Question

If the product of two whole numbers is $1$ , can we say that one or both of them will be $1?$ Justify through examples.

Answer 1

Hint:In this question we have been given a statement and we have to check whether one of the numbers or both numbers are equal to $1$ . So we will take any whole number as an example and one of them we will take as one, and then we check if their product is equal to one or not.

Complete step by step answer:
Let us first understand the definition of a whole number.
Whole Numbers: All the natural numbers including zero i.e. $0$ are called whole numbers. We know that all counting numbers are called natural numbers.For example; $1,2,3,9,10,22,25,999...$ are all examples of natural numbers. Now we know that by multiplying any whole number by $1$ we get the same whole number. So let us take some whole numbers and then multiply it with one: First whole number is $5$.Now we multiply $5$ with one and see the result:
$5 \times 1 = 5$

We can see that here the product is not equal to $1$.
Again we take another whole number i.e. $25$.
We will multiply this whole number with one: $25 \times 1 = 25$.
We can see that here also the product is not equal to one. Now let us take the whole number as $1$ i.e. both the numbers are one and then we find the product.
It gives us: $1 \times 1 = 1$
We can see that here the product is equal to one. From the above solution we can conclude that if only one number were $1$, then the product cannot be equal to $1$ .

Hence we can say that the product of two whole numbers will be equal to $1$ only if both the whole numbers are $1$.

Note:We should note that $0$ (Zero) is the smallest whole number. There is no largest whole number. If we multiply the whole number $1$ with zero, we get the result as zero. We can see the product as $0 \times 1 = 0$. So we can write this as if the product of two whole numbers is $0$, we can say that one of the numbers has to be zero. Because any number multiplied by zero gives the result as zero.