Solve the Division Equation: Finding the Number Where ?:1 = 0

Q: Why does dividing by 1 not change the number?

Division by 1 is like asking "how many groups of 1 fit into this number?" The answer is always the number itself! Think of it like sharing 5 cookies among 1 person - that person gets all 5 cookies.

Q: What if the question mark was a different number like 5?

If we had $ 5 \div 1 = 0 $, this would be impossible because 5 ÷ 1 always equals 5, not 0. Only when the missing number is 0 does the equation work.

Q: Is zero divided by any number always zero?

Yes! Zero divided by any non-zero number always gives zero. But remember: we can never divide by zero - that's undefined in mathematics.

Q: How do I remember the division by 1 rule?

Think of division as splitting into equal groups. When you split something into 1 group, you get the whole thing back unchanged! $ 8 \div 1 = 8 $, $ 0 \div 1 = 0 $.

Q: What's the difference between 0÷1 and 1÷0?

$ 0 \div 1 = 0 $ (zero split into 1 group = zero), but $ 1 \div 0 $ is undefined because you cannot split 1 into zero groups - it's impossible!

Division Properties with Zero Results

$?:1=0$

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Understand the problem

$?:1=0$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Understand the problem statement meaning $x \div 1 = 0$ .
Step 2: Apply the division property: any number divided by 1 remains unchanged.
Step 3: Recognize that since $x \div 1 = x$ , for it to equal 0, $x$ must indeed be 0.

Now, let's work through each step:
Step 1: The equation $x \div 1 = 0$ implies that $x$ divided by 1 equals 0.
Step 2: According to the division rule, $x = x \div 1$ . So for $x \div 1$ to be zero, $x$ must be 0.
Step 3: Solving for $x$ , we find that since $x = 0 \div 1$ , it naturally simplifies to $x = 0$ because zero divided by any number is zero.

Therefore, the solution to the problem is $x = 0$ .

The correct choice from the provided options is: 0

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Any number divided by 1 equals itself unchanged
Technique: Since $x \div 1 = x$ , if result is 0 then x must be 0
Check: Substitute back: $0 \div 1 = 0$ confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Thinking division by 1 changes the number
Don't assume dividing by 1 makes numbers smaller or different = wrong thinking! Division by 1 is the identity property - it never changes the value. Always remember that x ÷ 1 = x, so if the result is 0, then x must be 0.

Practice Quiz

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$1\times1000=$

FAQ

Everything you need to know about this question

Why does dividing by 1 not change the number?

Division by 1 is like asking "how many groups of 1 fit into this number?" The answer is always the number itself! Think of it like sharing 5 cookies among 1 person - that person gets all 5 cookies.

What if the question mark was a different number like 5?

If we had $5 \div 1 = 0$ , this would be impossible because 5 ÷ 1 always equals 5, not 0. Only when the missing number is 0 does the equation work.

Is zero divided by any number always zero?

Yes! Zero divided by any non-zero number always gives zero. But remember: we can never divide by zero - that's undefined in mathematics.

How do I remember the division by 1 rule?

Think of division as splitting into equal groups. When you split something into 1 group, you get the whole thing back unchanged! $8 \div 1 = 8$ , $0 \div 1 = 0$ .

What's the difference between 0÷1 and 1÷0?

$0 \div 1 = 0$ (zero split into 1 group = zero), but $1 \div 0$ is undefined because you cannot split 1 into zero groups - it's impossible!

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