What is 8 ÷ 0?
Answer – The expression is undefined.
Explanation:
Let’s begin by going over the definition of the mathematical operation of division:
If we divide a number x by another number y and it gives us a number z, z must be unique and the product of y and z must be x, i.e. .
To understand this better, let’s consider an example with known values:
Here, , , and .
Since 2 is the only result of dividing 10 by 5, it is unique. Also, multiplying 5 and 2 gives us 10. So the criterion of is satisfied. We can also say that dividing 10 by 5 is defined.
Any expression that doesn’t satisfy either condition of z being unique or is said to be undefined.
Let’s now use this information to answer the given question .
We begin by assuming that . If this is true, then .
But any number multiplied by 0 is always 0, and there exists no number which when multiplied by 0 gives 8.
So we can say that division of 8 by 0 is undefined. The same also applies to any other number divided by 0.
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