26/64 simplified
Understand the Problem
The question is asking to simplify the fraction 26/64 to its lowest terms. To do this, we will find the greatest common divisor (GCD) of 26 and 64 and divide both the numerator and the denominator by that number.
Answer
The simplified fraction is $\frac{13}{32}$.
Answer for screen readers
The simplified fraction of $\frac{26}{64}$ is $\frac{13}{32}$.
Steps to Solve
- Find the GCD of 26 and 64
To simplify the fraction, we first need to determine the greatest common divisor (GCD) of 26 and 64. We can do this using the method of prime factorization or the Euclidean algorithm.
The prime factorization of 26 is: $$ 26 = 2 \times 13 $$
The prime factorization of 64 is: $$ 64 = 2^6 $$
The common factors are the factors shared by both numbers. Here, the only common factor is 2.
- Divide the numerator and the denominator by the GCD
Now that we have the GCD, which is 2, we can simplify the fraction $\frac{26}{64}$ by dividing both the numerator and the denominator by 2.
$$ \frac{26 \div 2}{64 \div 2} = \frac{13}{32} $$
- Write the simplified fraction
After dividing, we get the simplified fraction: $$ \frac{13}{32} $$
The simplified fraction of $\frac{26}{64}$ is $\frac{13}{32}$.
More Information
When simplifying fractions, finding the GCD is a crucial step. In this case, we found that both 26 and 64 share the common factor of 2, allowing us to simplify the fraction effectively. This method can be used for any fraction to find its simplest form.
Tips
- Incorrect GCD Calculation: Sometimes, people might miscalculate the GCD, leading to improper simplification. To avoid this, ensure you enumerate all the factors accurately.
- Forgetting to Divide by the GCD: Some might recognize the GCD but forget to apply it to both the numerator and denominator. Make it a habit to always perform this step.
