac{1}{n} $, you're asking:
> "How many $ \frac{1}{n} $ pieces are in the whole number?"

And the answer is always:
> $ \text{Whole Number} \times n $

This matches what we saw in the models!