36/52 simplified
Understand the Problem
The question is asking to simplify the fraction 36/52 to its lowest terms. This involves dividing both the numerator and denominator by their greatest common divisor.
Answer
The simplified fraction of \(\frac{36}{52}\) is \(\frac{9}{13}\).
Answer for screen readers
The simplified fraction of (\frac{36}{52}) is (\frac{9}{13}).
Steps to Solve
- Find the Greatest Common Divisor (GCD)
To simplify the fraction, we first need to find the GCD of the numerator (36) and the denominator (52).
We can do this using prime factorization:
- The prime factorization of 36 is (2^2 \times 3^2).
- The prime factorization of 52 is (2^2 \times 13).
Now, identify the common factors: The GCD is (2^2 = 4).
- Divide the Numerator and Denominator by the GCD
Now that we have the GCD, we can simplify the fraction by dividing both the numerator and the denominator by 4:
$$ \text{Numerator: } \frac{36}{4} = 9 $$
$$ \text{Denominator: } \frac{52}{4} = 13 $$
So the simplified fraction is (\frac{9}{13}).
- Write the Simplified Fraction
After performing the division, we can state the simplified fraction clearly:
The simplified form of (\frac{36}{52}) is (\frac{9}{13}).
The simplified fraction of (\frac{36}{52}) is (\frac{9}{13}).
More Information
When simplifying fractions, it is essential to find the GCD. This reduces the fraction to its simplest form, making it easier to understand. Simplifying fractions is a common mathematical skill used in various applications, such as cooking, measurements, and problem-solving in everyday life.
Tips
- Incorrectly Finding GCD: Many people make mistakes while calculating the GCD. It's important to correctly identify all prime factors.
- Failing to Simplify: After finding the GCD, some may forget to actually divide the numerator and denominator by this number.