Solve for the Missing Factor: ? × 1 = 99

Q: Why does multiplying by 1 keep the number the same?

This is called the Identity Property of Multiplication! Think of it like this: if you have 99 groups of 1 cookie each, you still have 99 cookies total. The number 1 is neutral - it doesn't change anything.

Q: How is this different from multiplying by 0?

Great question! Multiplying by 0 always gives 0 (like having zero groups), but multiplying by 1 always gives the original number. They're complete opposites!

Q: What if the equation was ? × 1 = 0?

Then the answer would be 0! Since $ 0 \times 1 = 0 $. The identity property works for any number, including zero.

Q: Can I use this property backwards?

Absolutely! If you know $ 75 \times 1 = ? $, you immediately know the answer is 75. The identity property works both ways.

Q: Does this work with fractions and decimals too?

Yes! Examples: $ \frac{3}{4} \times 1 = \frac{3}{4} $ and $ 2.5 \times 1 = 2.5 $. The identity property works with all real numbers!

Identity Property with Missing Factors

$?\times1=99$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Any number multiplied by 1 is always equal to itself

00:10 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

$?\times1=99$

Step-by-step solution

To solve this problem, we need to apply the identity property of multiplication, which states:

For any number $a$ , multiplying by 1 yields the same number: $a \times 1 = a$ .

Let's proceed with solving the equation:

The given equation is: $? \times 1 = 99$

According to the identity property, the value of '?' must be equal to 99. This is because multiplying any number by 1 gives the number itself. Therefore, $99 \times 1 = 99$ .

Based on the properties of numbers, the correct value for '?' is $99$ .

Thus, among the multiple-choice options provided, the correct choice is Option 1: 99.

Therefore, the solution to the problem is $? = 99$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Identity Rule: Any number multiplied by 1 equals itself
Technique: Since $? \times 1 = 99$ , the missing factor is 99
Check: Substitute back: $99 \times 1 = 99$ ✓

Common Mistakes

Avoid these frequent errors

Thinking multiplication by 1 changes the number
Don't assume multiplying by 1 makes numbers smaller or larger = choosing wrong answers like 9 or 0! The identity property means 1 never changes a number's value. Always remember that multiplying by 1 keeps the original number exactly the same.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why does multiplying by 1 keep the number the same?

This is called the Identity Property of Multiplication! Think of it like this: if you have 99 groups of 1 cookie each, you still have 99 cookies total. The number 1 is neutral - it doesn't change anything.

How is this different from multiplying by 0?

Great question! Multiplying by 0 always gives 0 (like having zero groups), but multiplying by 1 always gives the original number. They're complete opposites!

What if the equation was ? × 1 = 0?

Then the answer would be 0! Since $0 \times 1 = 0$ . The identity property works for any number, including zero.

Can I use this property backwards?

Absolutely! If you know $75 \times 1 = ?$ , you immediately know the answer is 75. The identity property works both ways.

Does this work with fractions and decimals too?

Yes! Examples: $\frac{3}{4} \times 1 = \frac{3}{4}$ and $2.5 \times 1 = 2.5$ . The identity property works with all real numbers!

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