Fractions Equivalent to One Half | 4th Grade PDF Number and ... - Free Printable

Let's solve this step-by-step.

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🔍 Understanding the Task

We are asked to:
1. Write down the fraction of each shape that is shaded.
2. Check (✓) any fraction that is equivalent to ½.
3. List all fractions equivalent to ½ at the bottom.
4. Answer: *What do you notice?*

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✔ Step 1: Understand Equivalent Fractions

A fraction is equivalent to ½ if it simplifies to ½.

For example:
- $ \frac{2}{4} = \frac{1}{2} $
- $ \frac{3}{6} = \frac{1}{2} $
- $ \frac{4}{8} = \frac{1}{2} $

So, we need to find shapes where half of the parts are shaded, regardless of how many total parts there are.

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Now let’s go through each shape and determine the shaded fraction.

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🧮 Section A: Analyze Each Shape

We’ll go row by row.

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#### Row 1: Squares divided into 4 parts

1. Example:
- Shaded: 2 out of 4 → $ \frac{2}{4} $ → ✓ (equivalent to ½)

2. Second shape:
- 1 shaded out of 4 → $ \frac{1}{4} $ → ✘

3. Third shape:
- 3 shaded out of 4 → $ \frac{3}{4} $ → ✘

4. Fourth shape:
- 2 shaded out of 4 → $ \frac{2}{4} $ → ✓

✔ So far: $ \frac{2}{4} $, $ \frac{2}{4} $

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#### Row 2: Rectangles divided into 6 parts

1. First shape:
- 3 shaded out of 6 → $ \frac{3}{6} $ → ✓ (since $ \frac{3}{6} = \frac{1}{2} $)

2. Second shape:
- 2 shaded out of 6 → $ \frac{2}{6} $ → ✘

3. Third shape:
- 1 shaded out of 6 → $ \frac{1}{6} $ → ✘

4. Fourth shape:
- 3 shaded out of 6 → $ \frac{3}{6} $ → ✓

✔ $ \frac{3}{6} $, $ \frac{3}{6} $

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#### Row 3: Hexagons (6 equal parts)

1. First shape:
- 3 shaded out of 6 → $ \frac{3}{6} $ → ✓

2. Second shape:
- 4 shaded out of 6 → $ \frac{4}{6} $ → ✘

3. Third shape:
- 1 shaded out of 6 → $ \frac{1}{6} $ → ✘

4. Fourth shape:
- 3 shaded out of 6 → $ \frac{3}{6} $ → ✓

✔ $ \frac{3}{6} $, $ \frac{3}{6} $

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#### Row 4: Circles divided into 8 parts

1. First shape:
- 2 shaded out of 8 → $ \frac{2}{8} $ → ✓ ($ \frac{2}{8} = \frac{1}{4} $? Wait — no! $ \frac{2}{8} = \frac{1}{4} $ → ✘)

Actually: $ \frac{2}{8} = \frac{1}{4} $ → Not ½ → ✘

2. Second shape:
- 4 shaded out of 8 → $ \frac{4}{8} $ → ✓ ($ \frac{4}{8} = \frac{1}{2} $)

3. Third shape:
- 2 shaded out of 8 → $ \frac{2}{8} $ → ✘

4. Fourth shape:
- 4 shaded out of 8 → $ \frac{4}{8} $ → ✓

✔ $ \frac{4}{8} $, $ \frac{4}{8} $

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#### Row 5: Octagons (8 parts)

1. First shape:
- 4 shaded out of 8 → $ \frac{4}{8} $ → ✓

2. Second shape:
- 2 shaded out of 8 → $ \frac{2}{8} $ → ✘

3. Third shape:
- 4 shaded out of 8 → $ \frac{4}{8} $ → ✓

4. Fourth shape:
- 4 shaded out of 8 → $ \frac{4}{8} $ → ✓

✔ $ \frac{4}{8} $, $ \frac{4}{8} $, $ \frac{4}{8} $

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#### Row 6: Grids (3×3 = 9 parts)

1. First shape:
- Count shaded squares:
Let’s count:
Row 1: 2 shaded
Row 2: 2 shaded
Row 3: 2 shaded → Total = 6 shaded out of 9 → $ \frac{6}{9} $ → simplify: $ \frac{2}{3} $ → ✘

2. Second shape:
- Left column: 3 shaded
Middle column: 3 shaded
Right column: 0 → Total = 6 shaded → $ \frac{6}{9} $ → same as above → ✘

3. Third shape:
- Top two rows fully shaded: 2 × 3 = 6
Bottom row: 3 shaded → total = 9 → $ \frac{9}{9} $ → ✘

4. Fourth shape:
- 3 full columns shaded? No:
First column: 3 shaded
Second: 3 shaded
Third: 3 shaded → total = 9 → $ \frac{9}{9} $ → ✘

Wait — actually:

Let’s look again.

Actually, fourth shape:
- It's a 3×3 grid.
- Shaded: top-left 2×2 block → 4 shaded
- So $ \frac{4}{9} $ → ✘

But wait — let's double-check each one carefully.

