Sunday, June 14, 2015

Were you taught PEMDAS or BODMAS?

Either way, you were taught the Order of Operations.  I've been trying to educate people on Facebook math threads for over a year now, with limited success.  For instance, on a math thread that asks you to solve 40+40*0+1 most people think it's 1.  That is incorrect.

The Order of Operations, whether it's described by PEMDAS, BODMAS, or any other acronym, clearly states that you must do the Multiplication and Division Left To Right before Addition and Subtraction, also Left To Right.  Therefore in the above example you multiply 40*0 first, giving you 0, not 40.  Then addition, which is actually Summation of Positive and Negative Numbers, 40+0+1=41.

If your teacher taught you that Multiplication must be done before Division, or vice versa, please, smack them for me.  If they also taught that addition must be done before subtraction, smack them twice please.

Here is an example of when Parentheses actually are used to change the usual Order of Operations: 20/2(5+5).  First you solve the contents of the Parentheses, 5+5=10, then you do the Multiplication and Division left to right, 20/2=10, 10*10=100.  Also, All Divisions are Fractions, a Number Over Another Number, and cannot be reversed.  1/2 is NOT 2/1.  So when you multiply a Fraction against a Whole Number you are multiplying the Entire Fraction, not just part of it.  When multiplying a Fraction against a Whole Number you must convert the Whole Number into a Fraction.  So 20/2*10=20/2*10/1, 20*10=200, 2*1=2, 200/2=100.

The facts are plain and simple.  Multiplication was invented centuries ago as a shortcut for lots of additions and therefore has Always had precedence over addition since its invention way before anyone alive today was born.  It is NOT new math, it is not unique to Common Core curricula, and you are Not "Old School" if you don't remember being taught how to do math properly.  Exponents were invented as a shortcut to do lots of multiplications and therefore have Always had precedence over Multiplication since they were invented.  Parentheses and other Grouping Symbols have Always had precedence over everything else in order to Override the usual Order of Operations for simplification reasons.  Like 20/2*5+20/2*5 is Simplified by writing 20/2(5+5).

Oh, and it should not bear repeating, but I still do all the time on these math threads:  Anything times 0 is 0.  Always has been, always will be.  Multiplication by 0 is just an easier way of removing a value than applying the exact opposite value.  1-1=0, -1+1=0, 1*0=0.  It is very useful in programming, computers use Binary, 1s and 0s, to do everything, on and off, this is yes, that is no.  Is there an elephant standing in my room?  The answer is no, there are 0 elephants standing in my room.  Elephant times 0= the number of elephants standing in my room.