32/25 simplified
Understand the Problem
The question is asking to simplify the fraction 32/25 to its lowest terms, which involves finding the greatest common divisor (GCD) of the numerator and denominator.
Answer
The simplified fraction is $\frac{32}{25}$.
Answer for screen readers
The simplified fraction is $\frac{32}{25}$.
Steps to Solve
- Find the GCD of 32 and 25
To simplify the fraction, we first need to determine the greatest common divisor (GCD) of the numbers 32 and 25. The GCD is the largest number that divides both of them without leaving a remainder.
- 32 can be factored as: $32 = 2^5$
- 25 can be factored as: $25 = 5^2$
Since 32 and 25 have no common factors (other than 1), we find that:
$$ GCD(32, 25) = 1 $$
- Divide both numerator and denominator by GCD
Now that we have the GCD, we can simplify the fraction by dividing both the numerator (32) and the denominator (25) by their GCD (1).
$$ \frac{32}{25} = \frac{32 \div 1}{25 \div 1} = \frac{32}{25} $$
- Conclusion of simplification
Since the GCD is 1, the fraction remains the same. Thus, the fraction $\frac{32}{25}$ is already in its lowest terms.
The simplified fraction is $\frac{32}{25}$.
More Information
The fraction $\frac{32}{25}$ is an example of an improper fraction since the numerator is greater than the denominator. It can also be written as a mixed number, which would be $1 \frac{7}{25}$.
Tips
A common mistake is to incorrectly identify the GCD by assuming that two numbers share a common factor, leading to wrongly simplifying the fraction. To avoid this, always verify the prime factorization or use the Euclidean algorithm to find the GCD.
