Let's examine the steps to identify where the mistake was made in the simplification process.
Given expression:
[tex]\[
\frac{1+3^2}{5} + |-10| \div 2
\][/tex]
Step-by-Step Solution:
Step 1:
[tex]\[
\frac{1 + 3^2}{5} + 10 \div 2
\][/tex]
Explanation: The expression [tex]\( |-10| \)[/tex] evaluates to 10 because the absolute value of -10 is 10.
Step 2:
[tex]\[
\frac{1 + 9}{5} + 10 \div 2
\][/tex]
Explanation: The expression [tex]\( 3^2 \)[/tex] evaluates to 9.
Step 3:
[tex]\[
\frac{10}{5} + 10 \div 2
\][/tex]
Explanation: The expression [tex]\( 1 + 9 \)[/tex] evaluates to 10.
Step 4:
[tex]\[
2 + 10 \div 2
\][/tex]
Explanation: The expression [tex]\( \frac{10}{5} \)[/tex] evaluates to 2.
Step 5 (Where the mistake occurs):
[tex]\[
2 + 5
\][/tex]
Explanation: The expression [tex]\( 10 \div 2 \)[/tex] evaluates to 5. However, the mistake is made in the next step when the incorrect operation is performed.
So, the correct sequence of operations should end like this:
Correct Final Step:
[tex]\[
2 + 5 = 7
\][/tex]
In Step 5, instead of performing [tex]\( 2 + 5 \)[/tex], a different operation was performed, leading to an incorrect final result of [tex]\( 12 \div 2 = 6 \)[/tex].
Therefore, the mistake happens in Step 5.
Correct Answer:
A. Step 5
