Solve: -72/3 ÷ 0 - Understanding Division by Zero

Q: What if the numerator is also zero?

Even $ \frac{0}{0} $ is undefined! While it might seem like it should equal 1, mathematically it's an indeterminate form that could represent any number.

Q: How do I spot division by zero quickly?

Look for zero in the denominator of any fraction or after a division symbol (÷). As soon as you see this, the entire expression becomes invalid - no further calculation needed!

Q: Is this different from dividing zero by a number?

Yes! $ \frac{0}{5} = 0 $ is perfectly valid and equals zero. The problem only occurs when zero is in the denominator (bottom of the fraction).

Q: What should I write as my answer?

Write "undefined" or "invalid expression" or "no solution". Never try to give a numerical answer when division by zero is involved.

Division by Zero with Undefined Expressions

$-\frac{72}{3}:0=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Let's write division as a fraction

00:07 Cannot divide by 0

00:13 Therefore there is no solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-\frac{72}{3}:0=\text{ ?}$

Step-by-step solution

Let's write the expression in the form of a simple fraction:

$\frac{-\frac{72}{3}}{0}$

Since it is not possible to divide a number by 0, the expression is invalid.

Final Answer

The expression is invalid.

Key Points to Remember

Essential concepts to master this topic

Fundamental Rule: Division by zero is always undefined and invalid
Technique: First simplify $-\frac{72}{3} = -24$ , then recognize the division by zero
Check: Any expression with division by zero is invalid, no calculation needed ✓

Common Mistakes

Avoid these frequent errors

Attempting to calculate the numerator before recognizing division by zero
Don't calculate -72/3 = -24 and then try to divide by zero = confusion about what makes expressions invalid! This wastes time and misses the key concept. Always identify division by zero first - it immediately makes any expression undefined.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why can't we divide by zero?

Division asks "how many times does the divisor go into the dividend?" With zero, this question has no meaningful answer. Zero goes into any number an infinite number of times, making the result undefined.

What if the numerator is also zero?

Even $\frac{0}{0}$ is undefined! While it might seem like it should equal 1, mathematically it's an indeterminate form that could represent any number.

How do I spot division by zero quickly?

Look for zero in the denominator of any fraction or after a division symbol (÷). As soon as you see this, the entire expression becomes invalid - no further calculation needed!

Is this different from dividing zero by a number?

Yes! $\frac{0}{5} = 0$ is perfectly valid and equals zero. The problem only occurs when zero is in the denominator (bottom of the fraction).

What should I write as my answer?

Write "undefined" or "invalid expression" or "no solution". Never try to give a numerical answer when division by zero is involved.

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