Simplifying Proper Fractions to Lowest Terms (Harder Questions) (A) - Free Printable

It looks like you've uploaded an image of a completed worksheet titled "Simplifying Proper Fractions (A) Answers" from Math-Drills.com. This worksheet contains a list of fractions that have already been simplified to their lowest terms.

Since the worksheet is already solved, I can help explain how each fraction was simplified and provide a general guide on simplifying fractions. Let me walk you through the process with examples from the worksheet.

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🔍 How to Simplify a Fraction

To simplify a fraction to its lowest terms:
1. Find the Greatest Common Divisor (GCD) of the numerator and denominator.
2. Divide both the numerator and denominator by the GCD.
3. The result is the simplified fraction.

Let’s go over a few examples from the worksheet:

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✔ Example 1:

Problem: $ \frac{14}{21} $
- GCD of 14 and 21 is 7.
- $ \frac{14 ÷ 7}{21 ÷ 7} = \frac{2}{3} $
- ✔ Answer: $ \frac{2}{3} $

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✔ Example 2:

Problem: $ \frac{7}{287} $
- GCD of 7 and 287:
- 287 ÷ 7 = 41 → So GCD is 7.
- $ \frac{7 ÷ 7}{287 ÷ 7} = \frac{1}{41} $
- ✔ Answer: $ \frac{1}{41} $

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✔ Example 3:

Problem: $ \frac{76}{384} $
- GCD of 76 and 384:
- Prime factors:
- 76 = 2 × 2 × 19
- 384 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 2 = 2⁷ × 3
- Common factor: 4
- $ \frac{76 ÷ 4}{384 ÷ 4} = \frac{19}{96} $
- ✔ Answer: $ \frac{19}{96} $

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✔ Example 4:

Problem: $ \frac{4}{44} $
- GCD of 4 and 44 is 4.
- $ \frac{4 ÷ 4}{44 ÷ 4} = \frac{1}{11} $
- ✔ Answer: $ \frac{1}{11} $

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✔ Example 5:

Problem: $ \frac{203}{350} $
- GCD of 203 and 350:
- 203 = 7 × 29
- 350 = 2 × 5² × 7
- Common factor: 7
- $ \frac{203 ÷ 7}{350 ÷ 7} = \frac{29}{50} $
- ✔ Answer: $ \frac{29}{50} $

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🧠 Tips for Finding GCD Quickly:

- Use prime factorization.
- Or use the Euclidean algorithm (especially for large numbers).
- If one number divides evenly into the other, the smaller number is the GCD (if it divides).

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🔁 General Rule:

If the numerator and denominator share a common factor greater than 1, divide both by that factor until no more common factors exist.

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❗ Important Note:

All answers in your worksheet are correct, as they show proper simplification. For example:
- $ \frac{100}{450} = \frac{2}{9} $ → GCD is 50 → $ 100÷50 = 2 $, $ 450÷50 = 9 $
- $ \frac{155}{225} = \frac{31}{45} $ → GCD is 5 → $ 155÷5=31 $, $ 225÷5=45 $

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✔ Final Thoughts:

This worksheet is designed to practice reducing fractions using division by the GCD. It's a foundational skill in arithmetic and algebra.

Would you like me to:
- Generate a similar worksheet?
- Explain how to find GCD using prime factorization or Euclidean algorithm?
- Create a step-by-step solution for any specific problem?

Let me know!