Solve the Zero Equation: Finding the Missing Value in 0:?=0

Q: Why do all numbers work as the divisor?

Because zero divided by any non-zero number always equals zero! Think of it as sharing nothing among groups - you still have nothing. $ 0 \div 5 = 0 $, $ 0 \div 100 = 0 $, etc.

Q: What about dividing by zero itself?

Division by zero is undefined in mathematics! We can only divide zero by other numbers, not divide by zero. So $ 0 \div 0 $ is not allowed.

Q: How is this different from regular division problems?

Regular division like $ 12 \div ? = 3 $ has exactly one solution (4). But when zero is the dividend, infinitely many numbers work as the divisor!

Q: Can negative numbers work too?

Absolutely! All real numbers except zero work as divisors. $ 0 \div (-5) = 0 $, $ 0 \div (-100) = 0 $. The result is always zero.

Q: How do I check my understanding?

Pick any number and use multiplication to verify: If $ 0 \div 7 = 0 $, then $ 7 \times 0 = 0 $ ✓. This confirms your answer!

Zero Division Properties with Universal Solutions

$0:?=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's find the unknown together.

00:06 Remember, zero divided by any number is always zero.

00:26 And that's how we solve the question. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$0:?=0$

Step-by-step solution

To solve this problem, we need to evaluate the equation $0:?=0$ . When considering this equation, it implies determining what number, represented by '?', when multiplied by 0, results in 0.
According to the properties of multiplication involving zero, any number multiplied by zero results in zero. Mathematically, $a \cdot 0 = 0$ for any real number $a$ .
Thus, the equation $0:?=0$ is true for all real numbers 'x' because any real number multiplied by 0 equals 0.
Given the multiple-choice options, the appropriate conclusion is option 3, which states "All answers are correct".
Therefore, this problem confirms that for the equation $0:?=0$ , all real numbers satisfy the condition.

Therefore, the correct answer is All answers are correct.

Final Answer

All answers are correct

Key Points to Remember

Essential concepts to master this topic

Zero Property: Any number divided by zero equals zero universally
Technique: Test with examples: $0 \div 4 = 0$ , $0 \div 100 = 0$
Check: Verify by multiplication: if $0 \div a = 0$ , then $a \times 0 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Thinking zero division has only one solution
Don't assume $0 \div ? = 0$ has just one answer = missing the universal property! This ignores that zero divided by ANY non-zero number equals zero. Always remember that all non-zero real numbers work as divisors.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why do all numbers work as the divisor?

Because zero divided by any non-zero number always equals zero! Think of it as sharing nothing among groups - you still have nothing. $0 \div 5 = 0$ , $0 \div 100 = 0$ , etc.

What about dividing by zero itself?

Division by zero is undefined in mathematics! We can only divide zero by other numbers, not divide by zero. So $0 \div 0$ is not allowed.

How is this different from regular division problems?

Regular division like $12 \div ? = 3$ has exactly one solution (4). But when zero is the dividend, infinitely many numbers work as the divisor!

Can negative numbers work too?

Absolutely! All real numbers except zero work as divisors. $0 \div (-5) = 0$ , $0 \div (-100) = 0$ . The result is always zero.

How do I check my understanding?

Pick any number and use multiplication to verify: If $0 \div 7 = 0$ , then $7 \times 0 = 0$ ✓. This confirms your answer!

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