Solve Division Problem: What is +312 ÷ 0?

Q: What's the difference between 0 ÷ 312 and 312 ÷ 0?

$ 0 ÷ 312 = 0 $ because zero divided by any non-zero number equals zero. But $ 312 ÷ 0 $ is undefined because you cannot divide by zero!

Q: Does 312 ÷ 0 equal infinity?

No! While the values get very large as you divide by numbers closer to zero, infinity is not a number. Division by zero is simply undefined - it has no mathematical meaning.

Q: How do I recognize invalid expressions?

Look for zero in the denominator of any fraction or division problem. Expressions like $ \frac{x}{0} $, $ a ÷ 0 $, or $ \frac{5}{x-3} $ when x = 3 are all invalid.

Q: What should I write as my answer?

Write "undefined" or "invalid expression". Never write a number as the answer when dividing by zero - this shows you understand the mathematical rule!

Division by Zero with Undefined Expressions

$+312:0=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this step by step.

00:12 First, write the division as a fraction.

00:16 Remember, you cannot divide by zero.

00:21 So, there's no solution to this problem. Great job trying!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$+312:0=\text{ ?}$

Step-by-step solution

First, let's rewrite the expression in the form of a simple fraction:

$\frac{-312}{0}=$

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

Rule: Division by zero is undefined and mathematically impossible
Recognition: Any expression like $\frac{a}{0}$ is automatically invalid
Check: Always verify denominator is not zero before dividing ✓

Common Mistakes

Avoid these frequent errors

Thinking division by zero equals zero or infinity
Don't assume 312 ÷ 0 = 0 or 312 ÷ 0 = ∞! Division by zero creates a logical contradiction that breaks mathematics. Always recognize that any number divided by zero is undefined and invalid.

Practice Quiz

Test your knowledge with interactive questions

Convert $\frac{7}{2}$ into its reciprocal form:

FAQ

Everything you need to know about this question

Why can't I divide by zero?

Division asks "how many times does this number go into another?" But zero goes into any number infinitely many times, which creates a contradiction. Mathematics requires consistent answers, so division by zero is undefined.

What's the difference between 0 ÷ 312 and 312 ÷ 0?

$0 ÷ 312 = 0$ because zero divided by any non-zero number equals zero. But $312 ÷ 0$ is undefined because you cannot divide by zero!

Does 312 ÷ 0 equal infinity?

No! While the values get very large as you divide by numbers closer to zero, infinity is not a number. Division by zero is simply undefined - it has no mathematical meaning.

How do I recognize invalid expressions?

Look for zero in the denominator of any fraction or division problem. Expressions like $\frac{x}{0}$ , $a ÷ 0$ , or $\frac{5}{x-3}$ when x = 3 are all invalid.

What should I write as my answer?

Write "undefined" or "invalid expression". Never write a number as the answer when dividing by zero - this shows you understand the mathematical rule!

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