Integers

Subject: Compulsory Maths

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Overview

The absolute value of an integer is the numerical value without power to whether the sign is negative or positive. An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Integers

Review on Integers

source: www.ipracticemath.com Fig: Integers
source: www.ipracticemath.com
Fig: Integers

An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
The set of integers is denoted by the letter 'Z'.
Z = {. . . . . . . . . . -3, -2, -1, 0, 1 , 2, 3 . . . . . . . . .} is the set of integers. i.e. both +ve and -ve.
Z+ = {+1, +2, +3, +4, +5, +6 . . . . . . . . .} is the set of +ve integers.
Z-= {-1, -2, -3, -4, -5, -6 . . . . . . . . . } is the set of -ve integers.

In the above number line, the negative integers left to the zero are increasing.
i.e. -3< -2< -1< 0< 1< 2< 3< 4 and so on.

Absolute Value of Integers

source: www.slideshare.net Fig: Absolute Value of Integers
source: www.slideshare.net
Fig: Absolute Value of Integers

The absolute value of an integer is the numerical value without power to whether the sign is negative or positive. For example:
let A and B be two places in which A is -5 km left from zero and B is +5 km right from zero. Then, what can be the distance between A and B.
In simple sense,
Distance of A + Distance of B,
= -3 + 3
= 0, which is impossible.
But by using absolute value, we can write as:
Distance of (A + B) = |-3| + |3|
= 3 + 3
= 6 km.
In such case, the numerical value of either 3 or -3 will be same i.e. 3.

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Operation on Integers

source: www.slideshare.net Fig: Operation on Integers
source: www.slideshare.net
Fig: Operation on Integers

The fundamental operations of integers on number lines are:addition

  • addition
  • subtraction
  • multiplication
  • division

Things to remember
  • An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
  • The absolute value of an integer is the numerical value without power to whether the sign is negative or positive.
  • The set of integers is denoted by the letter 'Z'.
  • It includes every relationship which established among the people.
  • There can be more than one community in a society. Community smaller than society.
  • It is a network of social relationships which cannot see or touched.
  • common interests and common objectives are not necessary for society.
Videos for Integers
Add and Subtract Integers (Important Algebra Skill)
What are Integers?
Questions and Answers

Solution:

In addition, Here, (+4) + (+5)

 = +(4+5) = +9 ans.

Again, In subtraction, Here, (+9) - (+4)

 = + (5-4) = +5 ans.

Answer: The set of all the numbers both positive and negative including zero is called the set of integers.

Solution:

Here, (+5) + (-2)

 = +(5-2) = +3

Solution:

Here,  (-4) + (-6)

 = - (4+6) = -10

Solution:

Here, (-3) - (+8)

 = -(3+8) = -11

Solution:

In Addition, Here, (+3) + (-7)

 = (-7) + (+3)

 = -(7-3) = -4 ans.

Again, Here, (+5) - (-3)

 = (+5) + (+3) 

 = +(5+3) = +8 ans.

The rules of multiplication of integers are:

  • The product of a positive integer and a negative integer is a negative integer.
  • The product of two negative integers or two positive integers is a positive integer.

Solution:

Here, (+3) × (+2)

 = +6 ans.

 

 

Solution: 

Here,  (-2) × (+3)

 = (+2) × (-3) = -6

The rules of dividing the integers are: 

  • When you divide two integers with the same sign, the result is always positive.
  • When you divide two integers with different signs, the result is always negative.

Solution:

Here,  (+8) ÷ (+2)

 = (+4)

Solution:

Here, (-12) ÷ (-4)

If (-12) ÷ (-4) = (-3)

Then, (-12) ÷ (-4) = (+3)

Quiz

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