John simplified the expression below incorrectly. Shown below are the steps that John took. Identify and explain the error in John’s work.

Question

3 + (-15) ÷ (3) + (-8)(2)

−12 ÷ (3) + (−8)(2)

-4 + 16

12

Answer 1

John did not follow the order of operations when simplifying the expression. He solved the problem from left to right, starting with adding 3+(-15). Order of operations states that when we have multi-step problems we must simplify anything that is inside any form of groupings first, then solve all exponents, then do all multiplication and division in order from left to right, and finally, do all addition and subtraction in order from left to right. John solved addition before anything else, which should have been part of the final step of the problem. In this problem, John should have divided -15 by 3 first, then multiplied -8 by 2 next, and finally solved all of the addition.

Shown below are the correct steps for solving the problem:

3 + (-15) ÷ (3) + (-8)(2)

3 + (-5) + (-16)

-2 + (-16)

-18