Solve the Multiplication Equation: Finding the Factor in 15 × ? = 15

Q: Can the answer ever be 0 in multiplication problems like this?

Only if the result is 0! Since any number times 0 equals 0, if you see $ 15 \times ? = 0 $, then the answer would be 0. But here we need $ 15 \times ? = 15 $.

Q: What is the identity property of multiplication?

The identity property says that any number multiplied by 1 stays the same: $ a \times 1 = a $. The number 1 is called the multiplicative identity because it doesn't change other numbers.

Q: How do I solve similar problems like 7 × ? = 7?

Use the same thinking! Ask yourself: "What number times 7 gives me 7?" The answer is always 1 because of the identity property. Any number times 1 equals itself.

Q: Is there a division way to solve this?

Yes! You can think: $ ? = 15 \div 15 = 1 $. Division and multiplication are opposite operations, so dividing both sides by 15 gives you the missing factor.

Identity Property with Missing Factor

$15\times?=15$

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Step-by-step video solution

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00:00 Solve

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

00:09 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

$15\times?=15$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the equation given which is $15\times?=15$ .
Step 2: Apply the identity property of multiplication which tells us that any number multiplied by 1 is unchanged.
Step 3: Conclude that the unknown number should be 1, since $15 \times 1 = 15$ .

Now, let's work through each step:

Step 1: The given equation is $15\times?=15$ .

Step 2: According to the identity property of multiplication, $a \times 1 = a$ for any number $a$ . Here, $a$ is 15.

Step 3: Therefore, the number that fulfills the equation $15 \times ? = 15$ must be 1. When 15 is multiplied by 1, it stays 15.

Therefore, the solution to the problem is $1$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Identity Property: Any number multiplied by 1 equals itself
Technique: For 15 × ? = 15, the missing factor is 1
Check: Substitute back: 15 × 1 = 15 equals original result ✓

Common Mistakes

Avoid these frequent errors

Dividing to get zero as the answer
Don't think 15 ÷ 15 = 0 means the missing factor is 0! Zero times anything equals zero, not 15. Always remember that 15 × 0 = 0, not 15, so use the identity property instead.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why isn't the answer 15 since we see 15 on both sides?

Great question! While you see 15 on both sides, the missing factor isn't 15. Remember: $15 \times 15 = 225$ , not 15. We need the number that keeps 15 unchanged when multiplied.

Can the answer ever be 0 in multiplication problems like this?

Only if the result is 0! Since any number times 0 equals 0, if you see $15 \times ? = 0$ , then the answer would be 0. But here we need $15 \times ? = 15$ .

What is the identity property of multiplication?

The identity property says that any number multiplied by 1 stays the same: $a \times 1 = a$ . The number 1 is called the multiplicative identity because it doesn't change other numbers.

How do I solve similar problems like 7 × ? = 7?

Use the same thinking! Ask yourself: "What number times 7 gives me 7?" The answer is always 1 because of the identity property. Any number times 1 equals itself.

Is there a division way to solve this?

Yes! You can think: $? = 15 \div 15 = 1$ . Division and multiplication are opposite operations, so dividing both sides by 15 gives you the missing factor.

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