The product of two negative rational numbers is greater than either factor. Is this statement true, somethimes true, or never true?

Answer : - This statement is true sometimes.

For example:-

Case1: Let - 2 and - 3 are two negative rational numbers such that - 2 * - 3=6

and the factors of - 2 are 1,-1,2,-2 and factors of - 3 are - 1,1,3,-3

As we can see the product of - 2 and - 3 is greater than their factors.

Then it follows the statement.

Case2: Let - 6 and - 1/6 are two negative rational numbers such that - 6 * - 1/6=1

and the factors of - 6 are 1,-1,2,-2,3,-3,6,-6

As we can see the product of - 6 and - 1/6 is smaller than 2,3,6 which are the factors of - 6.

But it contradicts the statement.

Therefore the product of two negative numbers is sometimes greater than either factor.