Solve for the Unknown Factor: Find x in x × 7 = 7

Q: Why isn't the answer 7? Doesn't 7 × 7 = 49?

Great observation! While $ 7 \times 7 = 49 $, we need the product to equal 7, not 49. Only $ 1 \times 7 = 7 $ gives us the result we want.

Q: What makes 1 so special in multiplication?

The number 1 is called the multiplicative identity because it doesn't change any number when you multiply by it. Think of it like a mirror - whatever you multiply by 1 stays exactly the same!

Q: How do I solve similar problems like ? × 5 = 5?

Use the same pattern! Ask yourself: "What number times 5 gives me 5?" The answer is always 1, because 1 is the multiplicative identity for any number.

Q: Is there a trick to remember this?

Yes! Remember: "One times anything is that thing!" So if you see ? × [number] = [same number], the missing factor is always 1.

Multiplicative Identity with Unknown Factors

$?\times7=7$

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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

$?\times7=7$

Step-by-step solution

To solve this problem, we'll identify the correct value of $x$ using the property of multiplication:

Step 1: We have the equation $? \times 7 = 7$ .
Step 2: Recognize that 1 is the multiplicative identity, meaning multiplying 7 by 1 results in 7.
Step 3: Thus, $x = 1$ because multiplying 7 by 1 does not change its value.

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

Final Answer

Key Points to Remember

Essential concepts to master this topic

Identity Property: Any number multiplied by 1 equals itself
Technique: Recognize that $1 \times 7 = 7$ fits the pattern
Check: Verify by substituting: $1 \times 7 = 7$ ✓

Common Mistakes

Avoid these frequent errors

Confusing multiplication with addition
Don't think 7 + 0 = 7 means 7 × 0 = 7! Zero makes products equal zero, not the original number. Always remember that 1 is the multiplicative identity, meaning any number times 1 stays the same.

Practice Quiz

Test your knowledge with interactive questions

$$ 2+0= $$

FAQ

Everything you need to know about this question

Why isn't the answer 7? Doesn't 7 × 7 = 49?

Great observation! While $7 \times 7 = 49$ , we need the product to equal 7, not 49. Only $1 \times 7 = 7$ gives us the result we want.

What makes 1 so special in multiplication?

The number 1 is called the multiplicative identity because it doesn't change any number when you multiply by it. Think of it like a mirror - whatever you multiply by 1 stays exactly the same!

Could the answer be 0? What happens when I multiply by 0?

No! When you multiply any number by 0, you always get 0 as the result. Since $0 \times 7 = 0$ , not 7, zero cannot be our answer.

How do I solve similar problems like ? × 5 = 5?

Use the same pattern! Ask yourself: "What number times 5 gives me 5?" The answer is always 1, because 1 is the multiplicative identity for any number.

Is there a trick to remember this?

Yes! Remember: "One times anything is that thing!" So if you see ? × [number] = [same number], the missing factor is always 1.

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