Comparing Integers

Learn how to compare positive and negative numbers using inequality symbols and the number line.

Elementary20 minLesson
Printable worksheet

Definition

Comparing integers means determining which number is greater, smaller, or if they are equal.
We use inequality symbols to compare:
  • >> 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)
The Number Line Rule:
Numbers further RIGHT are GREATER\text{Numbers further RIGHT are GREATER}
Numbers further LEFT are SMALLER\text{Numbers further LEFT are SMALLER}
For example: −3>−7-3 > -7 because −3-3 is to the right of −7-7 on the number line.

Try it now

Which symbol makes this statement true? −5  ‾  −2-5 \;\underline{\quad}\; -2

Worked Examples

Compare −4-4 and −9-9. Which is greater?

1

Visualize on the number line

Place both numbers: −9-9 is at position −9-9, −4-4 is at position −4-4 → −4-4 is further right

2

Apply the rule

Numbers further right are greater → −4>−9-4 > -9

3

Verify with real-world context

−4°C-4°C is warmer than −9°C-9°C, so −4-4 is greater → Confirmed: −4>−9-4 > -9

Common Mistakes

Thinking −15>−5-15 > -5 because 15>515 > 5

Why it's wrong: With negative numbers, the absolute value (digit size) works opposite! −15-15 is further from zero in the negative direction, so it's actually smaller.

Correct: −5>−15-5 > -15 because −5-5 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: 5>35 > 3 and 3<53 < 5.

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: 0>−1>−1000 > -1 > -100. Zero is the boundary between positive and negative.

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Practice Problems

16 problems
Problem 1 of 16
Easy

Which symbol makes this statement true? −5  ‾  −2-5 \;\underline{\quad}\; -2

Why It Matters

Comparing integers is essential for understanding real-world situations:
  • Weather forecasting: Is −5°C-5°C colder than −2°C-2°C? Yes, because −5<−2-5 < -2
  • Elevation: Which is lower: −200-200 meters (below sea level) or −50-50 meters? −200<−50-200 < -50
  • Finance: A balance of −100-100 euros is worse than −20-20 euros because −100<−20-100 < -20
  • Sports: In golf, −5-5 (5 under par) is better than −2-2 (2 under par) because lower is better
Understanding how to compare integers helps you make sense of temperatures, debts, elevations, and many other measurements that can be positive or negative.

Real World Applications

Temperature Comparison

Weather forecasters compare temperatures to determine which days are colder or warmer.

Example:

Moscow recorded −18°C-18°C and Helsinki recorded −12°C-12°C. Since −12>−18-12 > -18, Helsinki was warmer.

1Try It Yourself

Three cities have the following temperatures: City A: −7°C-7°C, City B: −15°C-15°C, City C: −3°C-3°C

Order the cities from coldest to warmest.

Step 1: Write the mathematical expression

Compare: −15-15, −7-7, −3-3

Elevation Comparison

Geographers use negative numbers for elevations below sea level.

Example:

The Dead Sea is at −430-430 meters and Death Valley is at −86-86 meters. Since −430<−86-430 < -86, the Dead Sea is lower.

2Try It Yourself

A submarine is at −250-250 meters. A diver is at −30-30 meters. The ocean floor is at −400-400 meters.

Order these from deepest to shallowest.

Step 1: Write the mathematical expression

Compare: −400-400, −250-250, −30-30

Bank Balance Comparison

Banks show negative balances when you owe money (overdraft).

Example:

Account A shows −75-75 euros. Account B shows −20-20 euros. Since −20>−75-20 > -75, Account B is in better standing (owes less).

3Try It Yourself

Three friends check their accounts: Alex has −50-50 euros, Ben has 2525 euros, Carla has −10-10 euros.

Who has the most money? Who owes the most?

Step 1: Write the mathematical expression

Order: −50-50, −10-10, 2525

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 (−2>−10-2 > -10)

Frequently Asked Questions

Think of temperature: −3°C-3°C is warmer than −10°C-10°C. On the number line, −3-3 is closer to zero (further right), so it's greater. The rule is: for negatives, closer to zero = greater.
Think of temperature: −3°C-3°C is warmer than −10°C-10°C. On the number line, −3-3 is closer to zero (further right), so it's greater. The rule is: for negatives, closer to zero = greater.
Zero is neither positive nor negative. It's the boundary point. But zero IS greater than all negative numbers and less than all positive numbers.
The symbol always opens toward the bigger number, like a hungry mouth eating the larger value. Or remember: the small end points to the small number.
Even though 100 is a bigger digit than 1, we're talking about negative numbers. −100-100 is 100 units left of zero, while −1-1 is only 1 unit left. Further left = smaller, so −100<−1-100 < -1.

Glossary

Integer
A whole number that can be positive, negative, or zero (e.g., −5-5, 00, 1212)
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 <<, >>, ≤\leq, or ≥\geq
Number line
A visual representation of numbers arranged from least to greatest, left to right

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