4th Grade Fractions Math Notes by Teach Simple - Free Printable

Let's solve the "Equivalent Fractions with Models" worksheet step by step, explaining each problem and how to find equivalent fractions using visual models.

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🔍 Understanding the Concept: Equivalent Fractions

Equivalent fractions are different fractions that represent the same amount. For example, ½ and 2/4 are equivalent because they both represent half of a whole.

In this worksheet, we use area models (rectangles divided into parts) to show how fractions can be rewritten as equivalent ones by dividing or subdividing the model.

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## ✔ Teacher Problem: Example
- Original: 2/4
- New: 4/8

📌 How it works:

1. Start with a rectangle divided into 4 equal parts, 2 shaded → 2/4.
2. Break each of the 4 parts into 2 horizontal parts → now you have 8 total parts.
3. The 2 shaded parts become 4 shaded smaller parts.
4. So, 2/4 becomes 4/8.

✔ This shows:
2/4 = 4/8

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## 🔧 How to Solve Any Problem: Step-by-Step
1. Draw the original fraction on a grid.
2. Break each part into more pieces (usually horizontally or vertically).
3. Count the new total number of parts and the new number of shaded parts.
4. Write the new fraction.

Now let’s go through each problem.

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## 🟦 Buddy Problem #1
- Original: 1/4
- New: 2/8

🔍 Visual:

- A rectangle is split into 4 equal squares (2 rows × 2 columns), 1 shaded → 1/4.
- Then, each square is broken into 2 horizontal parts → now there are 8 small rectangles.
- The one shaded square becomes 2 shaded small parts.
- So, 1/4 = 2/8

✔ Correct!

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## 🟨 Buddy Problem #2
- Original: 2/2
- New: 4/4

🔍 Visual:

- A rectangle is split into 2 equal parts, both shaded → 2/2 = 1 whole.
- Each part is split into 2 horizontal parts → now 4 total parts, all shaded → 4/4.
- Since 2/2 = 1 and 4/4 = 1, they are equivalent.

✔ Correct!

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## 🟩 Independent Problem #1
- Original: 2/8
- New: 4/16

🔍 Visual:

- Rectangle divided into 8 parts (say, 2 rows × 4 columns), 2 shaded → 2/8.
- Now, break each of the 8 parts into 2 smaller parts → total parts = 16.
- The 2 shaded parts become 4 shaded smaller parts.
- So, 2/8 becomes 4/16.

✔ Correct!
2/8 = 4/16 (both simplify to 1/4)

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## 🟪 Independent Problem #2
- Original: 7/12
- New: 14/24

🔍 Visual:

- Rectangle divided into 12 parts (e.g., 3 rows × 4 columns), 7 shaded → 7/12.
- Now, each part is split into 2 smaller parts → total parts = 24.
- The 7 shaded parts become 14 shaded smaller parts.
- So, 7/12 becomes 14/24.

✔ Correct!
7/12 = 14/24 (both simplify to the same value)

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## ✔ Summary: All Problems Are Correct!

| Problem | Original | New | Equivalent? |
|--------|----------|-----|-------------|
| Teacher | 2/4 | 4/8 | ✔ Yes |
| Buddy #1 | 1/4 | 2/8 | ✔ Yes |
| Buddy #2 | 2/2 | 4/4 | ✔ Yes |
| Indep. #1 | 2/8 | 4/16 | ✔ Yes |
| Indep. #2 | 7/12 | 14/24 | ✔ Yes |

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## 🎯 Key Takeaway:
To create an equivalent fraction using models:
> Multiply both numerator and denominator by the same number (here, usually 2) — this matches the visual doubling of parts.

For example:
- 2/4 → multiply numerator and denominator by 2 → (2×2)/(4×2) = 4/8
- 7/12 → 7×2 / 12×2 = 14/24

This method ensures the value stays the same, just represented in more parts.

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✔ Final Answer: All given equivalent fractions are correct!
Each transformation follows the rule of multiplying numerator and denominator by 2, which matches the visual splitting of each piece into two smaller parts.