Solve the Division Equation: Finding the Number That Equals 0 When Divided by 7

Q: What's the difference between 0 ÷ 7 and 7 ÷ 0?

0 ÷ 7 = 0 (zero divided by any number is zero), but 7 ÷ 0 is undefined (you cannot divide by zero). These are completely different situations!

Q: How do I remember this rule?

Think of division as sharing: If you have 0 cookies to share among 7 people, each person gets 0 cookies. But you can't share 7 cookies among 0 people - that's impossible!

Q: Will this work with any number instead of 7?

Yes! Zero divided by any non-zero number always equals zero. So $ 0 ÷ 5 = 0 $, $ 0 ÷ 100 = 0 $, etc.

Division with Zero Properties

$?:7=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 0 divided by any number is always equal to 0

00:10 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$?:7=0$

Step-by-step solution

Let's solve this mathematical problem:

Step 1: Understand the problem
We need to find the number $n$ such that when divided by 7 it equals 0, or $n \div 7 = 0$ .
Step 2: Use properties of multiplication and zero
To solve for $n$ , we use the basic property of zero in multiplication: if $a \cdot b = 0$ , then either $a = 0$ , $b = 0$ , or both. Similarly, if $n \div 7 = 0$ , then $n = 0$ .
Step 3: Reasoning
Since any number divided by another number results in zero only when the dividend is zero, we conclude that $n$ must be 0.

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

Final Answer

Key Points to Remember

Essential concepts to master this topic

Zero Rule: Only zero divided by any number equals zero
Technique: If n ÷ 7 = 0, then n = 0 × 7
Check: Substitute back: 0 ÷ 7 = 0 ✓

Common Mistakes

Avoid these frequent errors

Confusing division by zero with division resulting in zero
Don't think 7 ÷ 0 = 0! Division by zero is undefined and impossible. Always remember: only when the dividend (top number) is zero can division equal zero.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why can't the answer be 7 since we're dividing by 7?

Great question! The number we're dividing by (the divisor) doesn't determine the answer. Only when the number being divided (dividend) is zero will any division equal zero.

What's the difference between 0 ÷ 7 and 7 ÷ 0?

0 ÷ 7 = 0 (zero divided by any number is zero), but 7 ÷ 0 is undefined (you cannot divide by zero). These are completely different situations!

How do I remember this rule?

Think of division as sharing: If you have 0 cookies to share among 7 people, each person gets 0 cookies. But you can't share 7 cookies among 0 people - that's impossible!

Will this work with any number instead of 7?

Yes! Zero divided by any non-zero number always equals zero. So $0 ÷ 5 = 0$ , $0 ÷ 100 = 0$ , etc.

How can I check if my answer is right?

Substitute your answer back into the original equation. If you think the answer is 0, check: $0 ÷ 7 = 0$ . Since this is true, 0 is correct!

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