• Skip to main content
  • Skip to primary sidebar
  • Skip to footer
  • NCERT Solutions
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • NCERT Exemplar Problems
  • English Grammar
    • Wordfeud Cheat
  • MCQ Questions

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

Integers

Contents

  • 1 Integers:
    • 1.1 Ordering Of Integers:
    • 1.2 Absolute value of an Integer:

Integers:

Corresponding to natural numbers 1, 2, 3, 4, 5,.. etc  we create new numbers —1, —2,  —3,  —4,  —5, … etc  called minus one, minus two, minus three, minus four, minus live, etc  respectively such that
1 + (—1) = 0
3 + (—3) = 0
4 +(—4) = 0 and soon.
—1 is also called negative of one and —1 and 1 are called the opposites of each other.
Similarly, —2 is also called negative of 2 and —2 and 2 are called the opposites of each other.
Also, —3 is called the negative of 3 and —3 and 3 are called the opposites of each other and soon.
Combining these new numbers with whole numbers, we obtain a new collection of numbers which is written as —3, —2, —1, 0, 1, 2, 3
These numbers are called integers.

Integers are “whole” numbers that have no fractional part. They can be positive or negative.

The set of all integers is denoted by Z
Positive Integers:
The numbers 1, 2, 3, 4, 5, 6…. i.e., natural numbers are called positive integers.
Negative Integers:
The numbers -4, -2, —3, —4, —5, —6 are called negative integers.

integers representation
The number 0 is simply an integer. It is neither positive nor negative
Positive integers are also written as +1, +2, +3… However, the plus sign (+) is usually omitted and understood.

Remark: We use the symbol ‘—‘ to denote the negative integers and the same symbol is used to indicate subtraction. But, the context will always make it clear whether we mean negative integer or subtraction.

Ordering Of Integers:

We know that 7 > 4 and from the number line shown above, we observe that 7 is to the right of 4.
Similarly, 4 > 0 and 4 is to the right of 0. Now, since 0 is to the right of –3 so, 0 > – 3. Again, – 3 is to the right of – 8 so, – 3 > – 8.
Thus, we see that on a number line the number increases as we move to the right and decreases as we move to the left.
Therefore, – 3 < – 2, – 2 < – 1, – 1 < 0, 0 < 1, 1 < 2, 2 < 3 so on.

integers
Hence, the collection of integers can be written as…, –5, –4, – 3, – 2, – 1, 0, 1, 2, 3, 4, 5…
Thus we arrive at the following fact:
Negative of a negative integer is a positive integer i.e., -(-a) = a for any integer a.
Clearly, 0 is the image of itself. Therefore, negative of zero is zero itself.

Absolute value of an Integer:

The absolute value of an integer is the numerical value of the integer regardless of its sign.
The absolute value of -7, written as |-7|, is 7.
The absolute value of -9, written as |-9|, is 9.
The absolute value of 8, written as |8|, is 8.
The absolute value of 0, written as |0|, is 0.

Note: The absolute value of an integer is always positive.

For any integer a, we have
|a| = {a, if a is positive or zero
= {-a, if a is negative

Read more on Integers:

  • Addition of Integers
  • Properties of Addition of Intergers
  • Subtraction of Integers and its Properties
  • Multiplication of Integers
  • Properties of Multiplication of Integers
  • Division of Integers
  • Properties of Division of Integers

 

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers

Recent Posts

  • CBSE Class 11 English Long Composition – Narratives
  • Selina Concise Chemistry Class 8 ICSE Solutions Chapter 8 Water
  • Selina Concise Chemistry Class 8 ICSE Solutions Chapter 9 Carbon and Its Compounds
  • Glimpses of India Extra Questions and Answers Class 10 English First Flight
  • Chapter Wise Important Questions CBSE Class 10 Hindi A-साना-साना हाथ जोड़ि
  • Selina Concise Mathematics Class 8 ICSE Solutions Chapter 15 Linear Inequations
  • CBSE Class 12 Business Studies Case Studies – Principles of Management
  • The Trees Extra Questions and Answers Class 10 English First Flight
  • MCQ Questions for Class 6 Science Chapter 11 Light Shadows and Reflection with Answers
  • NCERT Solutions for Class 11 Computer Science (Python) – Lists, Dictionaries and Tuples
  • NCERT Solutions for Class 8 English Honeydew Chapter 8 A Short Monsoon Diary
  • Article Writing Class 11 Format, Topics, Examples, Samples
  • Resources and Development Class 10 Important Questions Social Science Geography Chapter 1
  • NCERT Class 10 Maths Lab Manual – Arithmetic Progression II
  • Nelson Mandela: Long Walk to Freedom Extra Questions and Answers Class 10 English First Flight

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions