To identify the mistake, let's carefully go through each step of the given expression:
[tex]\[
\frac{1 + 3^2}{5} + |-10| \div 2
\][/tex]
We begin by evaluating each step:
Step 1:
[tex]\[
\frac{1 + 3^2}{5} + 10 \div 2
\][/tex]
In this step:
- [tex]\(3^2\)[/tex] is evaluated as [tex]\(9\)[/tex].
- The absolute value of [tex]\(-10\)[/tex] is taken as [tex]\(10\)[/tex].
Therefore, the expression simplifies to:
[tex]\[
\frac{1 + 9}{5} + 10 \div 2
\][/tex]
Step 1 is correct.
Step 2:
[tex]\[
\frac{1 + 9}{5} + 10 \div 2
\][/tex]
Here, [tex]\(1 + 9\)[/tex] is evaluated as [tex]\(10\)[/tex]. Thus, the expression becomes:
[tex]\[
\frac{10}{5} + 10 \div 2
\][/tex]
Step 2 is also correct.
Step 3:
[tex]\[
\frac{10}{5} + 10 \div 2
\][/tex]
Now, [tex]\( \frac{10}{5} \)[/tex] is evaluated as [tex]\(2\)[/tex]. This simplifies to:
[tex]\[
2 + 10 \div 2
\][/tex]
Step 3 is correct.
Step 4:
[tex]\[
2 + 10 \div 2
\][/tex]
Here, [tex]\(10 \div 2\)[/tex] is evaluated as [tex]\(5\)[/tex]. The expression becomes:
[tex]\[
2 + 5
\][/tex]
Step 4 is correct.
Step 5:
[tex]\[
2 + 5
\][/tex]
The sum [tex]\(2 + 5\)[/tex] should equal [tex]\(7\)[/tex]. However, in the steps provided, it is incorrectly shown as:
[tex]\[
12 \div 2
\][/tex]
This is incorrect because [tex]\(2 + 5\)[/tex] should be [tex]\(7\)[/tex], not [tex]\(12 \div 2\)[/tex].
Step 6:
This final step results from the incorrect value in Step 5:
[tex]\[
6
\][/tex]
Therefore, the mistake is in:
Step 5: where [tex]\(2 + 5\)[/tex] should correctly equal [tex]\(7\)[/tex], not [tex]\(12 \div 2\)[/tex].
The correct answer is:
A. Step 5
