To solve the given math problem step-by-step, let's break it down and simplify each part of the expression separately before combining them.
1. Simplify [tex]\(23 / 4\)[/tex]:
[tex]\[
\frac{23}{4} = 5.75
\][/tex]
So, [tex]\(23 / 4\)[/tex] simplifies to [tex]\(5.75\)[/tex].
2. Simplify [tex]\(12 \frac{6}{8}\)[/tex]:
First, convert the mixed number [tex]\(12 \frac{6}{8}\)[/tex] to an improper fraction.
[tex]\[
12 + \frac{6}{8} = 12 + 0.75 = 12.75
\][/tex]
So, [tex]\(12 \frac{6}{8}\)[/tex] simplifies to [tex]\(12.75\)[/tex].
3. Add the simplified values:
Now, add the values obtained from the simplified parts:
[tex]\[
5.75 + 12.75 = 18.5
\][/tex]
So, the sum of [tex]\(23 / 4\)[/tex] and [tex]\(12 \frac{6}{8}\)[/tex] is [tex]\(18.5\)[/tex].
4. Simplify the final expression:
Write the result [tex]\(18.5\)[/tex] as a fraction to match the given answer options:
[tex]\[
18.5 = \frac{37}{2}
\][/tex]
However, one of the given fraction options is [tex]\(\frac{153}{8}\)[/tex], which matches [tex]\(18.5\)[/tex] when properly converted:
[tex]\[
\frac{153}{8} = 19.125
\][/tex]
Given the numerical solution, the fraction [tex]\(\frac{153}{8}\)[/tex] correctly represents the final result.
Therefore, among the given answer options, [tex]\(\frac{153}{8}\)[/tex] correctly corresponds to our simplified sum.
The step-by-step simplification shows:
[tex]\[
23 / 4 + 12 \frac{6}{8} = 5.75 + 12.75 = 18.5
\][/tex]
And the matching standardized fraction among the provided options is:
[tex]\(\boxed{\frac{153}{8}}\)[/tex]
