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Raza
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Can someone prove that -4 x -4 =16?
cronxeh said:what a de ja vu... i swear I've seen this before somewhere
Raza said:Thank you all, I finally get this.
A substitute teacher was asking me this question and I couldn't answer her at all
WORLD-HEN said:If I understand correctly, you want me to prove that negative times negative is positive, right?
[tex] -a(a-a) = 0 [/tex]
This statement is true since [tex] (a-a) = 0 [/tex]
Using the distributive law :
[tex] -a(a-a)=0[/tex]
[tex] -a^2 + (-a \times -a) = 0[/tex]
[tex] -a \times -a = a^2[/tex]
So, substituting 4 for a gives
[tex] -4 \times -4 = 4^2 [/tex]
[tex] -4 \times -4 = 16[/tex]
Raza said:your probability won't work if they are two different numbers, let say -5 and -3. How will you work that out?
eNathan said:http://www.google.com/search?hl=en&q=-4*-4&btnG=Google+Search
Is that simple enought. No, it probally not. But its fairly simple. The concept of a negative number is totally different from that of real numbers. A negative number is not only the asbsense of a real number, but its used to make up for the non-existance of the real numbers. This is why a negative times a negative is a positive.
jcsd said:Negative numbers ARE real numbers.
There's a simple amendmnt you make to the proof I made earlier so that it proves (-a)(-b) = ab rather than (-a)(-a) = aa.
Zurtex said:eNathan I can't help thinking when reading your posts that you don't really understand the number system that well.
A negative number: -a is defined such that: a + (-a) = 0. That is it, there is no more to it, however from this and the other rules of real numbers we can prove that -1*(a) = -a, -1*-1=1, (-a)*b = -(a*b) and many other useful identities.
Just because the square root of a negative number is imaginary it does not mean it is not the 'true' square root of the number.
I think you would find it rather helpful to look up the mathematical definitions of the words 'real', 'imaginary' and 'complex'. As well as looking up what Natural Number, Integers and Quotients are.
mathwonk said:this has nothing to do with negative numbers, -a is not a negative number, it is the additive inverse of a.
a need not be a real number at all, a could belong to any additive group.
In any case even if a were a real number, -a is mereoly the opposite of a, if a is zero, -a is zero not negative, and if a is negative then -a is positive.
-a is not read "negative a", but "minus a" or "additive inverse of a", or "the number you add to a to get zero".
the word negative means "less than zero". this am,kes no sense in amny situations where -a makes perfect sense, for example complex numbers where there are no negative complex numbers, since "greater than" and "less than" are not defined for complex numbers, for the same reason you cannot say which horse on a merry go round is in "front".
Imaginary are mathematical though, the word real means a well known and defined set in mathematics it does not mean the English word 'real' as in something that exists.eNathan said:Nah, I already know what those are. what I mean when I said that negative roots are not REAL numbers, but imaginary, is this.
Sqr(-25)=5i Right? 5*5=25? -5*5=25? There is not mathematical root, unless you get into imaginary numbers.
And the point I was trying to get at is the concept of negative numbers. They are not like positive numbers, in the sense that they are the exact oposite, or inverse of it. Nevermind tho...No need to start a huge argument, as I sense it might happen.
The rule for multiplying negative numbers is that when two negative numbers are multiplied together, the result is always a positive number.
This is because when two negative numbers are multiplied together, the negative signs cancel out and the result is a positive number.
Yes, the result of -4 multiplied by -4 will always be 16, since the rule for multiplying negative numbers always applies.
The significance of this is that it demonstrates the mathematical concept of negative numbers and how they behave when multiplied together. It also shows the importance of understanding mathematical rules and properties.
In real-life scenarios, -4 multiplied by -4 can represent situations where two negative quantities are being combined. For example, if you owe $4 and then borrow another $4, you would have a total debt of $16. It can also represent situations where two negative forces are acting in the same direction, resulting in a positive outcome.