Solve Multiplication Equation: Find the Factor in 1 × ? = 100

Q: Why is the answer 100 and not 1?

The identity property tells us that $ 1 \times \text{any number} = \text{that same number} $. Since we need $ 1 \times ? = 100 $, the missing number must be 100!

Q: What if the equation was ? × 1 = 100 instead?

The answer would still be 100! Multiplication is commutative, meaning $ 1 \times 100 = 100 \times 1 = 100 $. The order doesn't matter.

Q: Is there a trick to remember the identity property?

Think of 1 as the "do nothing" number in multiplication. Just like adding 0 doesn't change a number, multiplying by 1 keeps everything the same!

Q: How do I check if my answer is right?

Simply substitute your answer back: $ 1 \times 100 = 100 $. If both sides are equal, you're correct! This verification step is always important.

Q: Could the answer ever be 0 for this type of problem?

Only if the result was 0! Since $ 1 \times 0 = 0 $, but our equation gives $ 1 \times ? = 100 $, the answer must be 100, not 0.

Identity Property with Single Factor

$1\times?=100$

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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

00:08 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

$1\times?=100$

Step-by-step solution

To solve this problem, we apply the identity property of multiplication:

Step 1: Recall that any number multiplied by 1 remains the original number. This property is fundamental in arithmetic and states $a \times 1 = a$ , where $a$ is any real number.
Step 2: Apply this property to the problem. Here, $? \times 1 = 100$ , which implies that the unknown number must be 100 since multiplying any number by 1 does not change its value.

Therefore, by applying the identity property of multiplication, the solution to our problem is clearly:

$100$

Final Answer

100

Key Points to Remember

Essential concepts to master this topic

Identity Property: Any number multiplied by 1 equals itself
Technique: If $1 \times ? = 100$ , then ? must be 100
Check: Substitute back: $1 \times 100 = 100$ ✓

Common Mistakes

Avoid these frequent errors

Confusing the position of 1 and the unknown
Don't think 1 × ? = 100 means dividing 100 by something = wrong reasoning! This leads to answers like 10 or other incorrect values. Always remember that 1 times any number gives you that exact same number.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why is the answer 100 and not 1?

The identity property tells us that $1 \times \text{any number} = \text{that same number}$ . Since we need $1 \times ? = 100$ , the missing number must be 100!

What if the equation was ? × 1 = 100 instead?

The answer would still be 100! Multiplication is commutative, meaning $1 \times 100 = 100 \times 1 = 100$ . The order doesn't matter.

Is there a trick to remember the identity property?

Think of 1 as the "do nothing" number in multiplication. Just like adding 0 doesn't change a number, multiplying by 1 keeps everything the same!

How do I check if my answer is right?

Simply substitute your answer back: $1 \times 100 = 100$ . If both sides are equal, you're correct! This verification step is always important.

Could the answer ever be 0 for this type of problem?

Only if the result was 0! Since $1 \times 0 = 0$ , but our equation gives $1 \times ? = 100$ , the answer must be 100, not 0.

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