Division Involving Zero

For any real number a, $frac{a}{0}$ is undefined

For any non-zero real number a, $frac{0}{a}$ = 0

$frac{0}{0}$ is indeterminate

For any real number a, $frac{a}{0}$ is undefined

Dividing any real number by zero is undefined and sometimes taken as infinity. Division is spptting into equal parts or groups.

Let us consider an example: Suppose there are 12 ice cream cups and 4 friends want to share them. How do they spanide the ice cream cups?

$frac{12}{4}$ = 3; So they get 3 each: Now, let us try spaniding the 12 ice cream cups among zero people. How much does each person get?

Does that question make sense? No, it doesn t.

We can t share among zero people, and we can t spanide by 0.

Suppose we could get some number k by spaniding any real number a by zero

Let us assume $frac{a}{0}$ = k. Then k × 0 = a. There is no such number k which when multipped by zero will give a. So k does not exist and therefore $frac{a}{0}$ is said to be undefined.

For any non-zero real number a, $frac{0}{a}$ = 0

If zero is spanided by any non-zero real number a, we get 0 as the result. If zero items are spanided among a number of people, share got by each person will be zero only

$frac{0}{0}$ is indeterminate

Division of zero by zero is a quantity that cannot be found and is called indeterminate.

Find the value of $frac{0}{5}$

Solution

Step 1:

For example, $frac{3}{4}$ = 3 × $frac{1}{4}$ .

Step 2:

Similarly, $frac{0}{5}$ = 0 × $frac{1}{5}$ = 0

as the product of zero and any number is zero.

Evaluate $frac{7}{0}$

Solution

Step 1:

By definition, spanision of any number by zero is not defined.

Step 2:

So, $frac{7}{0}$ is not defined.

Evaluate $frac{0}{13}$

Solution

Step 1:

Zero spanided by any number is zero.

Step 2:

So, $frac{0}{13}$ = 0