Integers
Whole numbers along with the negative numbers are called Integers.There are different types of numbers, natural numbers, whole numbers, fractions, decimals etc.
Natural Numbers = 1,2,3,4,5,…
Whole Numbers = 0,1,2,3,4,…
Fractions = ½, 1/3, 1/4, … These numbers lie between the two whole numbers.
Decimals = 0.1, 0.2, 0.3, … These numbers are also lie between the two whole numbers.
The numbers …, -4, -3,-2, -1, 0 ,1,2,3,4, … etc. are called integer.
1,2,3,4,… are Positive integer.
-1,-2,-3,… are Negative numbers.
The collection of Positive numbers(natural numbers) , Zero and Negative numbers are known as integers.
This is an Integers line, all numbers to the right of 0 are positive and all numbers to the left of zero are negative numbers.
Zero (0) is an integer which is neither positive nor negative.
Zero is less than all positive numbers and greater than all negative numbers.
Negative numbers < 0 < Positive numbers.
Proper use of signs
Words | Sign | Example |
1) Profit | Positive | Profit of $50 = + 50 |
2)Loss | Negative | Loss of $35 = - 35 |
3) South | Negative | 50 km south = - 50 |
4) East | Positive | 50 cm to East = + 50 |
5) West | Negative | 2 km to west = -2 |
6) North | Positive | 5 km to north = + 5 |
7) Rise | Positive | A rise of 50 points = + 50 |
8) Fall | Negative | A fall of 20 points = - 20 |
9) Deposit | Positive | A deposit of $67 = + 67 |
10)Withdraw | Negative | A withdrawal of $45 from a bank = - 67 |
11) Above | Positive | 50^{0}C above 0^{0} = + 50^{0}C |
12) Below | Negative | 20^{0}C below 0^{0} sea level = - 20^{0}C |
Comparison of Integers
1) Every positive integer is greater than every negative integer.
Example :
(i) 4 > -4
(ii) 3 > -1
(iii) 1 > -1
(iv) 0 > -6
2) When two numbers are negative then the number which is nearest to zero is greater than the number which is away from zero.
Example :
(i) -2 > -6
(ii) -4 > -5
(iii) -1 > -20
On the basis of this we arrange the numbers in ascending or descending order.
Example :
Arrange the following integers in ascending order :
-20,-65, 25,5,-10.
Solution : The smallest number is -65.
The next one is -20.
The next one is -10.
The next one is 5.
The last one is 25.
So, the numbers in ascending order are : -65,-20,-10,5,25.
Integers
• Absolute value
• Absolute Value Equation
• Addition of positive and negative numbers
• Multiplication of Numbers
• Division of Numbers
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