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

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 does zero divided by a negative number still equal zero?

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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?

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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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