Solve the Equation: Zero Times Unknown Equals Zero

Q: Why do all the answer choices work for this equation?

Because of the zero property of multiplication! When zero is multiplied by any number (positive, negative, whole, fraction), the result is always zero. So 1, 2, 10, or even 1000 would all work.

Q: Is there ever a number that doesn't work with zero?

No! Every real number works. Whether it's $ 0 \times (-50) $ or $ 0 \times 2.5 $, the answer is always zero. This is what makes zero special in multiplication.

Q: What if the equation was different, like 5 × ? = 0?

Then only zero would work! If any non-zero number is multiplied by something to get zero, that something must be zero. The zero property only works when zero is being multiplied, not when it's the result.

Q: How is this different from addition with zero?

Great question! With addition, $ 0 + ? = 0 $ only works when ? = 0. But with multiplication, $ 0 \times ? = 0 $ works for any number because zero 'absorbs' everything in multiplication.

Q: Can I use this property to solve harder problems?

Absolutely! The zero property helps solve equations like $ x(x-5) = 0 $. If a product equals zero, then at least one factor must be zero, so x = 0 or x = 5.

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

00:15 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$0\times?=0$

2

Step-by-step solution

To solve this problem, let's focus on the principle of multiplication concerning zero:

Step 1: Understand that any number multiplied by zero equals zero.
Step 2: Apply this understanding to the given equation $0 \times ? = 0$ .
Step 3: Recognize that since zero multiplied by any number results in zero, the missing value can be any real number.

Now, let's work through these steps:

Step 1: The multiplication property of zero states that when a number is multiplied by zero, the product is always zero.

Step 2: In the equation $0 \times ? = 0$ , we need to determine what value of the question mark satisfies this condition. Based on the multiplication property of zero, we know that this condition holds for any real number.

Step 3: Therefore, regardless of what number we replace the question mark with, as long as it’s a real number, the equation will be true since $0 \times \text{any number} = 0$ .

Therefore, the solution to this problem is that all values satisfy the equation. This conclusion matches the choice "All answers are correct."

Therefore, the correct answer is All answers are correct.

3

Final Answer

All answers are correct

Key Points to Remember

Essential concepts to master this topic

Zero Property: Any number multiplied by zero always equals zero
Technique: $0 \times 5 = 0$ , $0 \times 100 = 0$ , $0 \times (-3) = 0$
Check: Test with any number: $0 \times 1 = 0$ , $0 \times 2 = 0$ , $0 \times 10 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Assuming only one specific number works
Don't think that only 1 or 10 satisfies $0 \times ? = 0$ = missing the universal property! This ignores that zero multiplied by ANY number gives zero. Always remember that zero times anything equals zero, so ALL real numbers work.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why do all the answer choices work for this equation?

+

Because of the zero property of multiplication! When zero is multiplied by any number (positive, negative, whole, fraction), the result is always zero. So 1, 2, 10, or even 1000 would all work.

Is there ever a number that doesn't work with zero?

+

No! Every real number works. Whether it's $0 \times (-50)$ or $0 \times 2.5$ , the answer is always zero. This is what makes zero special in multiplication.

What if the equation was different, like 5 × ? = 0?

+

Then only zero would work! If any non-zero number is multiplied by something to get zero, that something must be zero. The zero property only works when zero is being multiplied, not when it's the result.

How is this different from addition with zero?

+

Great question! With addition, $0 + ? = 0$ only works when ? = 0. But with multiplication, $0 \times ? = 0$ works for any number because zero 'absorbs' everything in multiplication.

Can I use this property to solve harder problems?

+

Absolutely! The zero property helps solve equations like $x(x-5) = 0$ . If a product equals zero, then at least one factor must be zero, so x = 0 or x = 5.

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Solve the Equation: Zero Times Unknown Equals Zero

Zero Property with Any Number Multiplication

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