In the problem12÷2(6-7+4) x 2, is the 12 divided first or the 2 multiplied by the parentheses first?

Question

My understanding of PEMDAS is that you would divide the 12 by 2 before multiplying anything by the result of the inner parentheses. And the online math solver shows this as well. I get 36 for the same reason the math solver gets 36. But another person insists that this is only correct if you have a function Otherwise, he says the 2 connected to the parenthesis is PART OF the parentheses and has to be done first which returns a result of 4. What is the correct way to solve this? Thank you.

Answer 1

Here is the step-by-step with justifications below:

12 ÷ 2(6 - 7 + 4) x 2

According to PEMDAS, we must always evaluate the part(s) of our expression or equation that is inside or in between PARENTHESES or grouping symbols.

So, what do we find inside of the parenthese above?

(6 - 7 + 4) is what we see in parentheses, so we must simplify this part first.

6 - 7 = -1

-1 + 4 = 3

Now we have

12 ÷ 2(3) x 2

Now, does the order of operations (PEMDAS) tell us that we should do multiplication next and then division? That can be a bit confusing.... the operations of multiplication and division, when found in the same expression, should be computed moving left to right. If you have division on the left side of the expression and then multiplication is further right, then you will do the division and then multiplication. This same rule applies to the 2 operations of Addition and Subtraction.

12 ÷ 2(3) x 2 = 12 ÷ 2 x 3 x 2 =

6 x 3 x 2 = 18 x 2 = 36