Find the Missing Symbol in 0:-412.5?0: Mathematical Operation Puzzle

Zero Division Properties with Comparison Symbols

Fill in the missing symbol (?):

0:412.5?0 0:-412.5\text{?}0

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's add the correct sign, alright?
00:10 Think of division like a fraction, with the numerator on top.
00:15 When zero is divided by any number, it always equals zero.
00:20 We can apply this rule to our exercise now.
00:23 But, remember, never divide by zero. That's very important.
00:28 Great job! And that's how we solve this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing symbol (?):

0:412.5?0 0:-412.5\text{?}0

2

Step-by-step solution

First let's solve the exercise on the left-hand side:

0412.5= \frac{0}{-412.5}=

Here we must remember the formula:

0x=0 \frac{0}{x}=0

In other words, when we divide 0 by any number, the result will always be 0.

Now we have:

0?0 0\text{?}0

Therefore, the answer is:

0=0 0=0

3

Final Answer

=

Key Points to Remember

Essential concepts to master this topic
  • Zero Division Rule: Zero divided by any non-zero number equals zero
  • Technique: Calculate 0412.5=0 \frac{0}{-412.5} = 0 first, then compare values
  • Check: Verify that 0 = 0 is true by confirming both sides equal ✓

Common Mistakes

Avoid these frequent errors
  • Thinking zero divided by a negative gives a negative result
    Don't assume 0412.5=0 \frac{0}{-412.5} = -0 or some negative value! Zero divided by ANY non-zero number (positive or negative) always equals zero. Always remember: zero has no sign when it's the result of division.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( (+6)\cdot(+9)= \)

FAQ

Everything you need to know about this question

Why does zero divided by a negative number still equal zero?

+

Zero has no sign! When you divide zero by any non-zero number, the result is always zero. Think of it this way: how many groups of -412.5 can you make from nothing? The answer is zero groups!

What would happen if we had -412.5 divided by 0 instead?

+

That would be undefined! Division by zero is impossible in mathematics. But 0412.5 \frac{0}{-412.5} is perfectly fine and equals zero.

How do I know which comparison symbol to use?

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First calculate the left side completely: 0412.5=0 \frac{0}{-412.5} = 0 . Then compare: is 0 less than, greater than, or equal to 0? Since they're the same, use =.

Is there a trick to remember the zero division rule?

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Yes! Remember: "Zero divided by anything (except zero) is zero." It doesn't matter if the divisor is positive, negative, big, or small - the answer is always zero.

Could the answer be 'not possible to calculate'?

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No! 0412.5 \frac{0}{-412.5} is completely calculable. "Not possible" only applies when dividing BY zero, not when zero is being divided.

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