Dividing Fractions with Models worksheet: Practice dividing unit fractions by whole numbers using visual fraction models.

Let's solve each problem step by step using visual models and the concept of dividing a unit fraction by a whole number.

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🔍 Concept:

When you divide a unit fraction (like $ \frac{1}{n} $) by a whole number $ d $, you are splitting that fraction into $ d $ equal parts.

So:
$$
\frac{1}{n} \div d = \frac{1}{n} \times \frac{1}{d} = \frac{1}{n \times d}
$$

We can use this rule and verify it with the models.

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✔ Example Given:

$$
\frac{1}{2} \div 6 = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}
$$
The model shows $ \frac{1}{2} $ split into 6 equal parts → each part is $ \frac{1}{12} $. ✔️

Now let’s solve each problem.

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Problem 1:

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

- The top bar represents $ \frac{1}{3} $
- It's divided into 6 equal parts (red rectangles)
- So we're splitting $ \frac{1}{3} $ into 6 pieces.

Each piece is:
$$
\frac{1}{3} \div 6 = \frac{1}{3} \times \frac{1}{6} = \frac{1}{18}
$$

✔ Answer: $ \boxed{\frac{1}{18}} $

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Problem 2:

$$
\frac{1}{9} \div 9
$$

- Top bar: $ \frac{1}{9} $
- Divided into 9 equal parts (purple rectangles)

Each part is:
$$
\frac{1}{9} \div 9 = \frac{1}{9} \times \frac{1}{9} = \frac{1}{81}
$$

✔ Answer: $ \boxed{\frac{1}{81}} $

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Problem 3:

$$
\frac{1}{7} \div 3
$$

- Top bar: $ \frac{1}{7} $
- Divided into 3 equal parts (blue rectangles)

Each part is:
$$
\frac{1}{7} \div 3 = \frac{1}{7} \times \frac{1}{3} = \frac{1}{21}
$$

✔ Answer: $ \boxed{\frac{1}{21}} $

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Problem 4:

$$
\frac{1}{5} \div 10
$$

- Top bar: $ \frac{1}{5} $
- Divided into 10 equal parts (green rectangles)

Each part is:
$$
\frac{1}{5} \div 10 = \frac{1}{5} \times \frac{1}{10} = \frac{1}{50}
$$

✔ Answer: $ \boxed{\frac{1}{50}} $

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Problem 5:

$$
\frac{1}{4} \div 8
$$

- Top bar: $ \frac{1}{4} $
- Divided into 8 equal parts (yellow rectangles)

Each part is:
$$
\frac{1}{4} \div 8 = \frac{1}{4} \times \frac{1}{8} = \frac{1}{32}
$$

✔ Answer: $ \boxed{\frac{1}{32}} $

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✔ Final Answers:

| Problem | Expression | Answer |
|--------|--------------------|------------|
| 1 | $ \frac{1}{3} \div 6 $ | $ \frac{1}{18} $ |
| 2 | $ \frac{1}{9} \div 9 $ | $ \frac{1}{81} $ |
| 3 | $ \frac{1}{7} \div 3 $ | $ \frac{1}{21} $ |
| 4 | $ \frac{1}{5} \div 10 $ | $ \frac{1}{50} $ |
| 5 | $ \frac{1}{4} \div 8 $ | $ \frac{1}{32} $ |

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🧠 Summary Rule:

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

This matches the visual models — splitting a small piece into more parts makes each even smaller.