Solve the Multiplication Equation: Finding the Number in ?×10=0

Q: Why can't the answer be 1 or 10?

Let's check: $ 1 \times 10 = 10 $ (not 0) and $ 10 \times 10 = 100 $ (not 0). Only zero gives us the product of 0!

Q: What is the zero property of multiplication?

The zero property states that any number multiplied by zero equals zero. Also, if a product equals zero, then at least one factor must be zero.

Q: Could there be other numbers that work?

No! In multiplication, if the product is zero, then exactly one or more factors must be zero. Since 10 ≠ 0, the unknown must be 0.

Q: How do I solve equations like this quickly?

Ask yourself: "What number times 10 gives me 0?" Since only 0 × anything = 0, the answer is always 0 when the product is zero.

Q: What if the equation was ? × 0 = 0 instead?

Then any number would work! Since anything times zero equals zero, the unknown could be 1, 5, 100, or any number at all.

Zero Property of Multiplication with Unknown Factors

$?\times10=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the missing number

00:03 0 multiplied 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

$?\times10=0$

Step-by-step solution

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

Step 1: Identify the given information.
Step 2: Apply the properties of multiplication with zero.
Step 3: Select the correct answer based on this property.

Now, let's work through each step:
Step 1: We have an equation $? \times 10 = 0$ .
Step 2: Using the basic property of multiplication, we know that any number multiplied by zero results in a zero product. Conversely, if the product is zero, then at least one of the factors must be zero.
Step 3: Since 10 is not zero, the number represented by "?" must be zero for the product to be zero.

The possible answer choices are:

Choice 1: 1
Choice 2: 10
Choice 3: 0
Choice 4: 11

Based on our analysis, the unknown value in the equation must be zero for the product to be zero. Therefore, the correct answer is choice 3: $0$ .

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

Final Answer

Key Points to Remember

Essential concepts to master this topic

Zero Property: Any number multiplied by zero equals zero
Technique: Since $? \times 10 = 0$ , the unknown must be 0
Check: Substitute back: $0 \times 10 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Thinking the unknown could be 10 since 10 appears in the equation
Don't assume the unknown equals 10 just because 10 is visible = wrong answer of 100! This ignores the zero property completely. Always remember that if any factor is zero, the entire product must be 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 1 or 10?

Let's check: $1 \times 10 = 10$ (not 0) and $10 \times 10 = 100$ (not 0). Only zero gives us the product of 0!

What is the zero property of multiplication?

The zero property states that any number multiplied by zero equals zero. Also, if a product equals zero, then at least one factor must be zero.

Could there be other numbers that work?

No! In multiplication, if the product is zero, then exactly one or more factors must be zero. Since 10 ≠ 0, the unknown must be 0.

How do I solve equations like this quickly?

Ask yourself: "What number times 10 gives me 0?" Since only 0 × anything = 0, the answer is always 0 when the product is zero.

What if the equation was ? × 0 = 0 instead?

Then any number would work! Since anything times zero equals zero, the unknown could be 1, 5, 100, or any number at all.

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