A mistake was made in the steps shown to simplify the expression. Which step includes the mistake?

$\frac{1+3^2}{5}+|-10| \div 2$

Step 1: $=\frac{1+3^2}{5}+10 \div 2$

Step 2: $=\frac{1+9}{5}+10 \div 2$

Step 3: $=\frac{10}{5}+10 \div 2$

Step 4: $=2+10 \div 2$

Step 5: $=12 \div 2$

Step 6: $=6$

AStep 3
BStep 4
CStep 5
DStep 1

Question

05-11-2026
Mathematics

Answered

A mistake was made in the steps shown to simplify the expression. Which step includes the mistake?

$\frac{1+3^2}{5}+|-10| \div 2$

Step 1: $=\frac{1+3^2}{5}+10 \div 2$

Step 2: $=\frac{1+9}{5}+10 \div 2$

Step 3: $=\frac{10}{5}+10 \div 2$

Step 4: $=2+10 \div 2$

Step 5: $=12 \div 2$

Step 6: $=6$

AStep 3
BStep 4
CStep 5
DStep 1

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-05T14:43:41-05:00

The expression is $\frac{1+3^2}{5} + |-10| \div 2$.
Following PEMDAS, exponents and grouping symbols are evaluated first, resulting in $\frac{10}{5} + 10 \div 2 = 2 + 10 \div 2$.
Step 5 incorrectly performs the addition ($2+10=12$) before the division ($10 \div 2$), which violates the rule that division must precede addition.
The first error occurs in $\boxed{Step 5}$.

Explanation

Analyzing the expression and initial steps

To evaluate the expression $\frac{1+3^2}{5} + |-10| \div 2$, we must follow the standard order of operations, often abbreviated as PEMDAS/BODMAS:

Parentheses (including grouping symbols like fraction bars).
Exponents (powers and roots).
Multiplication and Division (from left to right).
Addition and Subtraction (from left to right).

In our case, the expression is:
\[\frac{1+3^2}{5} + |-10| \div 2\]
First, we address the grouping symbols (the numerator) and the absolute value:

The numerator is $(1+3^2)$, and the absolute value is $|-10| = 10$.

Substituting these gives $\frac{1+3^2}{5} + 10 \div 2$. This matches the transition to Step 1.

Evaluating the steps and identifying the mistake

Continuing with the correct sequence of operations:

Step 1: $\frac{1+3^2}{5} + 10 \div 2$ (Correct, as shown above)
Step 2: $\frac{1+9}{5} + 10 \div 2$ (Correct, the exponent $3^2 = 9$ is calculated)
Step 3: $\frac{10}{5} + 10 \div 2$ (Correct, the addition in the numerator $1+9=10$ is calculated)
Step 4: $2 + 10 \div 2$ (Correct, the division $\frac{10}{5} = 2$ is calculated)

Now, the expression is $2 + 10 \div 2$. Following the order of operations, division must be performed before addition:

$2 + (10 \div 2) = 2 + 5 = 7$.

However, Step 5 shows $=12 \div 2$, which indicates that addition ($2+10=12$) was performed before division. This is an incorrect application of the order of operations.

Final conclusion

The mistake was introduced in Step 5, where the addition $2 + 10$ was calculated before the division $10 \div 2$. According to the order of operations, division precedes addition. Therefore, the correct calculation should result in $2 + 5 = 7$, not $6$. The correct choice is Step 5.

Examples

Understanding the order of operations is crucial in many practical areas such as programming, engineering, and finance. For instance, if a spreadsheet software like Excel evaluated $2+10/2$ by adding first, it would yield $6$ instead of the correct value $7$. This would lead to significant errors in financial reports or engineering models. Properly applying the sequence ensures that calculations are consistent, accurate, and reliable, which is essential for any technical or scientific work.