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Wait — let’s re-analyze Row 6:

Each grid is 3×3 = 9 squares.

1. First shape:
- Shaded:
Row 1: 2
Row 2: 2
Row 3: 2 → total = 6 → $ \frac{6}{9} = \frac{2}{3} $ → ✘

2. Second shape:
- Left column: 3 shaded
Middle column: 3 shaded
Right: 0 → total = 6 → $ \frac{6}{9} $ → ✘

3. Third shape:
- Top two rows: all shaded → 2 × 3 = 6
Bottom row: all shaded → 3 → total = 9 → $ \frac{9}{9} $ → ✘

4. Fourth shape:
- Only top-left 2×2 block shaded → 4 shaded → $ \frac{4}{9} $ → ✘

So none in row 6 are equivalent to ½.

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✔ Final List of Fractions Equivalent to ½

From above:

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

Wait — but we only need to write the fractions that are equivalent to ½.

But since some are repeated, list unique ones or just list all that are equivalent.

But the instruction says:
> "Write all the fractions from above that are equivalent to ½"

So write them as they appear.

But note: we don’t have to repeat unless required. But since the question asks for *all* fractions from above that are equivalent, we should list each one.

But actually, we can list the distinct ones.

But let’s be careful.

Looking back at the worksheet, we are to check the boxes next to each shape.

So for each shape, we write the fraction and check if it equals ½.

Let’s now list all fractions that are equivalent to ½.

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✔ All Shapes That Are Equivalent to ½

| Shape | Fraction | Equivalent to ½? |
|-------|---------|------------------|
| 1st (example) | $ \frac{2}{4} $ | ✓ |
| 4th (row 1) | $ \frac{2}{4} $ | ✓ |
| 1st (row 2) | $ \frac{3}{6} $ | ✓ |
| 4th (row 2) | $ \frac{3}{6} $ | ✓ |
| 1st (row 3) | $ \frac{3}{6} $ | ✓ |
| 4th (row 3) | $ \frac{3}{6} $ | ✓ |
| 2nd (row 4) | $ \frac{4}{8} $ | ✓ |
| 4th (row 4) | $ \frac{4}{8} $ | ✓ |
| 1st (row 5) | $ \frac{4}{8} $ | ✓ |
| 3rd (row 5) | $ \frac{4}{8} $ | ✓ |
| 4th (row 5) | $ \frac{4}{8} $ | ✓ |

So total of 11 shapes are equivalent to ½.

But the fractions are:

- $ \frac{2}{4} $ → appears twice
- $ \frac{3}{6} $ → appears four times
- $ \frac{4}{8} $ → appears five times

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✔ Step 2: Write Down the Fractions Equivalent to ½

So we write:

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

Or, if listing unique ones:

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

But since the question says "all the fractions from above", it likely wants all instances.

But typically, in such worksheets, they expect the distinct fractions.

Let’s see the wording:
> "Write all the fractions from above that are equivalent to ½"

So if multiple shapes have the same fraction, we may write it multiple times.

But usually, we list distinct ones.

To be safe, we can write:

> $ \frac{2}{4},\ \frac{3}{6},\ \frac{4}{8} $

Because these are the different fractions that equal ½.

But let’s verify:
- $ \frac{2}{4} = \frac{1}{2} $ ✔
- $ \frac{3}{6} = \frac{1}{2} $ ✔
- $ \frac{4}{8} = \frac{1}{2} $ ✔

All good.

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✔ What Do You Notice?

Answer:
All the fractions that are equivalent to $ \frac{1}{2} $ have numerators that are exactly half of their denominators.

Or:

> The numerator is always half of the denominator.

Or:

> These fractions all simplify to $ \frac{1}{2} $.

Or:

> When the number of shaded parts is half the total number of parts, the fraction is equivalent to $ \frac{1}{2} $.

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✔ Final Answers

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#### Fractions equivalent to ½:

$$
\boxed{\frac{2}{4},\ \frac{3}{6},\ \frac{4}{8}}
$$

(These are the distinct fractions that appear and are equivalent to ½.)

Alternatively, if repeating is required, list all 11, but that seems redundant.

Most likely, they want the unique fractions.

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#### What do you notice?

> I notice that all these fractions represent the same amount — half of the whole. Even though the numbers are different, they all simplify to $ \frac{1}{2} $. Also, in each case, the numerator is half the denominator.

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✔ Summary of Checked Boxes

You would check the boxes next to:

- Row 1: 1st and 4th
- Row 2: 1st and 4th
- Row 3: 1st and 4th
- Row 4: 2nd and 4th
- Row 5: 1st, 3rd, 4th
- Row 6: none

So 11 shapes checked.

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✔ Final Answer Boxed

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

> What do you notice?
> $$
> \boxed{\text{They all simplify to } \frac{1}{2} \text{ because the numerator is half the denominator.}}
> $$

Let me know if you'd like a printable version with checks filled in!