Solve the Multiplication Equation: Finding the Number in ? × 4 = 0

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

Then any number could be the answer! This is because any number multiplied by 0 equals 0. But in our problem, we're multiplying by 4, so only 0 works.

Q: How do I remember the Zero Product Property?

Think of it this way: "To get zero as a result, you need zero as an ingredient." Just like you can't bake a cake without flour, you can't get zero without having zero somewhere in your multiplication!

Q: Could there be other answers besides 0?

No, only 0 works! Try any other number: 1 × 4 = 4, 2 × 4 = 8, 10 × 4 = 40. None of these equal 0. Only 0 × 4 = 0.

Q: Is this the same as solving 4x = 0?

Yes! $ ? \times 4 = 0 $ is the same as $ 4x = 0 $. To solve it, divide both sides by 4: $ x = \frac{0}{4} = 0 $.

Zero Product Property with Missing Factors

$?\times4=0$

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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 multiplied by any number always equals 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

$?\times4=0$

Step-by-step solution

First, we examine the equation $? \times 4 = 0$ . The Zero Product Property tells us that for any number multiplied by another to result in zero, at least one of the numbers must be zero.

Since the right side of the equation is zero, $?$ must be zero because any real number multiplied by zero results in zero, regardless of the other factor.
Therefore, we can conclude:

The solution to the problem is $\boxed{0}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Zero Property: Any number multiplied by zero equals zero
Technique: If ? × 4 = 0, then ? must be 0
Check: Substitute back: 0 × 4 = 0 ✓

Common Mistakes

Avoid these frequent errors

Thinking the answer could be 4 or any other non-zero number
Don't assume ? could be 4 because 4 × 4 = 16, not 0! Only zero multiplied by any number gives zero. Always remember that for any multiplication to equal zero, at least one factor 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 4 since we're multiplying by 4?

Great question! The number we're multiplying by (which is 4) is different from the missing number we're looking for. Since 4 × 4 = 16, not 0, the answer can't be 4.

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

Then any number could be the answer! This is because any number multiplied by 0 equals 0. But in our problem, we're multiplying by 4, so only 0 works.

How do I remember the Zero Product Property?

Think of it this way: "To get zero as a result, you need zero as an ingredient." Just like you can't bake a cake without flour, you can't get zero without having zero somewhere in your multiplication!

Could there be other answers besides 0?

No, only 0 works! Try any other number: 1 × 4 = 4, 2 × 4 = 8, 10 × 4 = 40. None of these equal 0. Only 0 × 4 = 0.

Is this the same as solving 4x = 0?

Yes! $? \times 4 = 0$ is the same as $4x = 0$ . To solve it, divide both sides by 4: $x = \frac{0}{4} = 0$ .

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