Math Worksheets: Reducing Fractions: Reducing Fractions: Reducing ... - Free Printable

The image you've uploaded is an answer key for a math worksheet titled "Reducing Mixed Fractions 1 – Simplest Form". It shows how to reduce mixed fractions (a whole number plus a fraction) to their simplest form.

Let’s go through each problem step by step and explain the process of reducing mixed fractions to their simplest form.

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🔍 What does "simplest form" mean?

A fraction is in simplest form when the numerator and denominator have no common factors other than 1. This means we divide both the numerator and denominator by their greatest common divisor (GCD).

For mixed numbers, we only simplify the fractional part, not the whole number.

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✔ Step-by-step Solutions:

#### 1. $ 4 \frac{10}{15} $
- Fraction: $ \frac{10}{15} $
- GCD of 10 and 15 = 5
- Divide numerator and denominator by 5:
$$
\frac{10 \div 5}{15 \div 5} = \frac{2}{3}
$$
- Result: $ 4 \frac{2}{3} $

✔ Answer: $ 4 \frac{2}{3} $

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#### 2. $ 3 \frac{4}{8} $
- Fraction: $ \frac{4}{8} $
- GCD of 4 and 8 = 4
- $ \frac{4 \div 4}{8 \div 4} = \frac{1}{2} $
- Result: $ 3 \frac{1}{2} $

✔ Answer: $ 3 \frac{1}{2} $

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#### 3. $ 3 \frac{4}{6} $
- Fraction: $ \frac{4}{6} $
- GCD of 4 and 6 = 2
- $ \frac{4 \div 2}{6 \div 2} = \frac{2}{3} $
- Result: $ 3 \frac{2}{3} $

✔ Answer: $ 3 \frac{2}{3} $

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#### 4. $ 3 \frac{6}{8} $
- Fraction: $ \frac{6}{8} $
- GCD of 6 and 8 = 2
- $ \frac{6 \div 2}{8 \div 2} = \frac{3}{4} $
- Result: $ 3 \frac{3}{4} $

✔ Answer: $ 3 \frac{3}{4} $

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#### 5. $ 3 \frac{4}{12} $
- Fraction: $ \frac{4}{12} $
- GCD of 4 and 12 = 4
- $ \frac{4 \div 4}{12 \div 4} = \frac{1}{3} $
- Result: $ 3 \frac{1}{3} $

✔ Answer: $ 3 \frac{1}{3} $

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#### 6. $ 3 \frac{5}{10} $
- Fraction: $ \frac{5}{10} $
- GCD of 5 and 10 = 5
- $ \frac{5 \div 5}{10 \div 5} = \frac{1}{2} $
- Result: $ 3 \frac{1}{2} $

✔ Answer: $ 3 \frac{1}{2} $

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#### 7. $ 3 \frac{3}{12} $
- Fraction: $ \frac{3}{12} $
- GCD of 3 and 12 = 3
- $ \frac{3 \div 3}{12 \div 3} = \frac{1}{4} $
- Result: $ 3 \frac{1}{4} $

✔ Answer: $ 3 \frac{1}{4} $

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#### 8. $ 1 \frac{9}{12} $
- Fraction: $ \frac{9}{12} $
- GCD of 9 and 12 = 3
- $ \frac{9 \div 3}{12 \div 3} = \frac{3}{4} $
- Result: $ 1 \frac{3}{4} $

✔ Answer: $ 1 \frac{3}{4} $

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#### 9. $ 1 \frac{15}{20} $
- Fraction: $ \frac{15}{20} $
- GCD of 15 and 20 = 5
- $ \frac{15 \div 5}{20 \div 5} = \frac{3}{4} $
- Result: $ 1 \frac{3}{4} $

✔ Answer: $ 1 \frac{3}{4} $

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#### 10. $ 3 \frac{3}{6} $
- Fraction: $ \frac{3}{6} $
- GCD of 3 and 6 = 3
- $ \frac{3 \div 3}{6 \div 3} = \frac{1}{2} $
- Result: $ 3 \frac{1}{2} $

✔ Answer: $ 3 \frac{1}{2} $

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📌 Summary of Key Steps:

1. Identify the fractional part of the mixed number.
2. Find the greatest common divisor (GCD) of the numerator and denominator.
3. Divide both the numerator and denominator by the GCD.
4. Write the simplified fraction back with the same whole number.

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✔ Final Answers (as shown in the key):

| Original | Simplified |
|--------|------------|
| $ 4 \frac{10}{15} $ | $ 4 \frac{2}{3} $ |
| $ 3 \frac{4}{8} $ | $ 3 \frac{1}{2} $ |
| $ 3 \frac{4}{6} $ | $ 3 \frac{2}{3} $ |
| $ 3 \frac{6}{8} $ | $ 3 \frac{3}{4} $ |
| $ 3 \frac{4}{12} $ | $ 3 \frac{1}{3} $ |
| $ 3 \frac{5}{10} $ | $ 3 \frac{1}{2} $ |
| $ 3 \frac{3}{12} $ | $ 3 \frac{1}{4} $ |
| $ 1 \frac{9}{12} $ | $ 1 \frac{3}{4} $ |
| $ 1 \frac{15}{20} $ | $ 1 \frac{3}{4} $ |
| $ 3 \frac{3}{6} $ | $ 3 \frac{1}{2} $ |

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This worksheet helps students practice simplifying fractions by identifying common factors and reducing them correctly — a fundamental skill in working with fractions! 🎯

Let me know if you'd like a printable version or want to create your own problems!