Math worksheet from Brighterly that teaches dividing whole numbers by fractions using visual models.

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

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🔷 Understanding the Concept

When you divide a whole number by a unit fraction (like $ \frac{1}{3} $), you're asking:
"How many parts of size $ \frac{1}{n} $ are in the whole number?"

For example, $ 4 \div \frac{1}{3} $ means: "How many $ \frac{1}{3} $'s are in 4?"

Each whole is divided into thirds, so:
- 1 whole = 3 thirds
- 4 wholes = $ 4 \times 3 = 12 $ thirds

So, $ 4 \div \frac{1}{3} = 12 $

We’ll apply this logic to all problems.

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✔ Problem 1: $ 4 \div \frac{1}{3} $

- Each whole is divided into 3 equal parts ($ \frac{1}{3} $).
- There are 4 wholes.
- So total number of $ \frac{1}{3} $ parts = $ 4 \times 3 = 12 $
- Answer: $ \boxed{12} $

✔ Check model: Top row shows 4 wholes, each split into 3 parts → $ 4 \times 3 = 12 $ small parts.

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✔ Problem 2: $ 8 \div \frac{1}{4} $

- Each whole is divided into 4 parts ($ \frac{1}{4} $).
- 8 wholes → $ 8 \times 4 = 32 $ parts of $ \frac{1}{4} $
- Answer: $ \boxed{32} $

✔ Check model: 8 yellow rectangles, each split into 4 parts → $ 8 \times 4 = 32 $

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✔ Problem 3: $ 2 \div \frac{1}{6} $

- Each whole is divided into 6 parts ($ \frac{1}{6} $).
- 2 wholes → $ 2 \times 6 = 12 $ parts
- Answer: $ \boxed{12} $

✔ Check model: 2 large rectangles, each split into 6 parts → $ 2 \times 6 = 12 $

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✔ Problem 4: $ 7 \div \frac{1}{4} $

- Each whole is divided into 4 parts ($ \frac{1}{4} $).
- 7 wholes → $ 7 \times 4 = 28 $ parts
- Answer: $ \boxed{28} $

✔ Check model: 7 pink rectangles, each split into 4 parts → $ 7 \times 4 = 28 $

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✔ Problem 5: $ 3 \div \frac{1}{9} $

- Each whole is divided into 9 parts ($ \frac{1}{9} $).
- 3 wholes → $ 3 \times 9 = 27 $ parts
- Answer: $ \boxed{27} $

✔ Check model: 3 green rectangles, each split into 9 parts → $ 3 \times 9 = 27 $

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📌 General Rule:

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

Because dividing by $ \frac{1}{n} $ is the same as multiplying by $ n $.

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✔ Final Answers:

1) $ 4 \div \frac{1}{3} = \boxed{12} $
2) $ 8 \div \frac{1}{4} = \boxed{32} $
3) $ 2 \div \frac{1}{6} = \boxed{12} $
4) $ 7 \div \frac{1}{4} = \boxed{28} $
5) $ 3 \div \frac{1}{9} = \boxed{27} $

Let me know if you'd like a printable version or explanation for non-unit fractions!