Fractions in Simplest Form Worksheet and Answer Guide by ... - Free Printable

You’ve uploaded an Answer Sheet that shows 20 fraction simplification problems, with the answers already filled in. Since you asked to “solve the problem and explain the solution,” I’ll assume you want me to:

✔ Verify each answer
✔ Explain how to simplify each fraction (step-by-step for a few examples)
✔ Confirm whether all answers are correct

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## ✔ OVERALL VERDICT:
All 20 answers on the sheet are CORRECT.

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## 🔍 HOW TO SIMPLIFY A FRACTION (General Rule):

To write a fraction in simplest form, divide both the numerator and denominator by their Greatest Common Factor (GCF) — the largest number that divides both evenly.

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## 📚 EXAMPLE EXPLANATIONS (for selected problems):

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Problem 1: ³⁄₉ → ¹⁄₃

- GCF of 3 and 9 is 3
- Divide numerator and denominator by 3:
3 ÷ 3 = 1
9 ÷ 3 = 3
→ ¹⁄₃ ✔

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Problem 2: ²¹⁄₅₄ → ⁷⁄₁₈

- GCF of 21 and 54?
Factors of 21: 1, 3, 7, 21
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
→ GCF = 3
- 21 ÷ 3 = 7
- 54 ÷ 3 = 18
→ ⁷⁄₁₈ ✔

*(Note: Some might think 7 and 18 have a common factor, but 7 is prime and doesn’t divide 18 — so this is simplified.)*

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Problem 3: ³⁄₁₂ → ¹⁄₄

- GCF of 3 and 12 = 3
- 3 ÷ 3 = 1
- 12 ÷ 3 = 4
→ ¹⁄₄ ✔

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Problem 4: ⁶⁄₃₀ → ¹⁄₅

- GCF of 6 and 30 = 6
- 6 ÷ 6 = 1
- 30 ÷ 6 = 5
→ ¹⁄₅ ✔

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Problem 5: ⁸⁄₁₂ → ²⁄₃

- GCF of 8 and 12 = 4
- 8 ÷ 4 = 2
- 12 ÷ 4 = 3
→ ²⁄₃ ✔

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Problem 6: ¹⁵⁄₃₀ → ¹⁄₂

- GCF = 15
- 15 ÷ 15 = 1
- 30 ÷ 15 = 2
→ ¹⁄₂ ✔

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Problem 7: ⁴⁄₁₀ → ²⁄₅

- GCF = 2
- 4 ÷ 2 = 2
- 10 ÷ 2 = 5
→ ²⁄₅ ✔

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Problem 8: ⁷⁄₁₄ → ¹⁄₂

- GCF = 7
- 7 ÷ 7 = 1
- 14 ÷ 7 = 2
→ ¹⁄₂ ✔

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Problem 9: ²⁄₁₂ → ¹⁄₆

- GCF = 2
- 2 ÷ 2 = 1
- 12 ÷ 2 = 6
→ ¹⁄₆ ✔

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Problem 10: ¹⁶⁄₂₄ → ²⁄₃

- GCF = 8
- 16 ÷ 8 = 2
- 24 ÷ 8 = 3
→ ²⁄₃ ✔

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Problem 11: ¹²⁄₁₅ → ⁴⁄₅

- GCF = 3
- 12 ÷ 3 = 4
- 15 ÷ 3 = 5
→ ⁴⁄₅ ✔

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Problem 12: ⁹⁄₁₅ → ³⁄₅

- GCF = 3
- 9 ÷ 3 = 3
- 15 ÷ 3 = 5
→ ³⁄₅ ✔

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Problem 13: ⁶⁄₁₈ → ¹⁄₃

- GCF = 6
- 6 ÷ 6 = 1
- 18 ÷ 6 = 3
→ ¹⁄₃ ✔

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Problem 14: ¹²⁄₂₀ → ³⁄₅

- GCF = 4
- 12 ÷ 4 = 3
- 20 ÷ 4 = 5
→ ³⁄₅ ✔

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Problem 15: ²⁄₈ → ¹⁄₄

- GCF = 2
- 2 ÷ 2 = 1
- 8 ÷ 2 = 4
→ ¹⁄₄ ✔

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Problem 16: ¹¹⁄₃₃ → ¹⁄₃

- GCF = 11
- 11 ÷ 11 = 1
- 33 ÷ 11 = 3
→ ¹⁄₃ ✔

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Problem 17: ¹²⁄₄₈ → ¹⁄₄

- GCF = 12
- 12 ÷ 12 = 1
- 48 ÷ 12 = 4
→ ¹⁄₄ ✔

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Problem 18: ²⁰⁄₃₀ → ²⁄₃

- GCF = 10
- 20 ÷ 10 = 2
- 30 ÷ 10 = 3
→ ²⁄₃ ✔

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Problem 19: ¹⁸⁄₂⁷ → ²⁄₃

- GCF = 9
- 18 ÷ 9 = 2
- 27 ÷ 9 = 3
→ ²⁄₃ ✔

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Problem 20: ²¹⁄₆₃ → ¹⁄₃

- GCF = 21
- 21 ÷ 21 = 1
- 63 ÷ 21 = 3
→ ¹⁄₃ ✔

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## ✔ FINAL CHECK:

All 20 problems were solved correctly using the standard method of dividing numerator and denominator by their GCF.

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## 💡 TEACHING TIP:

When teaching fraction simplification, encourage students to:

- List factors or use prime factorization to find GCF
- Check if the resulting fraction can be simplified further (e.g., after simplifying ⁶⁄₈ to ³⁄₄, check if 3 and 4 have any common factors — they don’t, so it’s done)
- Practice with visual models (like pie charts or grids) to reinforce understanding

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✔ Conclusion: The answer sheet is 100% accurate. All fractions are written in simplest form correctly.

Let me know if you’d like printable worksheets, practice problems, or video-style explanations!