Simplifying Fractions worksheet with matching exercise and challenge question.

Let’s solve this “Simplifying Fractions” worksheet step by step.

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## 🎯 Goal:
Simplify each fraction on the LEFT and each fraction on the RIGHT to its simplest form, then match them by drawing a line between equivalent fractions.

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## ✔ Step 1: Simplify the LEFT column

1. ⁴⁄₆

- GCF of 4 and 6 is 2.
- Divide numerator and denominator by 2 → ⁴⁄₆ = ²⁄₃

2. ²⁄₆

- GCF of 2 and 6 is 2.
- ²⁄₆ = ¹⁄₃

3. ⁴⁄₈

- GCF of 4 and 8 is 4.
- ⁴⁄₈ = ¹⁄₂

4. ⁶⁄₈

- GCF of 6 and 8 is 2.
- ⁶⁄₈ = ³⁄₄

5. ¹⁰⁄₁₅

- GCF of 10 and 15 is 5.
- ¹⁰⁄₁₅ = ²⁄₃

6. ³⁄₁₂

- GCF of 3 and 12 is 3.
- ³⁄₁₂ = ¹⁄₄

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## ✔ Step 2: Simplify the RIGHT column

A. ²⁄₈

- GCF of 2 and 8 is 2.
- ²⁄₈ = ¹⁄₄

B. ⁸⁄₁₀

- GCF of 8 and 10 is 2.
- ⁸⁄₁₀ = ⁴⁄₅

C. ⁹⁄₁₂

- GCF of 9 and 12 is 3.
- ⁹⁄₁₂ = ³⁄₄

D. ²⁄₄

- GCF of 2 and 4 is 2.
- ²⁄₄ = ¹⁄₂

E. ³⁄₉

- GCF of 3 and 9 is 3.
- ³⁄₉ = ¹⁄₃

F. ⁴⁄₆

- GCF of 4 and 6 is 2.
- ⁴⁄₆ = ²⁄₃

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## ✔ Step 3: Match Equivalent Fractions

Now, let’s pair up the simplified forms:

| Left (simplified) | Right (simplified) | Match |
|-------------------|--------------------|-------|
| 1. ⁴⁄₆ → ²⁄₃ | F. ⁴⁄₆ → ²⁄₃ | ✔ 1 — F |
| 2. ²⁄₆ → ¹⁄₃ | E. ³⁄₉ → ¹⁄₃ | ✔ 2 — E |
| 3. ⁴⁄₈ → ¹⁄₂ | D. ²⁄₄ → ¹⁄₂ | ✔ 3 — D |
| 4. ⁶⁄₈ → ³⁄₄ | C. ⁹⁄₁₂ → ³⁄₄ | ✔ 4 — C |
| 5. ¹⁰⁄₁₅ → ²⁄₃ | F. ⁴⁄₆ → ²⁄₃ | ✔ 5 — F *(Note: same as #1)* |
| 6. ³⁄₁₂ → ¹⁄₄ | A. ²⁄₈ → ¹⁄₄ | ✔ 6 — A |

> 💡 Note: Both #1 and #5 simplify to ²⁄₃, so they both match with F (which also simplifies to ²⁄₃). That’s why it’s called a “Triple Match Challenge” — one answer on the right can match more than one on the left!

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## 🧠 Triple Match Challenge:

> *“The fractions ⁴⁄₆ and ¹⁰⁄₁₅ are equivalent. When put in simplest form, what do they equal?”*

We already found:
- ⁴⁄₆ = ²⁄₃
- ¹⁰⁄₁₅ = ²⁄₃

✔ So, they both equal ²⁄₃

> *Circle the answers that match above.*

→ Circle F (since F = ⁴⁄₆ = ²⁄₃), and also note that 1 and 5 on the left both match F.

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## ✍️ Final Answers to Fill In:

LEFT COLUMN:

1. ⁴⁄₆ = ²⁄₃
2. ²⁄₆ = ¹⁄₃
3. ⁴⁄₈ = ¹⁄₂
4. ⁶⁄₈ = ³⁄₄
5. ¹⁰⁄₁₅ = ²⁄₃
6. ³⁄₁₂ = ¹⁄₄

RIGHT COLUMN:

A. ²⁄₈ = ¹⁄₄
B. ⁸⁄₁₀ = ⁴⁄₅
C. ⁹⁄₁₂ = ³⁄₄
D. ²⁄₄ = ¹⁄₂
E. ³⁄₉ = ¹⁄₃
F. ⁴⁄₆ = ²⁄₃

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## 🔗 Matching Lines to Draw:
- 1 → F
- 2 → E
- 3 → D
- 4 → C
- 5 → F
- 6 → A

*(You may draw two lines to F: from 1 and 5)*

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## 🏁 Triple Match Answer:
> The fractions ⁴⁄₆ and ¹⁰⁄₁₅ are equivalent. When put in simplest form, they both equal ²⁄₃.
> Circle F (and optionally note that 1 and 5 also match F).

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✔ All done! This worksheet reinforces simplifying fractions and recognizing equivalent fractions — great practice for building number sense!