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INTEGER

Integer

Definition Of Integer

Integers are the set of whole numbers and their opposites.
{. . . -3, -2, -1, 0, 1, 2, 3 . . . } is the set of integers.

Video Examples: What are Integers?
 

Example of Integer

Following are some examples of integers.

-12,315
733,751
-10
121

Solved Example on Integer

Ques: Which of these sets orders the integers 25, -5, -15, 0, -30, 15 from least to greatest? 

Choices:

A. 0, - 5, - 15, - 30, 15, 25 
B. - 30, - 15, - 5, 0, 15, 25 
C. 15, 25, 0, - 30, - 15, - 5 
D. 25, 15, 0, - 30, - 15, - 5 
Correct Answer: B

Solution:

Step 1: Represent the integers on a number line as shown below.
Step 2: On a number line, the numbers increase in value from left to right.
Step 3: The order of the integers from the least to the greatest is 
- 30, - 15, - 5, 0, 15, and 25.

Quick Summary

  • Integers include positive and negative whole numbers, and zero.
  • Integers can be represented on a number line.
  • Integers are used in various mathematical operations and real-world applications.
\[ {\mathbb{Z}} = {\dots, -3, -2, -1, 0, 1, 2, 3, \dots} \]

⚠️ Common Mistakes

  • Confusing integers with whole numbers (forgetting negative numbers).
  • Incorrectly ordering negative integers (e.g., thinking -2 is less than -5).
  • Misunderstanding the concept of zero as an integer.

🌍 Real-World Uses

  • Tracking bank account balances, where negative numbers represent debt or overdraft.
  • Measuring temperature above and below zero degrees Celsius or Fahrenheit.
  • Representing altitude relative to sea level, where values below zero indicate locations below sea level.

📋 Standards Alignment

  • CCSS.MATH.CONTENT.6.NS.C.5
  • CCSS.MATH.CONTENT.7.NS.A.1

🔗 Related Links

🍎 Teacher Insights

Use a number line to visually represent integers. Emphasize the concept of opposites and the ordering of negative numbers. Relate integers to real-world scenarios like temperature or bank balances.

🎓 Prerequisites

  • Whole Numbers
  • Number Line
  • Basic Arithmetic Operations

Check Your Knowledge

Q1: Which of the following is an integer?

Q2: Order the following integers from least to greatest: -3, 0, -5, 2

Frequently Asked Questions

Q: Is zero an integer?
A: Yes, zero is an integer. It is neither positive nor negative.

Q: Are fractions integers?
A: No, fractions are not integers. Integers are whole numbers and their opposites.

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