When you multiply a negative number by a positive number what happens explain?

Answer 1

Multiplication is an abbreviation of addition:

4 x 5 is the same as:

adding 4 together 5 times: 4 x 5 = 4 + 4 + 4 + 4 + 4 = 20; or

adding 5 together 4 times: 4 x 5 = 5 + 5 + 5 + 5 = 20

When multiplying a negative number by a positive number, it can be thought of adding the negative number to itself the positive number of times.

eg -4 x 5 = -4 + -4 + -4 + -4 + -4 = -20

eg -5 x 4 = -5 + -5 + -5 + -5 = -20

Adding a negative number is the same as subtracting the number (as a positive number):

eg 7 + -3 = 7 - 3 = 4

eg -7 + -3 = -7 - 3 = -10

Answer 2

The result of a negative number multiplied by a positive number is a negative number.

It is probably easiest to understand it as follows:

Suppose that the two numbers A and B are both positive, so that (-B) is negative.

[B + (-B)] = 0

Now, anything multiplied by 0 is 0

so A*[B + (-B)] = 0.

Expanding this gives A*B + A*(-B) = 0.

This means that the second term A*(-B) is the additive inverse [opposite] of the first, A*B.

That is A*(-B) = -A*B