why (-1)*(-1)=+1?

Answer 1

You don't need to invoke the fact that a negative times a negative is a positive. It will follow from the distributive law : a(b+c) = ab + ac.

(-1) * (-1) + (-1) = (-1) * (-1 + 1) = (-1) * (0) = 0. Adding 1 to both sides then gives (-1) * (-1) = 1.

This can be modified to prove that a negative times a negative is a positive. Take positive numbers a and b. Then:

(-a) * (-b) + (-a * b) = (-a) * (-b + b) = (-a) * (0) = 0. Adding a * b to both sides we get (-a) * (-b) = a * b.

[Edit: For the record, "a negative times a negative is a positve" and "(-1) * (-1) = 1" are NOT axioms. They can be proved using the axioms (see above).]

Answer 2

It does seem a little counter-intuitive, doesn't it? That the product of two negative numbers is a positive number? But here's a real-world example that might help.

Imagine that you're in a hot-air balloon, and you've got the flame going so that your balloon is rising. Every second, you rise 5 inches. Think of the upward direction as being positive, and downward as negative.

Question 1: 3 seconds in the future, where will you be compared to where you are now? Answer: (+5 inches/second)*(+3 seconds) = +15 inches (in other words, 15 inches higher)

Question 2: 3 seconds ago, where were you compared to where you are now? Answer: (+5 inches/second)*(-3 seconds) = -15 inches (15 inches lower).

Now, change the scenario... the flame's not on, and your balloon is sinking at 5 inches every second.

Question 3: 3 seconds from now, where will you be? Answer: (-5 inches/second)*(+3 seconds) = -15 inches (15 inches lower).

Now, here's the crucial question:

QUESTION 4: 3 seconds ago, where were you? Answer: (-5 inches/second)*(-3 seconds) = +15 inches (15 inches higher).

So part of the real reason we say that the product of two negative numbers is a positive number is that it actually corresponds to real world experience. (The other part of it, which someone else will probably explain, is that the algebra works out cleanly that way.)

Hope that helps!

EDITED TO ADD: to the person who invoked the "double negative" rule of English, as in "not not tired" -- the only reason English works that way is because, in the 19th Century, grammarians like Samuel Johnson and his cronies decided that the logic of English should mimic the logic of algebra. In fact, plenty of languages, like Spanish, use double-negative constructions all the time without the negatives "canceling each other out."

Answer 3

Think of a square on a piece of graph paper. The coordinates of the corners are, let us say:

0,0
0,1
1,0
1,1

So it is a square with sides of 1 unit and area 1 square unit.

You could cut this square out and move it around the paper, making the coordiates what you wished. The area of the square would always be 1. So let us move it to the opposite side of the origin, so that the coordinates become:

0,0
0,-1
-1,0 and
-1,-1

each side is now -1 in length but the area is still 1 square unit.

Answer 4

Because 1*1 = 1 (anything multiplied by 1 equals itself), and two negatives multiplied together equal a positive.

Answer 5

Mathematicians have a set up a set of rules (or axioms) where one of the rules is that (-1)*(-1) = 1. If this wasn't true we would not have a lot basic operations we are used to like adding two negative numbers together. Which we cannot do if the above it is not true.

Answer 6

(-1)*(-1)= - (1*(-1)) = - (-1) = 1

Answer 7

look 2*2 means 2 plus 2 twice. So (-1)*(-1) means -1 plus -1,-1 times (-1)+(-1) one time gives -2 and doing it 0 times gives -1 and doing it -1 times gives 1.

Answer 8

two negatives equal a positive - it's weird, right?

2x2 = 4 ...if I give you 2 apples 2 times, you have 4

-1 * -1 = 1 if I take one apple away from you a negative amount of times, it's the same as if I gave you one

Answer 9

Not exactly a question, cmon its a fundamental rule. 2 negatives always make a positive. If i ask why is 1+1=2, can u explain? We all know its is, but why...its just silly

Answer 10

(-1)*(-1)=1 because when you multiply a negative by a negative it equals a positive but when you multiply a positive by a negative it equals a negative like 1*(-1)=-!