[Numeracy 239] Re: what is the difference between....

I think your hypotheses are  correct.  For the first example, the  
simplest explanation IMO, is that this follows the Order of Operations  
PEMDAS.
In the first example, there are no (  )P ,  so next in the PEMDAS  
order is exponentiation (E).  2 is raised to the second power,  
resulting in 4.  Next comes multiplication M, by -1.  the answer is -4.

In the second example, the parentheses are executed first, (-1 * 2).   
this answer is -2, which is then raised to the second power. Final  
answer is  4.
It is really based on PEMDAS ( order of operations).

In your second example,  I would clarify the language as such:  -/  
-6 / = -6
  This is the opposite( - )of the absolute value of -6, ( /-6 /. )
  The absolute value of -6, / - 6 / ,  is 6.
   The opposite of 6 is -6.
I would not use the term "absolute number".

Cheers!




Maureen Carro, MS, ET
Academic Learning Solutions
Alamo, CA
mcarro at lmi.net



On Mar 29, 2010, at 1:18 PM, George Demetrion wrote:


> Good afternoon colleagues.

>

>

> In my newly articulated and highly pleasant role as a Transition to  

> College math teacher, I've come ac ross the following

>

>

> -22

>

>  (-2)2

>

>

>

> According to my book the answer to the first problem is -4 while the  

> answer to the second is 4.  The examples are easy enough to follow,  

> but a little light on the explanation.  In the first problem the  

> notation in the book states that 2 is the base; thus (2.2)=4 and, I  

> assume, we keep the negative sign, so that the answer becomes -4.   

> The second problem is easy enough.  I get (-2.-2)=4.

>

>

> What's missing as far as I'm concerned is a clear and simple  

> explanation  of the reasoning behind the first problem - 22 d

>

>

> I deduced that the second problem is based on an order of operations  

> problem solving menthodology and I'm thinking the same thing for the  

> first problem in which the negative sign indicated a -1.  Thus, on  

> this hypothesis, I am carrying out an order of operation (exponent  

> first, including the implied paranthesis (2.2) multiplied by -1 in  

> which this later stage is last on the order of operations process.

>

>

> Questions:

>

>

> 1. Is my hypothesis for problem #1 correct?

>

> 2.  If not, what would be the correct explanation?

>

> 3. Whether or not the hypothesis is correct what woould be the  

> simplist accurate explanation  to provide my students with?

>

>

> One more question -/-6/= -6, which I translate to mean is that the  

> opposite of the absolute number -6 has an absolute value of 6;  

> therefore its opposite is -6.

>

>

> a)  is this correct

>

> b) If so, is there an easier way to state it?

>

> c) If it is correct what is the best way to teach it to TCC students  

> with limited mathematical experience

>

> d) If it is incorrect, what would be the correct answer?

>

>

>

> Okay, we're just about through with integers.  Onto fractions.

>

>

> Best,

>

>

> George Demetrion

>

>

> ----------------------------------------------------

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