Identifying Meaningless Expressions (ME): Mathematical Validation Exercise

Q: What's the difference between 0:20 and 20:0?

0:20 means "zero divided by twenty" which equals zero. 20:0 means "twenty divided by zero" which is undefined. The position of zero matters!

Q: Can I ever divide by zero in any situation?

No! Division by zero is never allowed in mathematics. It doesn't matter if it's $ \frac{1}{0} $, $ \frac{100}{0} $, or $ \frac{0}{0} $ - all are meaningless expressions.

Q: How do I identify meaningless expressions quickly?

Look for the denominator in any division or fraction. If the bottom number (denominator) is zero, the expression is meaningless. The top number (numerator) can be zero - that just makes the answer zero.

Q: What should I write if I encounter division by zero?

Write "undefined" or "meaningless expression". Never try to calculate a numerical answer when dividing by zero!

Division by Zero with Expression Validation

Which of the expressions is a meaningless expression (ME)?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the meaningless expression (ME)

00:03 0 divided by any number always equals 0

00:07 However, division by 0 is not allowed, therefore ME

00:11 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which of the expressions is a meaningless expression (ME)?

Step-by-step solution

To solve this problem, we will evaluate each of the given expressions to determine which one is a meaningless expression due to division by zero:

First Expression: $0:20$
In mathematical terms, this expression translates to $\frac{0}{20}$ . Division of zero by any non-zero number is defined and equals zero. Therefore, this expression is meaningful.
Second Expression: $20:0$
This translates to $\frac{20}{0}$ . Division by zero is undefined in mathematics. Therefore, this expression is meaningless.

Hence, the expression $20:0$ is a meaningless expression.

Therefore, the meaningless expression is $20:0$ .

Final Answer

20:0

Key Points to Remember

Essential concepts to master this topic

Rule: Division by zero is undefined and creates meaningless expressions
Technique: Check denominators: $\frac{20}{0}$ is undefined, $\frac{0}{20} = 0$
Check: Any expression with zero in denominator is meaningless ✓

Common Mistakes

Avoid these frequent errors

Confusing zero dividend with zero divisor
Don't think $\frac{0}{20}$ and $\frac{20}{0}$ are both meaningless! Only division BY zero is undefined. Always remember: zero divided by a number equals zero, but a number divided by zero is meaningless.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why is dividing by zero undefined?

Division asks "how many times does this number fit into another?" But zero fits into any number infinitely many times, making the answer impossible to determine. That's why $\frac{20}{0}$ has no mathematical meaning.

What's the difference between 0:20 and 20:0?

0:20 means "zero divided by twenty" which equals zero. 20:0 means "twenty divided by zero" which is undefined. The position of zero matters!

Can I ever divide by zero in any situation?

No! Division by zero is never allowed in mathematics. It doesn't matter if it's $\frac{1}{0}$ , $\frac{100}{0}$ , or $\frac{0}{0}$ - all are meaningless expressions.

How do I identify meaningless expressions quickly?

Look for the denominator in any division or fraction. If the bottom number (denominator) is zero, the expression is meaningless. The top number (numerator) can be zero - that just makes the answer zero.

What should I write if I encounter division by zero?

Write "undefined" or "meaningless expression". Never try to calculate a numerical answer when dividing by zero!

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