[Numeracy 238] Re: what is the difference between....

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mdr151 at aol.com mdr151 at aol.com
Mon Mar 29 19:31:03 EDT 2010

Yes, George you are correct on both accounts and yes a lot of textbooks do not do a very good job of explaining why.

In your first problem you are correct to assume the order of operations of doing the exponent first and then negating the answer. I sometimes read this as "take the opposite of " 2 squared. Therefore in order to square a negative number, the negative number must be enclosed in parentheses as is shown in your second example. Coincidentally newer versions of scientific calculators with scrolling screens will show the negative in parentheses if one enters -2 and then the x^2 key.

Also your question about absolute value is also correct. You would perform the absolute value of -6 which is 6 and then "take the opposite" of that as is implied by the negative sign outside of the parentheses.

Hope this helps.

Pam Meader
Math Department Chair
Porltand Adult Education
Portland, Maine

-----Original Message-----
From: George Demetrion <gdemetrion at msn.com>
To: Numeracy List <numeracy at nifl.gov>
Sent: Mon, Mar 29, 2010 4:18 pm
Subject: [Numeracy 235] what is the difference between....

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


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.


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.


George Demetrion


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