What is 36/39 in simplest form?
Understand the Problem
The question is asking to simplify the fraction 36/39 to its simplest form by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by that number.
Answer
The simplest form of the fraction $\frac{36}{39}$ is $\frac{12}{13}$.
Answer for screen readers
The simplest form of the fraction $\frac{36}{39}$ is $\frac{12}{13}$.
Steps to Solve
- Find the GCD of 36 and 39
To simplify the fraction, we first need to determine the greatest common divisor (GCD) of the numerator (36) and the denominator (39). The GCD is the largest integer that divides both numbers without leaving a remainder.
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.
The factors of 39 are: 1, 3, 13, 39.
The common factors are: 1 and 3.
Thus, the GCD is 3.
- Divide both the numerator and denominator by the GCD
Now that we have the GCD (3), we divide both the numerator and the denominator of the fraction by this number.
For the numerator: $$ \frac{36}{3} = 12 $$
For the denominator: $$ \frac{39}{3} = 13 $$
- Write the fraction in its simplest form
Now that we have simplified both parts, we can write the fraction in its simplest form:
$$ \frac{36}{39} = \frac{12}{13} $$
The simplest form of the fraction $\frac{36}{39}$ is $\frac{12}{13}$.
More Information
When simplifying fractions, the GCD helps reduce the numbers to their smallest form. The fraction $\frac{12}{13}$ cannot be simplified further as 12 and 13 have no other common factors.
Tips
- Forgetting to find the GCD accurately. Always check the factors carefully.
- Not dividing both the numerator and the denominator, which results in an incomplete simplification.
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