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jakep069
07-26-2009, 07:50 AM
I have a good grasp of operations on negatice and positive numbers when: +, -, /, *

- * - = +

+ * - = -

- / - = +

- / + = -

a + (-b) = a - b

a - (-b) = a + b

However, if I just stick to the above laws I think I should be alright. Would that be a good solution. My text book has an example trying to use absolute values
eg 2 + (-6) = -(6-2) = -4 - Yes I understand this OK, but they are trying to add it as a step. WHAT FOR ? Is there an actual legitemate reason, or are they just trying to explain a process? I can get from step 1 to the answer without the second step. Is that OK?

Also, in this part of the text there are other examples where eg 12 / 3 = 4, -12 / - 3 = 4, -12 / 3 = -4, -(12 / 3) = -4, and 12 / -3 = -4 - I understand all that NO PROBLEMS, but when doing algebraic math problems with neg operations and in calculus you can be half way through a problem and the lecturer, instructor, or a 'you tube dude' aparently, indescrimenantly just changes an entire math statement from + to -, or does this to an algebraic term, or some sort of expression and I don't know why.

For the above example where there is a - sign in the -12/3, -(12/3) is it for example that it just doesn't matter as the answer is going to be neg anyway. If it is then I just don't know why the signs are being moved. I was watching a hard, algebraic, worked example on you tube and the instructor said 'well I don't want a - numerator, so I will just move it... Who is he? The math god? Why would he have moved it?

Please help.

Jason

royhaas
07-26-2009, 08:15 AM
Moving signs around is often a matter of taste; sometimes it leads to a simplification within the larger problem. There's more than one way to skin a cat.

Loren
07-26-2009, 12:35 PM
Re: 2 + (-6) = -(6-2) = -4

It seems to me your text is showing how to follow the rule for adding numbers with opposite signs. The rule is "To add numbers with opposite signs, find the difference of their absolute values and attach the sign of the larger absolute value." That's what the middle expression indicates. They found the difference of |2| and |-6| which is "6-2=4". Then they attached the sign preceding the 6 because |-6| > |2|.
In answer to your question, that middle step is not necessarily displayed.

Loren
07-26-2009, 12:52 PM
>>>Also, in this part of the text there are other examples where eg 12 / 3 = 4, -12 / - 3 = 4, -12 / 3 = -4, -(12 / 3) = -4, and 12 / -3 = -4 - I understand all that NO PROBLEMS, but when doing algebraic math problems with neg operations and in calculus you can be half way through a problem and the lecturer, instructor, or a 'you tube dude' aparently, indescrimenantly just changes an entire math statement from + to -, or does this to an algebraic term, or some sort of expression and I don't know why.

You should NEVER indiscriminately (note spelling) change the sign of expression. If the sign is changed, there is a reason. One of the more elusive patters is something like...
\frac{a-b}{-c}=\frac{b-a}{c}
At first glance, it appears that we have simply thrown away the negative sign in the denominator. But, looking carefully, we see that the fraction has gone through the following process...
\frac{a-b}{-c}=\frac{(-1)(-a+b)}{(-1)\cdot c}=\frac{(-1)}{(-1)}\cdot\frac{b-a}{c}=1\cdot\frac{b-a}{c} =\frac{b-a}{c}

The above example demonstrates a situation where you might want the numerator to be the binomial b-a rather than a-b for a particular reason. Or sometimes you want the sign of a fraction to be positive rather than negative or visa versa. The bottom line is that...

\frac{-a}{b}=-\frac{a}{b}=\frac{a}{-b}

and

-\frac{-a}{b}=-\frac{a}{-b}=+\frac{-a}{-b}=+\frac{a}{b}