Solve the Division Equation: Finding the Number in ?:1=3

Q: Why does any number divided by 1 stay the same?

Think of division as sharing equally! If you have 3 cookies and divide them among 1 person, that person gets all 3 cookies. The amount doesn't change when there's only 1 group to share with.

Q: Is this the same as multiplying by 1?

Yes! Both dividing by 1 and multiplying by 1 are identity operations - they don't change the original number. That's why $ x \div 1 = x $ and $ x \times 1 = x $.

Q: What if the problem was ? ÷ 3 = 1?

Then you'd need to work backwards! If something divided by 3 equals 1, then that something must be 3 × 1 = 3. Always think: what number makes the equation true?

Q: Can the answer ever be 0 in this type of problem?

Only if the equation was $ ? \div 1 = 0 $! Since our equation shows the result is 3, the answer must be 3. Remember: division by 1 preserves the original value.

Division Properties with Identity Element

$?:1=3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 Any number divided 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

$?:1=3$

Step-by-step solution

To solve this problem, let's follow a systematic approach:

Step 1: Recognize the given expression $?:1=3$ . This states that a number, when divided by 1, results in 3.
Step 2: Apply the division property of 1. The rule is $x \div 1 = x$ , meaning any number divided by 1 results in the same number.
Step 3: Utilize the given result $3$ in accordance with the property: Here, $x \div 1 = 3$ implies $x = 3$ .

Thus, the solution to the problem is that the number is $\boxed{3}$ .

This solution matches directly with , confirming it aligns with the division principle discussed.

Therefore, the solution to the problem is $3$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Division Rule: Any number divided by 1 equals itself
Technique: Apply property $x \div 1 = x$ directly to find $x = 3$
Check: Substitute back: $3 \div 1 = 3$ ✓

Common Mistakes

Avoid these frequent errors

Confusing division by 1 with multiplication by 1
Don't think $? \div 1 = 3$ means the unknown is 1 = wrong answer 1! Division by 1 doesn't change the number, so if something divided by 1 equals 3, that something must BE 3. Always remember: dividing by 1 leaves the original number unchanged.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why does any number divided by 1 stay the same?

Think of division as sharing equally! If you have 3 cookies and divide them among 1 person, that person gets all 3 cookies. The amount doesn't change when there's only 1 group to share with.

Is this the same as multiplying by 1?

Yes! Both dividing by 1 and multiplying by 1 are identity operations - they don't change the original number. That's why $x \div 1 = x$ and $x \times 1 = x$ .

What if the problem was ? ÷ 3 = 1?

Then you'd need to work backwards! If something divided by 3 equals 1, then that something must be 3 × 1 = 3. Always think: what number makes the equation true?

How is this different from ? ÷ ? = 3?

When one part is known (like the 1 in our problem), you can use division properties directly. When both parts are unknown, you need more information or additional equations to solve.

Can the answer ever be 0 in this type of problem?

Only if the equation was $? \div 1 = 0$ ! Since our equation shows the result is 3, the answer must be 3. Remember: division by 1 preserves the original value.

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