Question

A multiplication problem has 3 positive factors and 4 negative factors.

What is the sign of the product?

A.
positive

B.
negative

Answer 1

1) Well, we have something like this:
(+) x (+) x (+) x (-) x (-) x (-) x (-)

that is, we have 3 positive factors, and 4 negative factors multiplying together (we really don't care what the numbers are exactly, we just want to follow the signs).

2) We know that (+) x (+) = (+). That is, positive times positive is positive. So, the first three positives just become some positive.

[(+) x (+) x (+)] x (-) x (-) x (-) x (-) = (+) x (-) x (-) x (-) x (-)

3) We also know that (-) x (-) = (+). So, we get
(+) x [(-) x (-)] x [(-) x (-)] = (+) x (+) x (+) = (+).

The final answer must be positive.

There are many other ways to solve this, but this is one that will do the job. :)