Question

Product of two negative integers is a negative integer.
A) True
B) False

Answer 1

Hint: Here the given question is related to the integers. We have to check whether it is true or false. For this, first we have to know the definition of the integers and about the positive, negative integers. Then we consider the table of multiplication of integers and sign conversion and check whether it is true or false.

Complete step by step answer:
In mathematics, there are different kinds of numbers namely, natural numbers, whole numbers, integers, rational numbers, irrational numbers and real numbers.
The combination or pack of positive and negative natural numbers along with the number zero is known as integers. The integers are usually represented by ($$I$$).
In a number line we write the integers. Because the number line contains both positive and negative numbers. So, we can say that the number on the right side of the number line is termed as positive and the numbers on the left of a number line are termed as negative and the number which separates these two types of number by zero lies in between the positive and negative numbers.
Example of positive integers are:
1, 2, 3, 5, 10, 25, …. so on
Example of negative integers are:
-1, -2, -3, -5, -10, -25, …. so on
Now consider, the table of multiplication of integers or sign conversion table:
$$ + \times + = + $$
$$ + \times - = - $$
$$ - \times + = - $$
$$ - \times - = + $$
Product of two negative integers will obviously be a positive integer. When you multiply a negative integer with another negative integer the product will be a positive integer because two negative signs cancel each other.
Let’s take an example:
Assume -5 and -10 be a two negative integer, then its product is 50
$$ \Rightarrow \,\, - 5 \times - 10 = 50$$.
Therefore, the given statement “Product of two negative integers is a negative integer.” is
False.

Note:
For two integers we follow the rule of table of multiplication of integers. Suppose if we have a product of more than two integers we need to follow the property that the product of an odd number of negative integers is negative and the product of an even number of negative integers is a positive.