Question

Complete these sentences to describe the multiplication of signed numbers. The product of two positive integers is always . The product of two negative integers is always . The product of a positive integer and a negative integer is always . The product of any integer and –1 is always .

Answer 1

The product of two positive integers is always positive.

The product of two negative integers is always positive.

The product of a positive integer and a negative integer is always negative.

The product of any integer and –1 is always opposite of that number.

Explanation:

Rule of multiplication of sign:

First Second Resultant

(+) × (+) = (+)

(-) × (-) = (+)

(+) × (-) = (-)

(-) × (+) = (-)

From the above table we can say that:

The product of two positive integers is always positive.

The product of two negative integers is always positive.

The product of a positive integer and a negative integer is always negative.

Let x be an unknown integer.

The product of an unknown integer and -1 is

`x* (-1)=-x`

Therefore, the product of any integer and –1 is always opposite of that number.

Answer 2

The product of two positive integers is always POSITIVE . The product of two negative integers is always POSITIVE. The product of a positive integer and a negative integer is always NEGATIVE . The product of any integer and –1 is always THE OPPOSITE OF THAT INTEGER .