Select the statement that describes this expression: [tex]13 + \frac{1}{2} \times (6 \div 2 + 6)[/tex]

A. 13 more than half of 6 more than the quotient of 6 and 2

B. 13 more than half of the quotient of 6 and 6 minus 2

C. Half of 13 multiplied by the quotient of 6 and 2 plus 3

D. 13 plus half of 6 divided by 2, then subtract 6



Answer :

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.