Prove mathematically that a negative number multiplied by a negative number, yields a positive product.?

Answer 1

Let a and b be any two real numbers. Consider the number x defined by

x = ab + (-a)(b) + (-a)(-b).

We can write
x = ab + (-a)[ (b) + (-b) ] (factor out -a)
= ab + (-a)(0)
= ab + 0
= ab.

Also,
x = [ a + (-a) ]b + (-a)(-b) (factor out b)
= 0 * b + (-a)(-b)
= 0 + (-a)(-b)
= (-a)(-b).

So we have
x = ab
and
x = (-a)(-b)

Hence, by the transitivity of equality, we have

ab = (-a)(-b).

Answer 2

Hmm... OK, let a and b be any two positive numbers and n = -b.

Then, trivially ab - ab = 0. Also, -ab = an, so ab + an = 0. Since we know ab is positive, then an must be negative. Therefore, the product of a positive number and a negative number must be negative.

Now let a and b be any two negative numbers and n = -b. (Note that n is positive.)

Again, ab - ab = 0 and -ab = an, so ab + an = 0. Since we know from the previous logic that an must be negative, it follows that ab must be positive. Therefore, the product of two negative numbers must be positive.

Answer 3

When both factors are negative, as in -4(-5), the sign of the product is positive. We are to take away -5 four times.

-4(-5) = -(-5) - (-5) -(-5) -(-5) becomes +5 +5 +5 +5

Of course, +5+5+5+5 = 20.

Remember that taking away a negative 5 is the same as adding a positive 5.

Guido

Answer 4

This is gonna sound really stupid...but a professor once told me that two negative people will have a positive relationship and that it's the same way with numbers....It helped me remember...Hope it helps you too!! :)

Answer 5

Well, it's common sense. A negetive number times a negetive number will always give you a positive number. Just think of peanut butter and jelly; peanut butter is way different than jelly, if you combine them together, you get a postive result :D

Answer 6

Let a and b be positive real numbers, so that

-a < 0 and -b <0. [Need to show (-a)(-b) > 0]

now, (-a)(-b) = (-1)(a)(-1)(b) = (-1)(-1)(a)(b) = (1)(a)(b)

= 1 (ab) = (ab) = ab > 0.

so, (-a)(-b) = ab = c >0 (c = ab, another real number). QED

Answer 7

The same concept with sentence construction!
You cannot "double negative in a sentence".
Example: He is not unworthy of the prize.
"Not" and "unworthy" is both negative so it yealds a positive structure!!! So thats how you handle it!!!
Good luck!!!!

Answer 8

it is a regulation, or convention, in arithmetic. you could, although, be sure that the manufactured from 2 destructive numbers is a superb quantity: you could in elementary terms divide an excellent quantity with a destructive quantity to derive a destructive quantity.