Dividing Unit Fractions (Visual) worksheet with step-by-step instructions and problems for dividing unit fractions by whole numbers.

Let's solve the problem step by step using visual reasoning and mathematical principles, based on the worksheet titled *"Dividing Unit Fractions (Visual)"*. The goal is to divide a unit fraction (a fraction with numerator 1) by a whole number.

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🔍 Understanding the Concept

When we divide a unit fraction like $ \frac{1}{n} $ by a whole number $ m $, we are essentially asking:
> "What is $ \frac{1}{n} \div m $? "

This means: How much of the whole is each part when you split $ \frac{1}{n} $ into $ m $ equal parts?

We can think of it as:
$$
\frac{1}{n} \div m = \frac{1}{n \times m}
$$

So dividing a unit fraction by a whole number gives another unit fraction with denominator $ n \times m $.

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✔ Step-by-Step Visual Example (from the top of the page)

The example shows:
> $ \frac{1}{3} \div 4 = ? $

#### Step 1: Start with a whole.
Draw a rectangle representing 1 whole.

#### Step 2: Split the whole into 3 equal parts → each is $ \frac{1}{3} $.
Now shade one of those parts to represent $ \frac{1}{3} $.

#### Step 3: Now split that $ \frac{1}{3} $ into 4 equal pieces.
Each piece is $ \frac{1}{4} $ of $ \frac{1}{3} $, which equals $ \frac{1}{12} $.

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

That’s because:
$$
\frac{1}{3} \div 4 = \frac{1}{3 \times 4} = \frac{1}{12}
$$

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Now let's solve each problem using this method.

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🧮 Solving Each Problem

#### 1) $ \frac{1}{2} \div 3 $
- Split $ \frac{1}{2} $ into 3 parts.
- Each part is $ \frac{1}{2 \times 3} = \frac{1}{6} $
✔ Answer: $ \frac{1}{6} $

#### 2) $ \frac{1}{8} \div 8 $
- $ \frac{1}{8} \div 8 = \frac{1}{8 \times 8} = \frac{1}{64} $
✔ Answer: $ \frac{1}{64} $

#### 3) $ \frac{1}{7} \div 2 $
- $ \frac{1}{7} \div 2 = \frac{1}{7 \times 2} = \frac{1}{14} $
✔ Answer: $ \frac{1}{14} $

#### 4) $ \frac{1}{3} \div 4 $
- $ \frac{1}{3} \div 4 = \frac{1}{3 \times 4} = \frac{1}{12} $
✔ Answer: $ \frac{1}{12} $

#### 5) $ \frac{1}{7} \div 4 $
- $ \frac{1}{7} \div 4 = \frac{1}{7 \times 4} = \frac{1}{28} $
✔ Answer: $ \frac{1}{28} $

#### 6) $ \frac{1}{5} \div 4 $
- $ \frac{1}{5} \div 4 = \frac{1}{5 \times 4} = \frac{1}{20} $
✔ Answer: $ \frac{1}{20} $

#### 7) $ \frac{1}{3} \div 6 $
- $ \frac{1}{3} \div 6 = \frac{1}{3 \times 6} = \frac{1}{18} $
✔ Answer: $ \frac{1}{18} $

#### 8) $ \frac{1}{4} \div 9 $
- $ \frac{1}{4} \div 9 = \frac{1}{4 \times 9} = \frac{1}{36} $
✔ Answer: $ \frac{1}{36} $

#### 9) $ \frac{1}{5} \div 6 $
- $ \frac{1}{5} \div 6 = \frac{1}{5 \times 6} = \frac{1}{30} $
✔ Answer: $ \frac{1}{30} $

#### 10) $ \frac{1}{2} \div 9 $
- $ \frac{1}{2} \div 9 = \frac{1}{2 \times 9} = \frac{1}{18} $
✔ Answer: $ \frac{1}{18} $

#### 11) $ \frac{1}{6} \div 6 $
- $ \frac{1}{6} \div 6 = \frac{1}{6 \times 6} = \frac{1}{36} $
✔ Answer: $ \frac{1}{36} $

#### 12) $ \frac{1}{9} \div 6 $
- $ \frac{1}{9} \div 6 = \frac{1}{9 \times 6} = \frac{1}{54} $
✔ Answer: $ \frac{1}{54} $

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✔ Final Answers:

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

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📌 How to Fill in the Box (Visual)

For each problem, draw a rectangle to represent the whole. Then:
1. Divide it into the denominator parts (e.g., 3 parts for $ \frac{1}{3} $).
2. Shade one part to show the unit fraction.
3. Then divide that shaded part into the number of groups (the divisor).
4. Each small piece is the answer.

Example: For $ \frac{1}{3} \div 4 $:
- Draw a square.
- Divide it into 3 vertical strips → shade one strip (that's $ \frac{1}{3} $).
- Divide that shaded strip into 4 horizontal parts → each tiny piece is $ \frac{1}{12} $.

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