Solve: Division of -12⅛ by Zero - Understanding Undefined Operations

Division by Zero with Mixed Numbers

1218:0?0 -12\frac{1}{8}:0\text{?}0

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Complete the appropriate sign
00:03 Let's write division as a fraction
00:06 Never divide by 0, ever!
00:12 Therefore there is no solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

1218:0?0 -12\frac{1}{8}:0\text{?}0

2

Step-by-step solution

Let's first turn our attention to the exercise on the left hand side :

12180= \frac{-12\frac{1}{8}}{0}=

Remembering the below formula:

x0 \frac{x}{0}

Since no number can be divided by 0 we are able to ascertain that the expression has no meaning.

3

Final Answer

There is no meaning to the expression

Key Points to Remember

Essential concepts to master this topic
  • Rule: Division by zero is undefined for all numbers
  • Technique: Any expression like 12180 \frac{-12\frac{1}{8}}{0} has no meaning
  • Check: If denominator equals zero, expression is undefined ✓

Common Mistakes

Avoid these frequent errors
  • Attempting to calculate division by zero
    Don't try to compute 1218÷0 -12\frac{1}{8} ÷ 0 = some number! Division by zero cannot produce any real number result. Always recognize that when the divisor is zero, the expression is undefined and has no meaning.

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 we divide by zero?

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Division asks "how many times does this number fit into another?" But zero cannot fit into any number because zero has no size. It's like asking "how many nothings make something?" - it simply has no answer!

What should I write when I see division by zero?

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Always write "undefined" or "no meaning" or "does not exist". Never try to calculate a numerical answer because there isn't one!

Does it matter what number is being divided by zero?

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No! Whether it's 50 \frac{5}{0} , 12180 \frac{-12\frac{1}{8}}{0} , or 10000 \frac{1000}{0} , they are all undefined. The number being divided doesn't matter - division by zero is always impossible.

Is this the same as 0 ÷ 0?

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Yes, 0 ÷ 0 is also undefined! Even though it might seem like it should equal 1, mathematically it's still impossible to determine a unique answer, so we call it undefined too.

What happens on a calculator when I divide by zero?

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Most calculators will show "Error" or "Cannot divide by zero". This confirms that division by zero is impossible - even machines can't do it!

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