Zero Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Why is 50\frac{5}{0} undefined? Explain using the definition of division.

Solution

  1. 1
    Division ab=c\frac{a}{b} = c means c×b=ac \times b = a.
  2. 2
    If 50=c\frac{5}{0} = c, then c×0=5c \times 0 = 5. But c×0=0c \times 0 = 0 for every value of cc.
  3. 3
    No value of cc satisfies this, so 50\frac{5}{0} is undefined.

Answer

50 is undefined\frac{5}{0} \text{ is undefined}
Division is the inverse of multiplication. Dividing by zero would require a number that, when multiplied by zero, gives a nonzero result — but the zero product property makes this impossible. Hence division by zero is undefined, not infinite.

About Zero

The number representing the absence of quantity; the additive identity and placeholder in positional notation.

Learn more about Zero →

More Zero Examples

Example 1 easy

Evaluate: (a) [formula], (b) [formula], (c) [formula].

Example 3 easy

Is zero even or odd? Justify.

Example 4 medium

The number [formula] has a zero in the tens place. How does removing that zero (writing 320 instead)

← All Zero Examples Zero Concept