Solve the Division Equation: Finding the Number That Equals 0 When Divided by 2

Q: Why can't the answer be 1 or 2?

Let's check: $ 1 ÷ 2 = 0.5 $ and $ 2 ÷ 2 = 1 $. Neither equals 0! Only zero divided by any non-zero number gives zero.

Q: What if I multiply both sides by 2?

Perfect! That's exactly the right approach. $ x ÷ 2 = 0 $ becomes $ x = 0 × 2 = 0 $. Multiplying both sides by the same number preserves equality.

Q: Is there a special rule about zero in division?

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

Q: How do I remember this type of problem?

Think: "What number gives me zero when I divide it?" The answer is always zero itself! $ 0 ÷ 2 = 0 $, $ 0 ÷ 5 = 0 $, $ 0 ÷ 100 = 0 $.

Q: Can I solve this without multiplication?

You could think logically: "What number divided by 2 gives 0?" Since only 0 ÷ anything = 0, the answer must be 0. But multiplying both sides is the formal algebraic method.

Division Equations with Zero Products

$?:2=0$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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

00:07 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

$?:2=0$

Step-by-step solution

To solve this problem, we'll proceed with the following steps:

Step 1: Recognize $x : 2 = 0$ as $\frac{x}{2} = 0$ , which can be restated for clarity.
Step 2: Multiply both sides of the equation by 2 to eliminate the division.
Step 3: Calculate to find the value of $x$ .

Now, let's work through each step:
Step 1: We have $\frac{x}{2} = 0$ .
Step 2: To solve for $x$ , multiply both sides by 2:
$2 \times \frac{x}{2} = 2 \times 0$
This simplifies to $x = 0$ , since multiplication of zero by any number remains zero.

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

Final Answer

Key Points to Remember

Essential concepts to master this topic

Zero Property: Any number divided by any non-zero number equals zero only if the number is zero
Technique: Multiply both sides by the divisor: $x ÷ 2 = 0$ becomes $x = 0 × 2 = 0$
Check: Substitute back into original equation: $0 ÷ 2 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Thinking the answer must be the divisor
Don't assume x = 2 just because we're dividing by 2! This gives 2 ÷ 2 = 1, not 0. The only number that equals zero when divided by any non-zero number is zero itself. Always remember: only zero divided by anything (except zero) equals zero.

Practice Quiz

Test your knowledge with interactive questions

$$ 2+0= $$

FAQ

Everything you need to know about this question

Why can't the answer be 1 or 2?

Let's check: $1 ÷ 2 = 0.5$ and $2 ÷ 2 = 1$ . Neither equals 0! Only zero divided by any non-zero number gives zero.

What if I multiply both sides by 2?

Perfect! That's exactly the right approach. $x ÷ 2 = 0$ becomes $x = 0 × 2 = 0$ . Multiplying both sides by the same number preserves equality.

Is there a special rule about zero in division?

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

How do I remember this type of problem?

Think: "What number gives me zero when I divide it?" The answer is always zero itself! $0 ÷ 2 = 0$ , $0 ÷ 5 = 0$ , $0 ÷ 100 = 0$ .

Can I solve this without multiplication?

You could think logically: "What number divided by 2 gives 0?" Since only 0 ÷ anything = 0, the answer must be 0. But multiplying both sides is the formal algebraic method.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Order of operations for beginners questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime