Identifying Meaningless Expressions (ME) in Mathematical Statements

Q: Why is dividing by zero undefined?

Think about it: if $ \frac{10}{2} = 5 $ because 2 × 5 = 10, then $ \frac{10}{0} $ would need a number that when multiplied by 0 gives 10. But any number times 0 equals 0, never 10!

Q: What's the difference between 0/700 and 700/0?

$ \frac{0}{700} = 0 $ because 0 divided by any non-zero number is 0. But $ \frac{700}{0} $ is undefined because you cannot divide any number by zero.

Q: Are there other meaningless expressions besides division by zero?

Yes! Examples include $ \sqrt{-4} $ (square root of negative numbers in basic math), $ 0^0 $ (zero to the zero power), and $ \frac{\infty}{\infty} $ (infinity divided by infinity).

Q: What should I write as the answer when I get division by zero?

Write "undefined" or "meaningless expression (ME)" depending on what your teacher prefers. Never write a number as the answer!

Q: Can calculators divide by zero?

Most calculators will show "Error" or "Math Error" when you try to divide by zero. This confirms that division by zero is not allowed in mathematics!

Division by Zero with Undefined Operations

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 (N/A)

00:03 Division by 0 is forbidden, therefore N/A

00:08 0 divided by any number is always equal to 0

00:13 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'll follow these steps:

Step 1: Identify the operations present in each expression.
Step 2: Determine if any expression involves division by zero.

Now, let's work through each step:
Step 1: The expression choices are $\frac{700}{0}$ and $\frac{0}{700}$ .
Step 2: Analyze each expression:

Expression $\frac{700}{0}$ : Divides 700 by 0. Division by zero is undefined in mathematics, making this a meaningless expression.
Expression $\frac{0}{700}$ : Divides 0 by 700. This results in 0, which is a defined mathematical operation and therefore not meaningless.

Therefore, the expression that is identified as a meaningless expression is $\frac{700}{0}$ .

Final Answer

700:0

Key Points to Remember

Essential concepts to master this topic

Rule: Division by zero is always undefined and meaningless
Technique: Check denominators: $\frac{700}{0}$ is undefined, $\frac{0}{700} = 0$
Check: Any fraction with zero in denominator is meaningless ✓

Common Mistakes

Avoid these frequent errors

Confusing zero in numerator vs denominator
Don't think $\frac{0}{700}$ and $\frac{700}{0}$ are both meaningless = wrong identification! Zero in numerator gives 0, but zero in denominator is undefined. Always check which position zero occupies in the fraction.

Practice Quiz

Test your knowledge with interactive questions

$$ 2+0= $$

FAQ

Everything you need to know about this question

Why is dividing by zero undefined?

Think about it: if $\frac{10}{2} = 5$ because 2 × 5 = 10, then $\frac{10}{0}$ would need a number that when multiplied by 0 gives 10. But any number times 0 equals 0, never 10!

What's the difference between 0/700 and 700/0?

$\frac{0}{700} = 0$ because 0 divided by any non-zero number is 0. But $\frac{700}{0}$ is undefined because you cannot divide any number by zero.

Are there other meaningless expressions besides division by zero?

Yes! Examples include $\sqrt{-4}$ (square root of negative numbers in basic math), $0^0$ (zero to the zero power), and $\frac{\infty}{\infty}$ (infinity divided by infinity).

What should I write as the answer when I get division by zero?

Write "undefined" or "meaningless expression (ME)" depending on what your teacher prefers. Never write a number as the answer!

Can calculators divide by zero?

Most calculators will show "Error" or "Math Error" when you try to divide by zero. This confirms that division by zero is not allowed in mathematics!

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