Fill the Gap: Find the Missing Number in 31,089 < ◻ < 31,099

Q: What's the difference between < and ≤ symbols?

The symbol means 'strictly less than' - it excludes the boundary number. The symbol ≤ means 'less than or equal to' - it includes the boundary. Since we have \( 31,089 , neither 31,089 nor 31,099 can be our answer.

Q: How many possible answers are there for this problem?

There are 9 possible correct answers: 31,090, 31,091, 31,092, 31,093, 31,094, 31,095, 31,096, 31,097, and 31,098. Any of these would satisfy the inequality!

Q: Why isn't 31,100 a valid answer?

Because $ 31,100 > 31,099 $! The number must be less than 31,099, so 31,100 is too big and falls outside our required range.

Q: What if I picked 31,080 instead?

That's incorrect because \( 31,080 . The number must be greater than 31,089, so 31,080 is too small and doesn't satisfy the first part of our inequality.

Q: How do I quickly check if my answer is correct?

Use a simple two-step check: 1) Is your number bigger than 31,089? 2) Is your number smaller than 31,099? If both answers are yes, you're correct!

Number Inequality with Range Identification

Fill in the missing number:

$31,089 < \Box < 31,099$

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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:

$31,089 < \Box < 31,099$

Step-by-step solution

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

Step 1: Identify the given boundaries: 31,089 and 31,099.
Step 2: Determine the range of numbers that can be placed in the box, considering the inequalities $31,089 < \Box < 31,099$ .
Step 3: Compare available choices against the range of valid numbers.

Now, let's work through each step:
Step 1: The problem specifies two boundary values, 31,089 and 31,099.
Step 2: We need to select a number greater than 31,089 but less than 31,099. Valid numbers in this set include 31,090, 31,091, 31,092, 31,093, 31,094, 31,095, 31,096, 31,097, and 31,098.
Step 3: Among the choices provided, only 31,093 lies within this range.

Therefore, the solution to this problem is $31,093$ .

Final Answer

$31,093$

Key Points to Remember

Essential concepts to master this topic

Range Rule: Find all integers between the two boundary values
Technique: List valid numbers: 31,090, 31,091, 31,092, 31,093, 31,094, 31,095, 31,096, 31,097, 31,098
Check: Verify 31,089 < 31,093 < 31,099 by comparing each inequality ✓

Common Mistakes

Avoid these frequent errors

Including the boundary numbers in the solution
Don't think 31,089 or 31,099 can be the answer = wrong choice! The < symbols mean strictly less than, not less than or equal to. Always choose numbers strictly between the boundaries, excluding the endpoints.

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 ≤ symbols?

The symbol < means 'strictly less than' - it excludes the boundary number. The symbol ≤ means 'less than or equal to' - it includes the boundary. Since we have $31,089 < \Box < 31,099$ , neither 31,089 nor 31,099 can be our answer.

How many possible answers are there for this problem?

There are 9 possible correct answers: 31,090, 31,091, 31,092, 31,093, 31,094, 31,095, 31,096, 31,097, and 31,098. Any of these would satisfy the inequality!

Why isn't 31,100 a valid answer?

Because $31,100 > 31,099$ ! The number must be less than 31,099, so 31,100 is too big and falls outside our required range.

What if I picked 31,080 instead?

That's incorrect because $31,080 < 31,089$ . The number must be greater than 31,089, so 31,080 is too small and doesn't satisfy the first part of our inequality.

How do I quickly check if my answer is correct?

Use a simple two-step check: 1) Is your number bigger than 31,089? 2) Is your number smaller than 31,099? If both answers are yes, you're correct!

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