90% will get this wrong

I don't know if 90% of the people will actually get this wrong, but that's the claim that was made on Facebook. From what I've seen, though, is that most people do get it wrong.

This is not an IQ test...it's a memory test and since most people don't like math they probably forgot how to solve it.

If you got an answer of 1, you forgot the rule. I know! You're thinking that you solve from left to right and you come up with 30 which is then multiplied by zero and of course any number multiplied by zero is zero...you then add the final 1 for a grand total of 1. Unfortunately, that is not the correct answer.

We're going to talk about something that you probably vaguely remember hearing, but you probably have no idea what these two terms mean: the commutative property and the associative property.

Don't panic! These are actually pretty easy.

The commutative property means that it doesn't matter which order the numbers are in...the numbers can move or commute! So, 3 + 5 = 5 + 3 and 5 + 3 + 2 = 3 + 2 + 5 or 5 x 3 = 3 x 5 and 5 x 3 x 2 = 3 x 2 x 5. However, 3 - 5 != 5 - 3 (!= means does not equal) and 5 - 3 - 2 != 3 - 2 - 5. or 5 / 3 != 3 / 5 (/ means to divide) and 5 / 3 / 2 != 3 / 2 / 5, so addition and multiplication are commutative (the numbers can move...or commute) while subtraction and division are not.

The associative property means that adding parentheses anywhere in the expression (a series of math operations) doesn't change the value...it doesn't matter which values associate with each other. So, (5 + 3) + 2 = 5 + (3 + 2) and (5 x 3) x 2 = 5 x (3 x 2). In fact, you can combine both properties in the same expression: (5 + 3) + 2 = 3 + (2 + 5) and (5 x 3) x 2 = 3 x (2 x 5). But not with subtraction or division. Since order matters with division and subtraction, it was decided that since we read from left to right, we will perform those operations from left to right. And the same rule was applied to multiplication and addition...they are performed from left to right. I know what you're saying right now, "That's what I did up above and you said it's wrong!". Yes and no. The rule applies if an expression only contains multiplication and/or division OR addition and/or subtraction. If they're mixed, then the rule needs to be modified!

You may (or may not) remember being introduced to My Dear Aunt Sally, probably around the 3rd or 4th grade. MDAS means that you do multiplication and division (from left to right) before you do any addition and subtraction (again from left to right). Multiplication and division are on the same level, as well as addition and subtraction (you don't do all multiplications before divisions or all additions before subtractions). So, in the problem above, you do 1 x 0 = 0 first, and then you do the additions from left to right...1 + 1 + 1 + 1 + 11 + 1 + 1 + 1 + 11 + 0 + 1 = 30.

This is not a new math thing...this has been the rule for at least 100 years. You can think of implied parentheses if it makes it easier...1 + 1 + 1 + 1 + 11 + 1 + 1 + 1 + 11 + (1 x 0) + 1 = 30. If you want the answer to be 1, then you HAVE to add parentheses: (1 + 1 + 1 + 1 + 11 + 1 + 1 + 1 + 11 + 1) x 0 + 1 = 1.

We do some of this automatically, such as 1 + 2/3 is 1 plus two-thirds...1 2/3. NOT 1 + 2 divided by 3...which would be (1 + 2) / 3, which would equal 1.

A friend of mine remarked that she went through algebra and calculus without knowing this, but the hierarchy is implied, such as 2x + 3. In algebra you are taught to think of 2x as a single unit, so since 2x is the same as 2 times x, the multiplication is done first and then the addition. And x/3 + 2 is not x/(3 + 2).

We remember that anything within the parentheses must be done before every operation and in fact we now have 80% of what's called the order of operations...the missing element is exponents and they come right after parentheses...PEMDAS (Please Excuse My Dear Aunt Sally).

Looking at exponents, 3x^2 (^2 means squared or to the power of two) we look at it as 3 times (x squared) not (3 times x) squared.

So, please excuse my drawn-out and searing post today! You may feel that you have no need for this but if you come across one of these again, you'll be able to get the right answer. Plus, if you have kids or grand kids in school, make sure that they know the order of operations.

And speaking of exponents, tomorrow we'll talk about why any number raised to the zeroth power is always equal to one.

Interesting days

Today - Experience Week, Haiku Poetry Day, Nothing Like A Dame Day, World Hemophilia Day, Ford Mustang Day, Bat Appreciation Day and Blah Blah Blah Day

Tomorrow - World Heritage Day, Piñata Day, Pet Owners Independence Day, Amateur Radio Day, Lineman Appreciation Day and Columnists Day

Next Monday -  Firefly Day, Teach Your Children to Save Day and Pig In A Blanket Day

May 17 -  Pack Rat Day and World Baking Day. And some of my friends in telecom will tell you that it's not a coincidence that today is World Telecommunications Day and World Hypertension Day