Since 1 divided by 0 doesn’t exist hence 0 has no
The Correct Answer and Explanation is:
Correct Answer:
Since 1 divided by 0 does not exist, 0 has no reciprocal.
Explanation
In mathematics, division by zero is undefined. This means that no number can be divided by zero in the usual arithmetic sense. To understand why, consider the idea of a reciprocal. The reciprocal of a number is another number that, when multiplied with the original, results in 1. For example, the reciprocal of 2 is 1/2 because:
2 × (1/2) = 1.
This concept works well for all non-zero numbers. However, when we try to apply it to zero, a problem arises.
Let us suppose that 0 has a reciprocal. That would mean there is some number “x” such that:
0 × x = 1.
But no matter what value x has, multiplying it by 0 always results in 0:
0 × x = 0.
This shows that it is impossible to find any number that when multiplied by 0 gives 1. Hence, 0 has no reciprocal.
This is directly connected to the idea that 1 divided by 0 does not exist. Division is essentially the reverse of multiplication. Saying “1 divided by 0” is like asking, “What number multiplied by 0 gives 1?” As we just proved, there is no such number.
In contrast, dividing 1 by any non-zero number gives a valid result. For instance, 1 ÷ 2 = 0.5, because 0.5 × 2 = 1. But with 0, this relationship breaks down.
In summary, because multiplication by 0 always yields 0, it is impossible for 0 to have a reciprocal. Therefore, since 1 divided by 0 is undefined, 0 has no reciprocal and this is a key concept in arithmetic and algebra.
