# [Numeracy 150] More about the double negative language-math link

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Michael Gyori tesolmichael at yahoo.com
Thu Feb 11 17:34:14 EST 2010

Greetings everyone,

Operators and integers are always multiplied to determine whether sums, differences, products, and quotients are positive or negative values.  Positive values are not preceded by the plus sign, i.e., we would write 5 + 10, not +5 [+] +10.  The resultant "golden rule" and language math link could be rendered as follows:

positive times positive = positive (corresponds to the English single positive rule, e.g. go means [yes] go);
positive times negative = negative (corresponds to the English single negative rule, e.g. "[not] go, not being negative, go being positive);
negative times positive = negative (corresponds to the English single negative rule, e.g. "go [not], go being positive, not being negative);
negative times negative = positive (corresponds to the English double negative rule, e.g. [not] [not] go means go).

Let's use the numbers 5 and 10 as an example:

When we add 5 and 10 (5 + 10), we actually mean +5 [+] +5, so... [+] times + = + (or positive, move up or to the right on the coordinate graph);
When we add 5 and -10, we actually mean +5 [+] -10, so... [+] times ― = ─  (or negative, move down or to the left on the coordinate graph);
When we subtract 10 from 5, we actually mean +5 [-] +10, so... [-] times [+] = ─ (or negative, move down or to the left on the coordinate graph);
When we subtract -10 from 5, we actually mean +5 [-] -10, so [-] times - = + (or positive, move up or to the right on the coordinate graph).

Whenever we multiply or divide, it becomes more apparent that we are multiplying operators by integers, for example:

5 x 10 is the same as +5 [x] +10.... (+ [x] + =+)
-5 x 10 is the same as -5 [x] +10..... (- [x] + = ─)
-5 / 10 ( / meaning divided by) is the same as -5 [/] +10... (- [x] + = ─)
-5 / -10 is the same as -5 [/] -10...(- [x] - = ─)

If you use a coordinate graph (with an "x" and "y" axis) - keeping in mind that a picture can be worth a thousand words - you can visually draw and trace the processes working with addends, subtrahends/minuends, factors, and divisors/dividends entail. Remember that multiplication is a fast way of adding, and that division is a fast way of subtracting.

I hope I'm not being confusing!

Michael

Michael A. Gyori
Maui International Language School
www.mauilanguage.com

________________________________
From: Michael Gyori <tesolmichael at yahoo.com>
To: The Math and Numeracy Discussion List <numeracy at nifl.gov>
Sent: Thu, February 11, 2010 7:08:18 AM
Subject: Re: The double negative language-math link

When I delve into integers, I always use coordinate graphs ("x" and "y" axes).  They can be used to concretely render what we do when we "take away" by moving either downward or to the left...

Michael A. Gyori
Maui International Language School
www.mauilanguage.com

________________________________
From: Michael Gyori <tesolmichael at yahoo.com>
To: The Math and Numeracy Discussion List <numeracy at nifl.gov>
Sent: Thu, February 11, 2010 6:57:58 AM
Subject: The double negative language-math link

Greetings everone,

Carol King stated,

If I am taking out taking out 8, as in 10 –  (-8), then I must be adding it.

I read it a few times and find myself perplexed by it, as much as I believe I understand its intent.

"Taking out" is a positive statement and regardless of how many times you say it, it remains positive, and what changes - perhaps, depending on how I choose to understand it -  is the number of times you (***yes***)  "take out." If I take out once, I have 2 left, and I cannot take take out again, because I can't take another 8 out of 2.

Alternatively,  I can understand the meaning to be that I am "taking out" the taking out of 8, which then could leave me to believe that I wanted to take out, then decided against it, such that I end up doing nothing.  I still have 10.

The problem, as I see it, is that we are getting into integers.  Negative values have no meaning in the world of the concrete, because once you have 0 left, that's it.  On the other hand, if we deal with negative balances (such as when you overdraw your balance in your checking account), you create meaning because it can and does happen.  In other words, negatives carry meaning in mathematical, but not physical (reality) terms...

Thoughts?

Michael

Michael A. Gyori
Maui International Language School
www.mauilanguage.com

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