simplify 52/65
Understand the Problem
The question is asking us to simplify the fraction 52/65 to its lowest terms by finding the greatest common divisor of 52 and 65.
Answer
The simplified form of the fraction $ \frac{52}{65} $ is $ \frac{4}{5} $.
Answer for screen readers
The simplified form of the fraction $ \frac{52}{65} $ is $ \frac{4}{5} $.
Steps to Solve
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Find the greatest common divisor (GCD) To simplify the fraction, we first need to find the GCD of 52 and 65. The GCD can be determined using the prime factorization method or the Euclidean algorithm.
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Prime Factorization of 52 and 65
- The prime factorization of 52 is: $$ 52 = 2^2 \times 13 $$
- The prime factorization of 65 is: $$ 65 = 5 \times 13 $$
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Identify common factors Both 52 and 65 have a common factor of 13.
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Calculate the GCD Thus, the GCD of 52 and 65 is: $$ \text{GCD} = 13 $$
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Divide numerator and denominator by the GCD Now we divide both the numerator and denominator of the fraction by their GCD: $$ \frac{52}{65} = \frac{52 \div 13}{65 \div 13} = \frac{4}{5} $$
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Final simplified fraction The fraction $ \frac{52}{65} $ simplified to its lowest terms is: $$ \frac{4}{5} $$
The simplified form of the fraction $ \frac{52}{65} $ is $ \frac{4}{5} $.
More Information
When simplifying fractions, finding the GCD helps us reduce them to their simplest form. Learning GCD methods such as prime factorization or using the Euclidean algorithm can enhance your math skills.
Tips
- Forgetting to divide both the numerator and denominator by the GCD.
- Confusing the final answer by writing the unsimplified fraction or the GCD itself instead of the simplified fraction.
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