Question

Which of the following will not represent zero?
A.\[1 + 0\]
B.\[0 \times 0\]
C.\[\dfrac{0}{2}\]
D.\[\dfrac{{10 - 10}}{2}\]

Answer 1

Hint: This is very simple to solve a problem. We will check the options one by one. The answer of the solution should not be zero. That is our answer. To solve this type of questions we should know the rules or simple ways of addition, subtraction, multiplication and division. That’s it!

Complete step-by-step answer:
Given are four different operations.
Let’s test them one by one.

A.\[1 + 0\]
Here we are given the additional operation. We know that when zero is added to any number the answer won’t change. It remains the same. So when a zero is added to 1 answer should be that the sum will be 1.
So this is the correct option.
But we will check for the remaining answers also.

B.\[0 \times 0\]
In the second option we are given the product of two zeros. Now the thing is, when any number is multiplied with zero the answer is zero only. Then that number can be any big number or a small number. But when zero is in the product with it the answer is zero.
So this is also not the correct option.

C.\[\dfrac{0}{2}\]
In the third case, the numerator of the fraction is zero. So the answer is zero.

D.\[\dfrac{{10 - 10}}{2}\]
In the last option when we subtract 10 from 10 we get the numerator as zero. And as we have seen just in the above case, the fraction with numerator zero is zero.

So, the correct answer is “Option A”.

Note: Note that, for the answer to be zero in case of addition, the number and its negation should be added. For zero as an answer in subtraction the same number should be subtracted from the same number.
For multiplication only products with zero will work and for division the numerator of the fraction should be zero.
But note that any number can never be divided by zero or a fraction with zero as the denominator is not defined.
Note that if option 3 is modified like, \[10 - \dfrac{{10}}{2}\] then the case will be changed. The answer now will be,
\[10 - \dfrac{{10}}{2} = 10 - 5 = 5\]
Hope this is clear!