27/20 simplified
Understand the Problem
The question is asking to simplify the fraction 27/20. The process involves dividing both the numerator and the denominator by their greatest common divisor (GCD). Since 27 and 20 have no common factors other than 1, the fraction is already in its simplest form.
Answer
The simplified form is \( \frac{27}{20} \).
Answer for screen readers
The simplified fraction is ( \frac{27}{20} ).
Steps to Solve
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Identify the GCD of the numbers
Since 27 and 20 have no common divisors other than 1, we determine their GCD.
The prime factorization shows:
- 27 is $3^3$
- 20 is $2^2 \times 5$
Both numbers share no common prime factors. Thus, the GCD is 1.
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Simplifying the fraction
When simplifying a fraction, divide both the numerator and the denominator by their GCD.
Since the GCD is 1:
$$ \frac{27 \div 1}{20 \div 1} = \frac{27}{20} $$
The fraction remains $\frac{27}{20}$. -
Conclusion about the fraction
The fraction $\frac{27}{20}$ is already in its simplest form, as further simplification isn't possible.
The simplified fraction is ( \frac{27}{20} ).
More Information
This fraction, ( \frac{27}{20} ), can also be expressed as a mixed number. Dividing gives ( 27 \div 20 = 1 ) with a remainder of 7, yielding ( 1 \frac{7}{20} ).
Tips
- Assuming there is a common factor without checking: Always perform the GCD calculation to confirm.
- Forgetting to divide both the numerator and denominator by the GCD: This results in an incorrect simplification.
