To analyze the steps and identify where the mistake occurs, let's go through each step carefully:
The initial expression is:
[tex]\[
\frac{1 + 3^2}{5} + |-10| \div 2
\][/tex]
Step 1:
[tex]\[
\frac{1 + 3^2}{5} + 10 \div 2
\][/tex]
This step simplifies [tex]\( |-10| \)[/tex] correctly to [tex]\( 10 \)[/tex]. No mistake here.
Step 2:
[tex]\[
\frac{1 + 9}{5} + 10 \div 2
\][/tex]
This step simplifies [tex]\( 3^2 \)[/tex] to [tex]\( 9 \)[/tex]. No mistake here.
Step 3:
[tex]\[
\frac{10}{5} + 10 \div 2
\][/tex]
This step adds [tex]\( 1 + 9 \)[/tex] to get [tex]\( 10 \)[/tex] in the numerator. No mistake here.
Step 4:
[tex]\[
2 + 10 \div 2
\][/tex]
This step simplifies [tex]\( \frac{10}{5} \)[/tex] to [tex]\( 2 \)[/tex]. No mistake here in the division part but we need to pay attention to the order of operations in the next step.
Step 5:
[tex]\[
12 \div 2
\][/tex]
This step adds [tex]\( 2 + 10 \)[/tex], which is incorrect because division should be performed before addition, following the order of operations (PEMDAS/BODMAS). The correct approach would have been to perform the division first:
[tex]\[
2 + 5 = 7
\][/tex]
Given this mistake in Step 5, Step 5 is where the mistake occurs.
The correct answer is:
B. Step 5
