Question

If you multiply four negative numbers, what is the sign of the product?

If you multiply five negative numbers, what is the sign of the product?

Based on the answers to these questions and the product rules, write a general rule for the sign of the product based on the number of
negative numbers in the expression.

Answer 1

If you multiply four negative numbers, what is the sign of the product?

You can test this with numbers, the easiest with -1:

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

General:

(-a)(-b)(-c)(-d) = abcd

The sign of the product of four negative numbers is positive.

If you multiply five negative numbers, what is the sign of the product?

Testing with -1:

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

General:

(-a)(-b)(-c)(-d)(-e) = -abcde

The sign of the product of five negative numbers is negative.

General rule: The product of an even number of negative numbers is positive. The product of an odd number of negative numbers is negative.

Answer 2

positive

Explanation:

(-a) (-a) (-a) (-a) = a

(-a)(-a) = a

a (-a) = -a

-a (-a) = a --> positive sign