Comparing Integers
Learn how to compare positive and negative numbers using inequality symbols and the number line.
Definition
- means greater than (the number on the left is larger)
- means less than (the number on the left is smaller)
- means equal to (both numbers have the same value)
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Worked Examples
Compare and . Which is greater?
Visualize on the number line
Place both numbers: is at position , is at position → is further right
Apply the rule
Numbers further right are greater →
Verify with real-world context
is warmer than , so is greater → Confirmed:
Answer: (negative four is greater than negative nine)
Common Mistakes
Thinking because
Why it's wrong: With negative numbers, the absolute value (digit size) works opposite! is further from zero in the negative direction, so it's actually smaller.
Correct: because is closer to zero (further right on the number line).
Confusing and symbols
Why it's wrong: It's easy to mix up which symbol points which way.
Correct: The symbol always 'eats' the bigger number. Think of it as a hungry alligator that always wants the larger meal: and .
Forgetting that zero is greater than all negatives
Why it's wrong: Zero might seem like 'nothing,' but it's actually greater than every negative number.
Correct: . Zero is the boundary between positive and negative.
Interactive Visual
Click on the number line to find the target number. Test your skills!
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
16 problemsWhich symbol makes this statement true?
Why It Matters
- Weather forecasting: Is colder than ? Yes, because
- Elevation: Which is lower: meters (below sea level) or meters?
- Finance: A balance of euros is worse than euros because
- Sports: In golf, (5 under par) is better than (2 under par) because lower is better
Real World Applications
Temperature Comparison
Weather forecasters compare temperatures to determine which days are colder or warmer.
Example:
Moscow recorded and Helsinki recorded . Since , Helsinki was warmer.
Three cities have the following temperatures: City A: , City B: , City C:
Order the cities from coldest to warmest.
Step 1: Write the mathematical expression
Compare: , ,
Elevation Comparison
Geographers use negative numbers for elevations below sea level.
Example:
The Dead Sea is at meters and Death Valley is at meters. Since , the Dead Sea is lower.
A submarine is at meters. A diver is at meters. The ocean floor is at meters.
Order these from deepest to shallowest.
Step 1: Write the mathematical expression
Compare: , ,
Bank Balance Comparison
Banks show negative balances when you owe money (overdraft).
Example:
Account A shows euros. Account B shows euros. Since , Account B is in better standing (owes less).
Three friends check their accounts: Alex has euros, Ben has euros, Carla has euros.
Who has the most money? Who owes the most?
Step 1: Write the mathematical expression
Order: , ,
Key Takeaways
- 1Use (less than) and (greater than) to compare integers
- 2On the number line: RIGHT = GREATER, LEFT = SMALLER
- 3Any positive number is greater than any negative number
- 4Zero is greater than all negative numbers but less than all positive numbers
- 5For negative numbers: closer to zero means greater ()
Frequently Asked Questions
Glossary
- Integer
- A whole number that can be positive, negative, or zero (e.g., , , )
- Greater than ()
- A symbol meaning the number on the left is larger than the number on the right
- Less than ()
- A symbol meaning the number on the left is smaller than the number on the right
- Inequality
- A mathematical statement that compares two values using , , , or
- Number line
- A visual representation of numbers arranged from least to greatest, left to right