To solve the expression [tex]\(13 + \frac{1}{2} \times (6 \div 2 + 6)\)[/tex], let's break it down step by step:
1. Evaluate the innermost operation inside the parentheses:
[tex]\[
6 \div 2 = 3
\][/tex]
2. Add the result to 6:
[tex]\[
3 + 6 = 9
\][/tex]
3. Multiply this result by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} \times 9 = 4.5
\][/tex]
4. Add this final result to 13:
[tex]\[
13 + 4.5 = 17.5
\][/tex]
Now, let's match this process to the statements provided:
1. 13 more than half of 6 more than the quotient of 6 and 2:
- Compute the quotient of 6 and 2: [tex]\(6 \div 2 = 3\)[/tex].
- Add 6 to the quotient: [tex]\(3 + 6 = 9\)[/tex].
- Take half of this sum: [tex]\(\frac{1}{2} \times 9 = 4.5\)[/tex].
- Finally, add 13 to this result: [tex]\(13 + 4.5 = 17.5\)[/tex].
This matching confirms that the correct interpretation of the expression is described by the statement:
13 more than half of 6 more than the quotient of 6 and 2.
