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I will assume you already agree that positive times negative is negative. Now consider this sequence:
-3 x 2 = -6
-3 x 1 = -3
-3 x 0 = 0
-3 x -1 = ???
What number would logically continue the sequence? The number to the right of the multiplication sign decreases by one at a time; the number to the right of the equal sign increase by 3 at a time, so the logical number is 3.
You might also reply, "To maintain the validity of certain mathematical rules, even for negative numbers - for example, the distributive property."
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Why don't negative numbers have square roots?
They can, but they are called imaginary numbers. This is because a "square" of something is the number that, when multiplied by itself, will equal the first number. A negative multiplied by a negative equals a positive, and positives can't turn into negatives on their own, so there are no square roots of negative numbers.
What is the rule for multiplying a negative times a positive number?
If two numbers are multiplied and one of them is negative, the answer will turn out negative. If the two numbers being multiplied are either both negative or both positive, the answer will turn out positive. Example: -2 * 2 = -4 -2 * -2 = 4 2 * 2 = 4
When you add two negatives what is the answer?
A negative ex. -4+(-4)=-8 The addition symbol between actually can turn into a subtraction symbol through very simple algebra because a positive times a negative is always a negative. So: -4-4=-8 is the same.
How do you turn 6 into a positive integer?
(6)
How can you turn the difference of two positive numbers is always positive into a false statement?
By subtracting a positive number from itself. 3 - 3 = 0
