Solve the Equation: Finding the Missing Factor in 61 × ? = 0

Q: Why can't the answer be 1, since 1 doesn't change numbers when multiplying?

While 1 is the multiplicative identity, it doesn't make products equal zero. Remember: $ 61 \times 1 = 61 $, not 0. Only multiplying by zero gives a product of zero.

Q: What if I thought the answer was 61 because it's the number in the equation?

That's a common guess, but $ 61 \times 61 = 3721 $, which is definitely not 0! The zero property of multiplication tells us only zero works as the missing factor.

Q: Does this zero property work with any number, not just 61?

Yes! Whether it's $ 5 \times ? = 0 $ or $ 1000 \times ? = 0 $, the answer is always zero. This is a universal mathematical property.

Q: How do I remember this rule for tests?

Think of it this way: "Zero kills everything!" When zero is involved in multiplication, the result is always zero, no matter what the other number is. This makes it easy to remember!

Q: What happens if both numbers in multiplication are zero?

If you have $ 0 \times 0 $, the answer is still 0! The zero property works even when both factors are zero.

Multiplication Property with Zero Factor

$61\times?=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:04 0 multiplied by any number always equals 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

$61\times?=0$

Step-by-step solution

To solve this problem, let's delve into the properties of multiplication:

Step 1: Identify the equation we're solving, $61 \times ? = 0$ .
Step 2: Recall a key mathematical property: any number multiplied by zero equals zero. This is known as the multiplication property of zero.
Step 3: Based on this property, $?$ must be zero because multiplying 61, or any number, by zero results in zero.

Given the understanding of the property above, the unknown number, $?$ , that satisfies the equation is zero.

The correct answer, according to the choices given, is choice 4, where $? = 0$ .

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 always equals zero
Technique: For $61 \times ? = 0$ , the missing factor must be 0
Check: Substitute back: $61 \times 0 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Trying to divide by zero to solve the equation
Don't think $? = 0 ÷ 61$ and then say division by zero is impossible = confusion! This misreads the equation structure. Always recognize that when any multiplication equals 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 1, since 1 doesn't change numbers when multiplying?

While 1 is the multiplicative identity, it doesn't make products equal zero. Remember: $61 \times 1 = 61$ , not 0. Only multiplying by zero gives a product of zero.

What if I thought the answer was 61 because it's the number in the equation?

That's a common guess, but $61 \times 61 = 3721$ , which is definitely not 0! The zero property of multiplication tells us only zero works as the missing factor.

Does this zero property work with any number, not just 61?

Yes! Whether it's $5 \times ? = 0$ or $1000 \times ? = 0$ , the answer is always zero. This is a universal mathematical property.

How do I remember this rule for tests?

Think of it this way: "Zero kills everything!" When zero is involved in multiplication, the result is always zero, no matter what the other number is. This makes it easy to remember!

What happens if both numbers in multiplication are zero?

If you have $0 \times 0$ , the answer is still 0! The zero property works even when both factors are zero.

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