Why 6÷2(1+2)=1 and NOT 9

Before the actual idea was ever thought of, let alone the actual development of a scientific calculator, the order of operations existed. As a mathematical rule, you must multiply and divide before you add and subtract.

You must also complete what is in parenthesis first before completing the actual problem. This is also known as PEMDAS (or Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction). In junior high, the easiest way to learn the order of operations is to remember "Please Excuse My Dear Aunt Sally".

The above problem is far from any kind of conjecture. In fact, some may consider it "easy" math. I have noticed that many people believe the answer is 9 simply because when they enter this problem into their calculators, shortly after hitting the equal sign, 9 is the answer they get.

Of course, using a calculator doesn't make you think because well, it does the thinking for you. However; add this problem into the calculator, as is will give you the wrong result because this, by default, goes against the Order of Operations.

So, you may ask "Sarah, why is the answer 1 and not 9?" It's simple and here is why...

Looking at the problem you see 6 divided into 2. You, then see a set of parenthesis that includes 1 added into 2.

You want to go ahead and do what is in parenthesis first.

1+2=3 (P)

The result is 3.

There are no exponents.

3x2=6 (M)

Taking 3, you want multiply that by 2. Why? Because the parenthesis outside mean you must multiply. You can't just jump to the 6 because the 6 is controlled by the division sign. If the division sign were not there, then you could go to 6 and the answer would be 9, however; because it is there, it is supported by the division sign. As you know already, part of the "Order of Operations" (or PEMDAS) is Multiplying before Dividing.

6÷6=1 (D)

Lastly, you want to take the result of 3x2 which equals 6 and divide it into the 6 which is controlled by the division sign and as a result, that will give you 1.

There is nothing to add. There is nothing to subtract.

When you enter this problem into a standard scientific calculator, the result is 9. 6÷2=3x3=9. When you attempt to go left to right, with 6 divided into 2 = 3 and then taking 3 x 1+2, you get 9. This is incorrect. Mathematics has a rule. You must follow them. If you don't, then 1 + 1 + 1 must equal 2 instead of 3.

The problem is actually written incorrectly, which can confuse anyone. One thing is certain, however; there is no confusion to what the right answer is.

The answer is 1.


Anonymous said…
The answer is 1. I study mathematics in college. This problem is not even college. Did grown people really get 9? Feel bad for them.