Why does a negative number multiplied by a negative number equal a positive number?

Question

i cant figure it out.

Answer 1

It is a rule!!!

Answer 2

Killer question. I did not know the answer so I searched the web. This is the answer that I found most conclusive and understandable. I hope it works for you as well:

The rule was invented so that accociative property (which is discussed in pre-algebra) would hold.
I'll construct a proof using -1 as an example of a negative number, so as not to confuse you with variables and so on. If you used any number besides -1, you would get to the same result.

Expanded proof

First, note that 1 + (-1) = 0. And any number multiplied by a zero is zero.

Knowing that, consider this simple equality:

2*(1 + (-1)) = 0

It is true because 1 + (-1) is zero. (see the section of adding signed numbers for details on this)

Since we want negative numbers to obey associative property (see it discussed in the pre-algebra section), the above equality can be rewritten as

2*1 + 2*(-1) = 0
If I subtract 2*1 from both sides of the equation, I would get
2*1 - 2*1 + 2*(-1) = 0 - 2*(-1)
I'll highlight

Since the highlighted parts cancel out, that simplifies to
2*(-1) = - 2*(-1)

Written in words, "the product of 2 by minus one is the opposite of the product of 2 and 1".

That's why the rule of multiplication of signed numbers was invented: so that associative property of multiplication and addition would hold true.

Answer 3

Remember that multiplication is simply repeated addition;
6 * 3 = 6+6+6 = 18 = 3+3+3+3+3+3

Multiplication by a negative number, therefore, can be regarded either as repeated addition or subtraction;
6 * (-3) = -6-6-6 = -18 = (-3)+(-3)+(-3)+(-3)+(-3)+(-3)

Multiplication of a negative number by a negative number is simply repeated subtraction;
(-6)*(-3) = -(-6)-(-6)-(-6) = 18 = -(-3)-(-3)-(-3)-(-3)-(-3)-(-3)

As long as you believe the negative of a negative number is positive, then the multiplication of a negative number by a negative number is positive.

Answer 4

One way to think of it (and I am meaning for this to be non-technical) is that -5 is the opposite of 5. So, the opposite of -5 would be 5. In essence, you're taking the opposite of an opposite which equals a regular positive number. Hopefully that's enough to help it make sense, but not so much that it further confuses the topic. Best luck!

Answer 5

My math instructor continually informed me this trick for remembering what happens with 2 unfavourable numbers: whenever you multiply or divide 2 unfavourable numbers, the two unfavourable signs and symptoms - and - integrate to type a plus + In different words, the two unfavourable signs and symptoms cancel one yet another out and ask your self an outstanding. subsequently, once you divide or multiply a unfavourable by making use of a unfavourable, you will get an outstanding answer.

Answer 6

Here's one way to look at it. The Cartesian coordinate plane has 4 quadrants, numbered counter-clockwise from I to IV. Quadrant I contains positive areas because all the products of numbers contained there are the result of multiplication of purely positive numbers: x values greater than zero and y values greater than zero. Quadrant II contains the product of hybrids: positives times negatives, so they are considered to be negative areas. LIkewise with quadrant IV. Notice that quadrants II and IV are vertical to each other

Now we come to that pesky quadrant III. It would seem logical and orderly for that quadrant, since areas contained in it are also the product of only one type of signed number, i..e negaitve, that those areas would also be considered positive, as are those in quadrant I, because it is vertical to quadrant I, just as quadrants II and IV are to each other, and just as areas in those quadrants have the same sign. Assigning positive values to the product of two negative numbers therefore adds balance, symmetry and completeness to the Cartesian plane.

Answer 7

Assume you loan $10 from Loanshark A. So you're now @ -$10. He tells you that he wants to repent from his sins and he charges you a negative interest of 10%. so -10 * -0.1 = 1. Notice it's positive and it look like you received a dollar.

Don't try too hard to progress from here or you're end up more miserable.

Answer 8

You give it a thought
If -1 X -1 = +1
and +1 X -1 = -1
then 1 = -1
and then 2 = 0
and 1=0
and last of all.....a=0
if a not equal 0
and a IS equal 0......we are 0 years old

Answer 9

If you take 2 and make it thrice (+3 times), you get 6.
If you take 2 and make it -thrice, you get -6.
Now apply the same logic on -2 X -3.
Apply the analogy TAKE as + and GIVE as -.
You would understand.

Answer 10

I'm not sure, but it positively has no negative affect on my life.

Answer 11

Like everyone else, I just know it does but do not know why. I am sure there is some sort of mathematical reason but I have never ran into it.