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Let's solve the problem step by step using visual reasoning and mathematical understanding of dividing unit fractions by whole numbers.

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🔍 Understanding the Concept:

We are dividing a unit fraction (like $ \frac{1}{3}, \frac{1}{4} $, etc.) by a whole number.

For example:
$$
\frac{1}{3} \div 4 = ?
$$

This means: *If you have one-third of a whole, and you divide that third into 4 equal parts, how big is each part?*

Visually, this can be shown by:

1. Starting with a whole.
2. Dividing it into 3 equal parts (to get $ \frac{1}{3} $).
3. Then taking just one of those thirds and splitting it into 4 equal pieces.
4. Each small piece is $ \frac{1}{12} $ of the original whole.

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

In general:
$$
\frac{1}{a} \div b = \frac{1}{a \times b}
$$

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Now let’s solve each problem:

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✔ Solutions with Explanation

#### 1) $ \frac{1}{3} \div 3 = ? $
- Divide $ \frac{1}{3} $ into 3 parts → each part is $ \frac{1}{9} $
- So: $ \frac{1}{3} \div 3 = \frac{1}{9} $

✔ Answer: $ \boxed{\frac{1}{9}} $

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#### 2) $ \frac{1}{8} \div 8 = ? $
- Take $ \frac{1}{8} $ and split it into 8 parts → each is $ \frac{1}{64} $
- So: $ \frac{1}{8} \div 8 = \frac{1}{64} $

✔ Answer: $ \boxed{\frac{1}{64}} $

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#### 3) $ \frac{1}{7} \div 2 = ? $
- Split $ \frac{1}{7} $ into 2 parts → each is $ \frac{1}{14} $
- So: $ \frac{1}{7} \div 2 = \frac{1}{14} $

✔ Answer: $ \boxed{\frac{1}{14}} $

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#### 4) $ \frac{1}{2} \div 4 = ? $
- Split $ \frac{1}{2} $ into 4 parts → each is $ \frac{1}{8} $
- So: $ \frac{1}{2} \div 4 = \frac{1}{8} $

✔ Answer: $ \boxed{\frac{1}{8}} $

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#### 5) $ \frac{1}{7} \div 4 = ? $
- Split $ \frac{1}{7} $ into 4 parts → each is $ \frac{1}{28} $
- So: $ \frac{1}{7} \div 4 = \frac{1}{28} $

✔ Answer: $ \boxed{\frac{1}{28}} $

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#### 6) $ \frac{1}{5} \div 4 = ? $
- Split $ \frac{1}{5} $ into 4 parts → each is $ \frac{1}{20} $
- So: $ \frac{1}{5} \div 4 = \frac{1}{20} $

✔ Answer: $ \boxed{\frac{1}{20}} $

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#### 7) $ \frac{1}{3} \div 6 = ? $
- Split $ \frac{1}{3} $ into 6 parts → each is $ \frac{1}{18} $
- So: $ \frac{1}{3} \div 6 = \frac{1}{18} $

✔ Answer: $ \boxed{\frac{1}{18}} $

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#### 8) $ \frac{1}{4} \div 9 = ? $
- Split $ \frac{1}{4} $ into 9 parts → each is $ \frac{1}{36} $
- So: $ \frac{1}{4} \div 9 = \frac{1}{36} $

✔ Answer: $ \boxed{\frac{1}{36}} $

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#### 9) $ \frac{1}{5} \div 6 = ? $
- Split $ \frac{1}{5} $ into 6 parts → each is $ \frac{1}{30} $
- So: $ \frac{1}{5} \div 6 = \frac{1}{30} $

✔ Answer: $ \boxed{\frac{1}{30}} $

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#### 10) $ \frac{1}{2} \div 9 = ? $
- Split $ \frac{1}{2} $ into 9 parts → each is $ \frac{1}{18} $
- So: $ \frac{1}{2} \div 9 = \frac{1}{18} $

✔ Answer: $ \boxed{\frac{1}{18}} $

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#### 11) $ \frac{1}{6} \div 6 = ? $
- Split $ \frac{1}{6} $ into 6 parts → each is $ \frac{1}{36} $
- So: $ \frac{1}{6} \div 6 = \frac{1}{36} $

✔ Answer: $ \boxed{\frac{1}{36}} $

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#### 12) $ \frac{1}{9} \div 6 = ? $
- Split $ \frac{1}{9} $ into 6 parts → each is $ \frac{1}{54} $
- So: $ \frac{1}{9} \div 6 = \frac{1}{54} $

✔ Answer: $ \boxed{\frac{1}{54}} $

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📝 Final Answers (Fill in the Box):

| Problem | Answer |
|--------|--------|
| 1) | $ \frac{1}{9} $ |
| 2) | $ \frac{1}{64} $ |
| 3) | $ \frac{1}{14} $ |
| 4) | $ \frac{1}{8} $ |
| 5) | $ \frac{1}{28} $ |
| 6) | $ \frac{1}{20} $ |
| 7) | $ \frac{1}{18} $ |
| 8) | $ \frac{1}{36} $ |
| 9) | $ \frac{1}{30} $ |
| 10) | $ \frac{1}{18} $ |
| 11) | $ \frac{1}{36} $ |
| 12) | $ \frac{1}{54} $ |

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✔ General Rule:

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

This rule works because you're dividing a smaller portion (the unit fraction) into even more parts.

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Let me know if you'd like visual diagrams for any of these!