Order of operations when solving 47−[83+16−51]÷8+13

Question

I’m a student in Applied Calculations and Measurements. We have a professor who posed the problem:

$$47-[83+16-51]÷8+13$$

He solved this as follows:

1. Group $8+13$
2. Divide $47-[83+16-51]$ by $21$.
3. The answer was 44.71.

I believe the answer is incorrect according to the order of operations. When I solved the problem I got:

$$ 47-[83+16-51]÷8+13\\ 47-[99-51]÷8+13\\ 47-[48]÷8+13\\ 47-[6]+13\\ 47+7\\ 54 $$

The class was divided with some using used the order of operations and some attempting to use the method he was teaching.

What went wrong here?

Answer 1

Given the equation you've provided: $$ \begin{align} 47-(83+16-51)/8+13&=47-48/8+13 \\ &=47-6+13 \\ &=54 \end{align} $$ your answer ($54$) is correct.

However, the professor's answer is true if we put $8+13$ in parentheses: $$ \begin{align} 47-(83+16-51)/(8+13)&=47-48/21 \\ &\approx 44.71 \\ \end{align} $$

There is no mistake in either case as PEMDAS was applied correctly.

The answer should lie in how the original expression was written. Perhaps the question was copied incorrectly at some point.