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

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 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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