4th Grade Math Worksheets PDF | Printable Math Worksheets - Free Printable

Let's solve this step-by-step.

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Objective:

Identify which fractions are equivalent to one half ($\frac{1}{2}$) by analyzing the shaded portions of each shape. Then, list all such fractions and observe a pattern.

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Step 1: Understand the Task

We need to:
1. Write the fraction of each shape that is shaded.
2. Check if the fraction is equivalent to $\frac{1}{2}$.
3. List all fractions that are equivalent to $\frac{1}{2}$.
4. Answer "What do you notice?"

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Step 2: Analyze Each Shape

We'll go row by row.

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#### Row 1 (Squares divided into 4 parts)

| Shape | Shaded Parts | Total Parts | Fraction | Equivalent to ½? |
|-------|--------------|-------------|----------|------------------|
| Example | 2 | 4 | $\frac{2}{4}$ ✔ | Yes (✓) |
| 1st | 1 | 4 | $\frac{1}{4}$ | No |
| 2nd | 3 | 4 | $\frac{3}{4}$ | No |
| 3rd | 2 | 4 | $\frac{2}{4}$ ✔ | Yes (✓) |

✔ So far: $\frac{2}{4}$ appears twice.

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#### Row 2 (Rectangles divided into 6 parts)

| Shape | Shaded | Total | Fraction | Equivalent to ½? |
|-------|--------|-------|----------|------------------|
| 1st | 3 | 6 | $\frac{3}{6}$ ✔ | Yes (✓) |
| 2nd | 2 | 6 | $\frac{2}{6}$ | No |
| 3rd | 1 | 6 | $\frac{1}{6}$ | No |
| 4th | 3 | 6 | $\frac{3}{6}$ ✔ | Yes (✓) |

✔ $\frac{3}{6}$ appears twice.

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#### Row 3 (Hexagons – 6 equal parts)

| Shape | Shaded | Total | Fraction | Equivalent to ½? |
|-------|--------|-------|----------|------------------|
| 1st | 3 | 6 | $\frac{3}{6}$ ✔ | Yes (✓) |
| 2nd | 4 | 6 | $\frac{4}{6}$ | No |
| 3rd | 1 | 6 | $\frac{1}{6}$ | No |
| 4th | 3 | 6 | $\frac{3}{6}$ ✔ | Yes (✓) |

✔ Again, $\frac{3}{6}$ appears.

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#### Row 4 (Circles divided into 8 parts)

| Shape | Shaded | Total | Fraction | Equivalent to ½? |
|-------|--------|-------|----------|------------------|
| 1st | 2 | 8 | $\frac{2}{8}$ | No |
| 2nd | 4 | 8 | $\frac{4}{8}$ ✔ | Yes (✓) |
| 3rd | 2 | 8 | $\frac{2}{8}$ | No |
| 4th | 4 | 8 | $\frac{4}{8}$ ✔ | Yes (✓) |

✔ $\frac{4}{8}$ appears twice.

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#### Row 5 (Octagons – 10 parts?) Wait: Let's count!

Wait — these shapes have 10 sections? Let’s check:

- First octagon: 10 segments → shaded = 5
- Second: shaded = 2 → total = 10
- Third: shaded = 5 → total = 10
- Fourth: shaded = 5 → total = 10

So yes, they're divided into 10 equal parts.

| Shape | Shaded | Total | Fraction | Equivalent to ½? |
|-------|--------|-------|----------|------------------|
| 1st | 5 | 10 | $\frac{5}{10}$ ✔ | Yes (✓) |
| 2nd | 2 | 10 | $\frac{2}{10}$ | No |
| 3rd | 5 | 10 | $\frac{5}{10}$ ✔ | Yes (✓) |
| 4th | 5 | 10 | $\frac{5}{10}$ ✔ | Yes (✓) |

✔ $\frac{5}{10}$ appears three times.

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#### Row 6 (Grids: 9 squares)

Each grid is $3 \times 3$ → 9 total squares.

| Shape | Shaded | Total | Fraction | Equivalent to ½? |
|-------|--------|-------|----------|------------------|
| 1st | 5 | 9 | $\frac{5}{9}$ | No |
| 2nd | 6 | 9 | $\frac{6}{9}$ | No (6/9 = 2/3)
| 3rd | 6 | 9 | $\frac{6}{9}$ | No |
| 4th | 4 | 9 | $\frac{4}{9}$ | No |

None of these are equivalent to $\frac{1}{2}$.
(We’d need 4.5 shaded — not possible.)

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Now, collect all fractions equivalent to $\frac{1}{2}$:

From above:

- $\frac{2}{4}$
- $\frac{3}{6}$
- $\frac{4}{8}$
- $\frac{5}{10}$

Note: These are all equivalent to $\frac{1}{2}$ because:

- $\frac{2}{4} = \frac{1}{2}$
- $\frac{3}{6} = \frac{1}{2}$
- $\frac{4}{8} = \frac{1}{2}$
- $\frac{5}{10} = \frac{1}{2}$

These can be simplified to $\frac{1}{2}$.

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Final Answers:

#### ✔ Write all the fractions from above that are equivalent to $\frac{1}{2}$:

$$
\frac{2}{4},\ \frac{3}{6},\ \frac{4}{8},\ \frac{5}{10}
$$

> (Note: Even though some appear multiple times, we list them once.)

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#### ✔ What do you notice?

> All these fractions simplify to $\frac{1}{2}$.
> The numerator is always half of the denominator.
> That is:
> $$
> \frac{2}{4} = \frac{1}{2},\quad \frac{3}{6} = \frac{1}{2},\quad \frac{4}{8} = \frac{1}{2},\quad \frac{5}{10} = \frac{1}{2}
> $$
> So, when the numerator is half the denominator, the fraction equals $\frac{1}{2}$.

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✔ Final Answer Summary:

Fractions equivalent to $\frac{1}{2}$:
$$
\boxed{\frac{2}{4},\ \frac{3}{6},\ \frac{4}{8},\ \frac{5}{10}}
$$

What do you notice?
$$
\boxed{\text{All these fractions have numerators that are half of their denominators.}}
$$

This shows that **any fraction where the numerator is half the denominator is equivalent to } \frac{1}{2}.