Integers

What is an Integer?

An integer is a whole number. Whole numbers greater than zero are called positive integers. Whole numbers less than zero are called negative integers.

Here is the set of all integers
{…, − 5, − 4, − 3, − 2, − 1, 0, 1, 2, 3, 4, 5, …}

Integers can be represented as evenly spaced points on the number line. Each negative integer is the mirror image of a positive integer with respect to the 0 mark. The integer 0 is neither positive nor negative. Negative integers are all less than any positive integer.

The following diagram explains what is an integer. Scroll down the page for more examples and solutions.

 

Integer Worksheets
Practice your skills with the following integer worksheets:
Printable & Online Integer Worksheets

Examples of Integers:
… -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 …
10, 100, 1000
-7, -50, -235

Examples of Numbers that are NOT Integers:
1.5 (contains a decimal part)
-3.78 (contains a decimal part)
1/2 (is a fraction)
-5/8 (is a fraction)
√2 (is an irrational number)
π (is an irrational number)

Real-World Examples of Integers

1. Temperature
   

• Positive Integers: Hot days (e.g., +30°C).
  
• Negative Integers: Freezing weather (e.g., -5°C).
  
• Zero: Water freezes at 0°C.
  

2. Money & Banking
   

• Positive: Your savings (+$500).
  
• Negative: Debt or overspending (-$200 on a credit card).
  
• Zero: A balanced budget ($0 owed).
  

3. Elevation & Depth
   

• Positive: Mountains (e.g., +2,500m above sea level).
  
• Negative: Ocean trenches (e.g., -10,000m in the Mariana Trench).
  
• Zero: Sea level (0m).
  

Exploring Integers for Grade 6
What are integers and their applications?

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Examples of Integers in real-world applications

1. Write an integer appropriate to each situation.
   a) Daniel owes $23
   b) Mary earned $250
   c) The temperature in the freezer is 18 degrees Celsius below zero.
   
2. Order these numbers from least to greatest −2, 0 −4, 4
   

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Defines integers and explains how to compare and order them

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Introduction to Integers
This video introduces integers, compares integers using inequality symbols, defines absolute value, and determine opposites of integers.
We can use the inequality notation to compare integers
a < b is read “a is less than b”
a > b is read “a is greater than b”
If you plot two numbers on the number line. The larger number is always to the right and the smaller number is to the left.
Opposites are two numbers that are the same distance from zero.

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Distinguish between Integers and Non-integers

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Integer Rap
A rap to help you remember what is an integer.

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Integers Rap

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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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