Find the Missing Operator: Solve 110 ? 110 = 1

Q: Why does dividing the same number by itself always equal 1?

This is a fundamental property of division! When you divide any number by itself, you're asking "how many groups of that number fit into itself?" The answer is always exactly 1 group.

Q: Is the colon (:) the same as the division sign (÷)?

Yes! The colon (:) is another way to write division, just like $ ÷ $ or the fraction bar. All three symbols mean the same operation.

Q: Should I check all the operations even if I find one that works?

Absolutely! In multiple choice questions, you should verify that only one answer is correct. Check that addition, subtraction, and other options don't work.

Q: What happens with 110 - 110?

Subtraction gives us $ 110 - 110 = 0 $, not 1. When you subtract identical numbers, the result is always zero, never 1.

Basic Operations with Equal Values

Choose the correct sign (?):

$110?110=1$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine which operations are correct

00:04 Calculate each possibility and select the correct one

00:08 Since addition increases the number, it isn’t the correct operation here

00:20 Since a number minus itself always results in 0, this operation isn’t suitable

00:30 Since a number divided by itself always results in 1, this is the correct operation

00:41 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the correct sign (?):

$110?110=1$

Step-by-step solution

To solve this problem, we'll determine which operation makes the equation $110?110=1$ true:

Step 1: Identify potential operations from the choices: addition $(+)$ , subtraction $(-)$ , division $(:)$ , and multiplication (not explicitly mentioned).
Step 2: Analyze whether any operation yields the result of 1.

Calculating:

Addition: $110 + 110 = 220 \neq 1$
Subtraction: $110 - 110 = 0 \neq 1$
Division: $110 \div 110 = 1$ , which matches the required result.

Therefore, substituting division $(:)$ into the equation satisfies the expression, resulting in:

$110 : 110 = 1$ .

The appropriate sign is division, represented by the symbol $:$ .

The solution to the problem is $\mathbf{\text{Choice 3: :}}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Division Rule: Any non-zero number divided by itself equals 1
Technique: Test each operation: $110 ÷ 110 = 1$
Check: Verify by calculating: division gives 1, other operations don't ✓

Common Mistakes

Avoid these frequent errors

Choosing addition because numbers are the same
Don't assume addition works just because both numbers are identical = $110 + 110 = 220$ , not 1! Same numbers can produce different results with different operations. Always test each operation to see which gives the target result.

Practice Quiz

Test your knowledge with interactive questions

$1\times1000=$

FAQ

Everything you need to know about this question

Why does dividing the same number by itself always equal 1?

This is a fundamental property of division! When you divide any number by itself, you're asking "how many groups of that number fit into itself?" The answer is always exactly 1 group.

What if the numbers were different, like 120 ÷ 110?

Then the answer wouldn't be 1! Division only equals 1 when the dividend and divisor are identical. For example, $120 ÷ 110 ≈ 1.09$ .

Is the colon (:) the same as the division sign (÷)?

Yes! The colon (:) is another way to write division, just like $÷$ or the fraction bar. All three symbols mean the same operation.

Should I check all the operations even if I find one that works?

Absolutely! In multiple choice questions, you should verify that only one answer is correct. Check that addition, subtraction, and other options don't work.

What happens with 110 - 110?

Subtraction gives us $110 - 110 = 0$ , not 1. When you subtract identical numbers, the result is always zero, never 1.

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