Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

## Tuesday, July 30, 2019

### 8÷2(2+2)

The math problem is 8÷2(2+2) and it seems to be trending all over the place, especially Facebook. Also written as 8/2(2+2), when you enter this problem into a calculator, you will get 16; however, that answer is incorrect. You see, every single time you solve any problem in mathematics, you must follow the Order of Operations. Commonly known as PEMDAS here in the United States (and BEMDAS in other parts of the world) it is crucial to follow this rule and apply it accordingly.

PEMDAS simply stands for Parenthesis, Exponents, Multiplication, Division, Addition and Subtraction. As an easy way to remember this, my teacher in 5th grade use to say "Please Excuse My Dear Aunt Sally" which was the way to remember this particular rule. But the question remains, how do you solve this particular problem?

As a mathematical rule, you must do what it is in parenthesis first. 2+2=4. (4) is your answer. There are no exponents, so you can skip this particular step. Now, you must go back to the beginning and apply the multiplication rule. Because the 8÷2 doesn't contain parenthesis, you must take 2(4) which is simply 2x4. Your answer will turn to 8.

Then, going back to the beginning of the problem, you must divide the first 8 into 2x4=8. This will give you one.

8÷2(2+2) is 8÷2(4) = P
No Exponents
8÷2(4) 2x4 = 8 = M
8÷8 = 1 = D
No Addition
No Subtraction

If the problem were written (8÷2)(2+2) your answer would be 16, as any linear problem would be solved, left-to-right. Every time you see a number and a () around another number, this represents multiplication. 2x4=8.

But because there are parenthesis representing only the 2+2, your answer is one.

The final answer is 1.

## Wednesday, October 10, 2012

### 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.