Question

The sign of the product of two unlike integers is ______.
A. Positive
B. Negative
C. Positive or Negative
D. Cannot be determined

Answer 1

Hint: Consider two integers ‘a’ and ‘b’. First negate ‘a’ and find the product of negative ‘a’ and positive ‘b’. Next negate ‘b’ and find the product of positive ‘a’ and negative ‘b’. Notice the signs of both the products and that will be our answer.

Complete step-by-step answer:
We are given to determine the sign of the product of two unlike integers.
Integers are numbers which can be written without fractional components. Integers can be either negative or positive. Fractions are not integers. For example 2, -4, -5, 7 are integers whereas 7.5, ${\displaystyle \frac{2}{3}}$ , $\sqrt{5}$ are not integers.
Here let us first consider two integers ‘a’ and ‘b’.
When ‘a’ is negated, we get –a.
Now we are finding the product of ‘-a’ and ‘b’.
 $\Rightarrow -a\times b=-\left(ab\right)$
When b is negated, we get –b.
Now we are finding the product of ‘a’ and ‘-b’.
 $\Rightarrow a\times -b=-\left(ab\right)$
As we can when a positive integer and negative integer (irrespective of their order) are multiplied, we get a negative result.
Therefore, the sign of the product of two unlike integers is always $negative$ .
So, the correct answer is “Option B”.

Note: Unlike integers are the integers which have opposite signs (like positive-negative or negative-positive) and like integers are the integers which have the same signs (like positive-positive or negative-negative). 2, 5 and -2, -5 are like integers whereas 2, -5 and -2, 5 are unlike integers. So be careful with the signs. When two like integers are multiplied, the result will always have a positive sign unlike ‘unlike’ integers.