Simplify 8/2(2+2)

Question

I am engaged in an argument with an educated individual who claims that under no circumstances may you assume that 8/4x = 2x due to the fact that 2x = x2 and is “its own thing”. However, my understanding of monomials is such that their numerical aspect may be divided or multiplied when obligated by PEMDAS. I believe that our disagreement stems from the unfortunate complications that arise when vertical fractions are converted to horizontal fractions without proper indication of the bounds of the numerator and denominator. He assumes that the bounds of the denominator in the equation in the Title extend to the end of the equation. However, I am nearly certain that this is an incorrect assumption, as my mathematical upbringing has led me to believe, and I understand that once the operation inside the parentheses is completed, division and multiplication are performed left to right. As such, the equation simplifies to 8/2(4), which simplifies to 4(4), which = 16.

Additionally, he supplied an example from a textbook where they had written “mx/bx = m/b”. In this example, the textbook authors want readers to assume that there are parentheses defining the bounds of the numerator and denominator. However, simplifying this equation according to PEMDAS yields m * x/b * x = mx^2/b. This is technically an error by the textbook authors, yes?

Answer 1

mx/mb = x/b

PEMDAS has M before D. Multiply 1st, Division next

that makes mx/mb = (mx)/(mb) = x/b

Not a texbook error, although some textbooks have more errors than you might suspect.