To determine which answer choice represents a ratio equal to [tex]\(27:81\)[/tex], we need to simplify the ratio [tex]\(27:81\)[/tex].
Step 1: Identify the greatest common divisor (GCD) of 27 and 81. The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
Step 2: The GCD of 27 and 81 is 27 (since 27 is a factor of both 27 and 81).
Step 3: Simplify the ratio [tex]\(27:81\)[/tex] by dividing both the numerator and the denominator by their GCD.
[tex]\[
\frac{27}{27} = 1
\][/tex]
[tex]\[
\frac{81}{27} = 3
\][/tex]
So, the simplified form of the ratio [tex]\(27:81\)[/tex] is [tex]\(1:3\)[/tex].
Now, let's compare this simplified ratio to the answer choices:
A. [tex]\(1:9\)[/tex]
B. [tex]\(2:9\)[/tex]
C. [tex]\(3:9\)[/tex]
D. [tex]\(3:27\)[/tex]
E. [tex]\(9:12\)[/tex]
The correct answer that matches the simplified ratio [tex]\(1:3\)[/tex] is not explicitly listed in the format [tex]\(1:3\)[/tex]. However, since [tex]\(1:3\)[/tex] is equivalent to none of the given options, it seems there might be an error in the provided choices. Based on the provided data and typical ratio simplification, we can confirm that the simplified form should be [tex]\(1:3\)[/tex]. None of the listed options are a match, indicating there might be a mistake in the given options.
