Identify the Missing Number Within the Range 27,832 to 27,860

Q: What's the difference between < and ≤ in this problem?

The symbol < means 'strictly less than' - the number cannot equal 27,860. If it were &leq;, then 27,860 would be allowed. Always check which inequality symbol is used!

Q: How do I know which numbers are too small or too large?

Compare each choice to both boundaries. For example, 27,830 is less than 27,832, so it's too small. 27,901 is greater than 27,860, so it's too large.

Q: Can there be more than one correct answer in the given range?

In multiple choice questions like this, there's typically only one correct answer among the choices. However, mathematically, there are many numbers between 27,832 and 27,860!

Q: What if I can't tell which number is bigger?

Line up the numbers by place value! Start from the left: 27,832 and 27,841 both start with '278', but in the tens place, 41 > 32, so 27,841 is larger.

Q: Do I need to check both sides of the inequality?

Yes, absolutely! A number must satisfy both conditions to be in the range. Check that it's greater than the left boundary AND less than the right boundary.

Number Range Identification with Inequality Boundaries

Fill in the missing number:

$27,832 < \Box < 27,860$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing number:

$27,832 < \Box < 27,860$

Step-by-step solution

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

Step 1: Identify the given range.
Step 2: Evaluate each choice to determine if it falls within the specified range.
Step 3: Confirm the correct answer by process of elimination.

Now, let's work through each step:
Step 1: The problem specifies the range $27,832 < \Box < 27,860$ .
Step 2: Let's examine each answer choice:
- Choice 1: $27,841$ . Check if $27,832 < 27,841 < 27,860$ . This is true.
- Choice 2: $27,830$ . This is not greater than 27,832.
- Choice 3: $27,901$ . This is not less than 27,860.
- Choice 4: $27,799$ . This is not greater than 27,832.
Step 3: The only number between 27,832 and 27,860 is $27,841$ .

Therefore, the solution to the problem is $27,841$ .

Final Answer

$27,841$

Key Points to Remember

Essential concepts to master this topic

Inequality Rule: Number must be greater than 27,832 AND less than 27,860
Technique: Check each choice: Is 27,841 > 27,832? Yes. Is 27,841 < 27,860? Yes
Check: Verify boundaries: 27,832 < 27,841 < 27,860 confirms the answer ✓

Common Mistakes

Avoid these frequent errors

Confusing inequality symbols with equation signs
Don't treat < as ≤ or think 27,832 itself can be the answer = boundary violation! The symbols < and > mean the number cannot equal the boundary values. Always choose numbers strictly between the given boundaries, not including them.

Practice Quiz

Test your knowledge with interactive questions

Select the appropriate sign:

$24,909\Box24,990$

FAQ

Everything you need to know about this question

What's the difference between < and ≤ in this problem?

The symbol < means 'strictly less than' - the number cannot equal 27,860. If it were ≤, then 27,860 would be allowed. Always check which inequality symbol is used!

How do I know which numbers are too small or too large?

Compare each choice to both boundaries. For example, 27,830 is less than 27,832, so it's too small. 27,901 is greater than 27,860, so it's too large.

Can there be more than one correct answer in the given range?

In multiple choice questions like this, there's typically only one correct answer among the choices. However, mathematically, there are many numbers between 27,832 and 27,860!

What if I can't tell which number is bigger?

Line up the numbers by place value! Start from the left: 27,832 and 27,841 both start with '278', but in the tens place, 41 > 32, so 27,841 is larger.

Do I need to check both sides of the inequality?

Yes, absolutely! A number must satisfy both conditions to be in the range. Check that it's greater than the left boundary AND less than the right boundary.

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