Spending time on Facebook and going through the math questions, I have found that an inordinate number of my Facebook friends are absolute failures at math. Not only that, but most people in general are absolute failures in basic mathematical principles.
My mathematical terminology here is not precise because I am not a mathematician, so forgive me for any transgressions math folks out there! The basics of what I'm going to talk about are, for the most part, correct when trying to explain all of this for the average mathematical layman out there.
My mathematical terminology here is not precise because I am not a mathematician, so forgive me for any transgressions math folks out there! The basics of what I'm going to talk about are, for the most part, correct when trying to explain all of this for the average mathematical layman out there.
Examples:
The equation or mathematical expression in the above picture is:
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 - 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 = ?
The equation or mathematical expression in the above picture is:
5 + 5 + 5 - 5 + 5 + 5 - 5 + 5 x 0 = ?
In both of these questions / polls, as you can see as of about 3:45 today ... most people got the answers completely and utterly incorrect. The first poll (the question with the ones in it) has been ongoing for about 5 months and still the majority of people answer ZERO, which is absolutely incorrect.
Their reasoning?
- ANYTHING MULTIPLIED BY ZERO IS ZERO! SO THE ANSWER IS ZERO!
- IF YOU WANTED ME TO GET 14 YOU SHOULD HAVE PUT PARENTHESIS AROUND THE MULTIPLICATION.
- THERE ARE NO PARENTHESES, SO THE ORDER OF OPERATIONS DOESN'T APPLY HERE.
- IT ISN'T ALGEBRA, SO THE ORDER OF OPERATIONS DOESN'T APPLY HERE.
- MY CALCULATOR SAYS IT'S ZERO!
These incorrect lines of reasoning are repeated ad nauseum in the comments sections for these questions. Some people are trolling, but the vast majority of responses like this are people attempting to legitimately defend their incorrect answer of zero.
The correct answer in the first example is 14, which only 37.4% of respondents got correct. The correct answer in the second example is 15, which only 38.6% of respondents got correct. So basically, more than 60% of people responding to simple (albeit lengthy) mathematical equations/expressions are either lazy or absolutely do not understand how the order of operations works in math. Actually, it's probably a bit more complex than my either/or dilemma here, but I'm leaving it at that.
Explaining PEMDAS and Its Usage:
For those reading who don't know, the order of operations (usually called PEMDAS in America, sometimes called BEMDAS in other locations) follows this basic structure:
Parentheses - (or Brackets in the case of BEMDAS)
Exponents
Multiplication
Division
Addition - performed from left to right, right along with subtraction!
Subtraction - performed from left to right, right along with addition!
According to the order of operations as laid out via PEMDAS, you have an order you seek out in the course of solving a mathematical expression. If the expression has parenthesis in it, you solve whatever is in parentheses first. If it has none (or you've already solved within the parenthesis), you move on to solving exponents (which includes roots which are basically exponents with values between one and zero. A negative exponent will basically turn a whole number into a fraction except one and zero. Anything to the power of zero is one, except for zero which is technically indeterminate but a calculator will tell you it's one. Don't let these tidbits blow your mind, I just find it pretty cool). If the equation has none (or you've already solved for the exponents), then you move on to multiplication and division. Once multiplication and division are complete, you go to the leftmost part of the expression and solve the addition and subtraction from left to right.
PEMDAS is a mnemonic acronym, and to help students further teachers will often teach them "Please Excuse My Dear Aunt Sally." For a cynical math teacher (and I believe there is plenty of reason for a teacher to be cynical given what I've seen), the mnemonic might be something more along the lines of "Please Excuse My Dumb Ass Students" if someone else is helping them grade homework, tests and quizzes!
Things that PEMDAS does not require to be applicable to solving a mathematical expression: parenthesis or "algebra". You use PEMDAS in algebra, geometry, trig, calculus, programming and physics -- oh, and in basic math!
Reasoning Behind Getting the Incorrect Answers (and Why These People Are Wrong):
"Anything multiplied by zero is zero! So the answer is zero!"
This is partially correct, because when a number is multiplied by zero ... the answer is zero. HOWEVER, if you follow the order of operations, you multiply by zero before you do any of your left-to-right addition or subtraction. So, in those mathematical expressions, by the time you get to add or subtract, you will be adding by a zero at the end, not multiplying by it.
"If you wanted me to get 14, you should have put parentheses around the multiplication!"
Parentheses in this situation are for noobs and pussies who can't remember the rest of PEMDAS. These examples for the Facebook questions are extremely simple mathematical expressions. If you cannot follow PEMDAS, I sincerely hope you are NOT seeking a career requiring any mathematical skills that involve anything past using your fingers to count. Parentheses are primarily used in situations where the rest of PEMDAS needs to be circumvented (you know, like in the case of writing out certain pieces of polynomial expressions) or if an extremely long and/or complex equation needs clarification.
"There are no parentheses so the order of operations doesn't apply here!"
Wrong. The order of operations applies in the majority of mathematical or computational situations whether or not there are parentheses, and that majority including these two examples. Parentheses are simply a starting point for you to figure out how to compute whatever expression or equation you got. No parentheses? No problem. Move onto the next part of PEMDAS. The end. Deal with it.
"It isn't algebra, so the order of operations doesn't apply here!"
Seriously? OK then, if the order of operations only applies in algebra, then it doesn't apply in geometry, trig, calculus, physics, programming, etc, etc. You realize that is incorrect, because it applies in all of these situations? Oh yes, and it also applies to the basic mathematics you learn in elementary school.
"My calculator says it's zero!"
Well, I guess your calculator isn't programmed to follow PEMDAS. Therefore ... operator error. Derp.
So How'd You Get What You Got?
I guess we'll start with the first one (the one with all the ones and which equals 14) and whittle it down piece by piece according to PEMDAS taken to the extremes of literalness.
1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0=? (P: none)
1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0=? (E: none)
1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0=? (M: 1x0=0)
1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+0=? (D: none)
1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+0=? (A: 1+1=2)
2+1+1+1+1+1+1+1+1-1+1+1+1+1+1+0=? (A: 2+1=3)
3+1+1+1+1+1+1+1-1+1+1+1+1+1+0=? (A: 3+1=4)
4+1+1+1+1+1+1-1+1+1+1+1+1+0=? (A: 4+1=5)
5+1+1+1+1+1-1+1+1+1+1+1+0=? (A: 5+1=6)
6+1+1+1+1-1+1+1+1+1+1+0=? (A: 6+1=7)
7+1+1+1-1+1+1+1+1+1+0=? (A: 7+1=8)
8+1+1-1+1+1+1+1+1+0=? (A: 8+1=9)
9+1-1+1+1+1+1+1+0=? (A: 9+1=10)
10-1+1+1+1+1+1+0=? (S: 10-1=9)
9+1+1+1+1+1+0=? (A: 9+1=10)
10+1+1+1+1+0=? (A: 10+1=11)
11+1+1+1+0=? (A: 11+1=12)
12+1+1+0=? (A: 12+1=13)
13+1+0=? (A: 13+1=14)
14+0=? (A: 14+0=14)
14
Yep, 14. Not 0.
After spelling that out, I don't think I need to work you through the equation with fives and zeros. And no, I will not help you with your math homework. Go do that crap on your own and keep it away from me!
In other news related to my post from yesterday, Penn State fired Coach Joe Paterno and President Graham Spanier during last night's Board of Trustees meeting.
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