Question

What is $0$ divided by $-2,$ is it no solution?

Answer 1

Hint: We know that the product of two numbers is zero if any of the numbers or both are zero. For any number $a,$ the product $a\cdot 0$ is $0.$ If we transpose the number $a$ ton the other side, we will get ${\displaystyle \frac{0}{a}}=0.$

Complete step by step solution:
We are asked to find what $0$ divided by $-2.$
We need to find the value when $-2$ divides $0.$
We know that, in Mathematics, $0$ stands for ‘nothing’.
We also know that by division we mean partition. So, when we divide ‘nothing’ by a certain value, we get nothing. This value can be any arbitrary value.
So, when we divide zero by any arbitrary value, the result will be zero.
We can explain this fact Mathematically.
We know that when a number is multiplied with zero, the product will be zero.
Let us take an arbitrary number $a.$ We know that the product of $a$ and zero will give us $a\cdot 0=0.$
Let us see what happens when we transpose $a$ from the left-hand side to the right-hand side.
We will get $0={\displaystyle \frac{0}{a}}.$
Since $a$ is an arbitrary number, this is true for every number.
That means, when we divide $0$ by $-2,$ we will get $0$ as the quotient.
That is, when $0$ is the dividend, the product will be $0.$
Therefore, we will get $-2\times 0=0.$
And this will give us ${\displaystyle \frac{0}{-2}}=0.$
We learn that the given statement has a solution.

Hence the solution of $0$ divided by $-2$ is $0.$

Note: When the divisor is zero, then the value is undefined. The quotient we obtain when a number is divided by zero is infinity. Therefore, any number divided by infinity will give the quotient zero. In the first case, we say no solution exists.