There are lots of posts floating around posing math problems such as this:
6 – 3 x 2 + 4 / 2 = ?
There is no trick and no magic to these types of problems. It all comes down to Order of Operations.
Order of Operations stipulates that multiplication and division are performed first, left to right. Then addition and subtraction are performed, left to right. That’s really all there is to it.
Performing mulitiplication and division first, left to right, the above problem simplifies to:
6 – 3 x 2 + 4 / 2 = 6 – 6 + 2
Then performing addition/subtraction, left to right, gives the answer of 2.
NOTE: 2 is THE answer to the above problem as stated. Not one answer out of many. THE answer.
When parentheses are introduced, the operations inside the parentheses are performed first. If the above problem is restated as follows:
(6 – 3) x (2 + 4) / 2 = ?
…it simplifies to:
(3) x (6) / 2 = 18 / 2 = 9
Note that parentheses are needed only to indicate that addition/subtraction operations are to be performed before multiplication/division.
That’s really all there is to it. You need never be fooled by one of these problems again.
And it all comes back to basic arithmetic, Q.E.D.