To simplify the fraction \(\frac{27}{36}\), we need to find the greatest common divisor (GCD) of the numerator (27) and the denominator (36). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.
### Step 1: Identify the numerator and denominator
The given fraction is \(\frac{27}{36}\), where:
- Numerator = 27
- Denominator = 36
### Step 2: Find the GCD of 27 and 36
For this part, we determine the greatest common divisor, which is the largest number that evenly divides both 27 and 36.
### Step 3: Simplify the fraction
Once we have the GCD, we divide both the numerator and the denominator by that GCD to simplify the fraction.
Given that the GCD of 27 and 36 is 9, we can proceed with the simplification:
[tex]\[
\begin{aligned}
\text{Simplified numerator} &= \frac{27}{9} = 3, \\
\text{Simplified denominator} &= \frac{36}{9} = 4.
\end{aligned}
\][/tex]
Therefore, the fraction \(\frac{27}{36}\) simplifies to \(\frac{3}{4}\).
So, the simplified form of [tex]\(\frac{27}{36}\)[/tex] is [tex]\(\frac{3}{4}\)[/tex].
