Solve the Division Problem: 0:3 Using Division Notation

Q: Why is 0 ÷ 3 equal to 0 and not undefined?

Great question! 0 ÷ 3 = 0 because we're dividing zero BY 3, not dividing BY zero. Think of it this way: if you have zero cookies to share among 3 people, each person gets zero cookies!

Q: What's the difference between 0 ÷ 3 and 3 ÷ 0?

0 ÷ 3 = 0 (zero divided by a number), but 3 ÷ 0 is undefined (dividing by zero). The key is which number is being divided and which is doing the dividing!

Q: Does 0 ÷ any number always equal 0?

Yes! Zero divided by any non-zero number always equals zero. Whether it's $ 0 \div 5 $, $ 0 \div 100 $, or $ 0 \div 3 $, the answer is always zero.

Q: How can I remember this rule?

Think of division as sharing equally. If you have nothing to share (zero), no matter how many groups you divide into, each group still gets nothing. Zero shared = zero for everyone!

Q: Can I check my answer using multiplication?

Absolutely! Since division and multiplication are opposite operations, check by multiplying: $ 0 \times 3 = 0 $. This confirms that $ 0 \div 3 = 0 $ is correct!

Zero Division with Non-Zero Divisors

$0:3=$

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Step-by-step video solution

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00:00 Solve

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

00:08 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

$0:3=$

Step-by-step solution

To solve this problem, we need to understand the basic property of division involving zero. When dividing zero by any non-zero number, the result is always zero. This can be written mathematically as:

$0 \div 3 = 0$

This stems from the fact that zero, when divided by any number, still yields zero because you are essentially distributing zero evenly across that number, which results in zero.

In simpler terms, if you have zero of something and you attempt to divide it among any number of groups, you will still end up with zero in each group.

Step 1: Recognize the problem involves dividing zero by a non-zero number.
Step 2: Apply the property $0 \div a = 0$ for any non-zero $a$ .
Step 3: Conclude $0 \div 3 = 0$ .

Therefore, the solution to the problem $0 \div 3$ is $0$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Zero divided by any non-zero number always equals zero
Technique: Apply $0 \div 3 = 0$ using the zero dividend property
Check: Verify by multiplication: $0 \times 3 = 0$ confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Confusing zero division with division by zero
Don't think $0 \div 3$ is undefined like $3 \div 0$ = undefined! Division BY zero is impossible, but zero divided by a non-zero number always gives zero. Always remember: zero as dividend (top) = zero result.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why is 0 ÷ 3 equal to 0 and not undefined?

Great question! 0 ÷ 3 = 0 because we're dividing zero BY 3, not dividing BY zero. Think of it this way: if you have zero cookies to share among 3 people, each person gets zero cookies!

What's the difference between 0 ÷ 3 and 3 ÷ 0?

0 ÷ 3 = 0 (zero divided by a number), but 3 ÷ 0 is undefined (dividing by zero). The key is which number is being divided and which is doing the dividing!

Does 0 ÷ any number always equal 0?

Yes! Zero divided by any non-zero number always equals zero. Whether it's $0 \div 5$ , $0 \div 100$ , or $0 \div 3$ , the answer is always zero.

How can I remember this rule?

Think of division as sharing equally. If you have nothing to share (zero), no matter how many groups you divide into, each group still gets nothing. Zero shared = zero for everyone!

Can I check my answer using multiplication?

Absolutely! Since division and multiplication are opposite operations, check by multiplying: $0 \times 3 = 0$ . This confirms that $0 \div 3 = 0$ is correct!

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