Solve: Division of -4/7 by Zero - Understanding Undefined Operations

Q: What if I get zero in the denominator during solving?

Stop immediately and write "undefined" or "no solution" as your answer. Don't try to continue calculating - the problem becomes invalid at that point.

Q: Is this the same as getting zero as an answer?

No! Getting zero as your final answer (like x = 0) is perfectly fine. The problem is when zero appears in the denominator of a fraction during your work.

Q: How do I recognize division by zero in different formats?

$ a ÷ 0 $ - direct division$ \frac{a}{0} $ - fraction form$ a:0 $ - ratio notationAll of these mean the same thing and are undefined!

Q: What should I write as my final answer?

Write "undefined", "invalid", or "no solution". Some teachers prefer specific wording, so check what your teacher wants you to use.

Division by Zero with Fraction Expressions

$-\frac{4}{7}:0=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem step by step.

00:08 Remember, you cannot divide by zero.

00:11 Think of division as writing it in fraction form.

00:16 So, in this case, there is no solution. And that's okay!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-\frac{4}{7}:0=\text{ ?}$

Step-by-step solution

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

$\frac{-\frac{4}{7}}{0}$

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 always undefined and invalid
Technique: Recognize $\frac{-\frac{4}{7}}{0}$ as impossible to evaluate
Check: Any expression with zero in denominator is undefined ✓

Common Mistakes

Avoid these frequent errors

Attempting to calculate division by zero
Don't try to divide -4/7 by 0 or guess at an answer! Division by zero has no mathematical meaning and cannot be computed. Always identify when zero appears in the denominator and declare the expression undefined.

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 that number?" But zero goes into any number infinitely many times, making the answer impossible to determine. That's why mathematicians declare it undefined.

What if I get zero in the denominator during solving?

Stop immediately and write "undefined" or "no solution" as your answer. Don't try to continue calculating - the problem becomes invalid at that point.

Is this the same as getting zero as an answer?

No! Getting zero as your final answer (like x = 0) is perfectly fine. The problem is when zero appears in the denominator of a fraction during your work.

How do I recognize division by zero in different formats?

$a ÷ 0$ - direct division
$\frac{a}{0}$ - fraction form
$a:0$ - ratio notation

All of these mean the same thing and are undefined!

What should I write as my final answer?

Write "undefined", "invalid", or "no solution". Some teachers prefer specific wording, so check what your teacher wants you to use.

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