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That's the way it is defined. And it's defined that way to maintain consistency in different properties of numbers. However, the following argument makes it look reasonable, at least. Let's assume it is already given that a positive number times a negative number is negative. (If this doesn't sound reasonable to you, please ask a separate question.)

Now consider the following sequence:

-10 x 3 = -30

-10 x 2 = -20

-10 x 1 = -10

-10 x 0 = 0

-10 x -1 = ...

Now consider the question: What number should you fill in to complete the sequence? The left number in each multiplication is constant, the middle number decreases by one at a time. The rightmost column obviously obviously increases by 10 at a time; if you continue the sequence, you inevitably get 10 - a positive number. Similarly, you get positive numbers if you replace the sequence with any other combination of numbers, such that the first number is negative, and the second number decreases at a constant rate.

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Q: Why is a negative number times negative number always a positive?
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How do you work out how to times a positive number by a negative number?

A positive number times a positive number will always get you a positive number A negative number times a negative number will always get you a positive number (same signs will get you a positive number) but A positive number times a negative number will always get you a negative number or A negative number times a positive number will always get you a negative number (different signs will get you a negative number)


Why does a negative number times a negative number produce a positive number?

Negative times negative is always a positive.


Why is the square of a number always a positive number?

The square of a number is always two numbers multiplied together. A positive times a positive is always positive, and a negative times a negative is always positive.


What is a positive times a negitive?

A positive number multiplied with a negative number will always be negative.


Why is any number raised to a even power positive?

A positive number times a positive number is always positive. A negative number times a negative number is always positive. Therefore, any square number will be positive. Any number to the fourth power (a square times a square) will always be positive. And so on.


What is negative 10 times negative 5?

-10 x -5 = +50A negative times a negative will always equal a positive number.A negative times a positive will always equal a negative number.A positive times a positive will always equal a positive number.- x - = +- x + = -+ x + = +


How do you square negative numbers?

Multiply the number by its self and the answer will always be positive (negative times a negative is positive)


Would a positive multiplied by a negative be a positive?

No. A positive times a negative is always negative. A negative times a negative is always a positive.


What is a negitaive times a positive?

A negative number times a positive number will give you a negative product.A negative number times a positive number will give you a negative product.A negative number times a positive number will give you a negative product.A negative number times a positive number will give you a negative product.


What is positive 6 times negative 2?

-12A negative times a positive is always a negative.A negative times a negative is always positive.


How do you multiply a negative number to a positive number?

A negative times a positive is always a negative. The rest is the same: just multiply as if they are both positive numbers and then add the negative sign at the end.


Why is a negative number times a negative number always equal a positive number?

because you are dividing with same signs