Number System with Funs and Facts
This post contains the funs and facts of Natural Numbers, Whole Numbers, Integers, Even Numbers, Odd Numbers and most important Question-Answers for all competitive viewers and New children who try to know the mathematics in easy way. Number System with Funs and Facts
Natural Number is a part of the Number System that includes all positive number from 1 to infinity excluding zero, fraction, decimal and negative numbers. It is also known as counting numbers. Generally used for calculation such as Addition, Subtraction, Multiplication & Division. It is represented by the capital letter “N”.
| Natural Number (N): 1,2,3,4,5,6,7,8,9,10…… |
Whole Number:
All natural number is the whole number including zero. In other words, you can say that all natural numbers are the whole number but, all the whole numbers are not the natural numbers. It is represented by the capital letter “W”.
| Whole Number (W): 0,1,2,3,4,5,6,7,8,9,10,….. |
Represent the Difference and Intersection of Set A and Set B
Let
set A={0,1,2,3,4,5,6,7,8,9,10,11,………….}
Set B={1,2,3,4,5,6,7,8,9,10,11,………….}
The above representation of set A and set B
i.e. A∩B
similarly, A-B=0
Integer:
Integers are the collection of both positive and negative of the whole number including ‘0’ and excluding the fraction. We can use all the integer for arithmetical operation like Addition, Subtraction, Multiplication and Division etc. It is represented by the capital letter “Z”.
| Integer (Z):…….-5,-4,-3,-2,-1,0,1,2,3,4,5,……….. |
There are three types of integer
| Zero Integer: It is neither positive nor negative integer. It is a neutral number. Positive Integer: 1,2,3,4,5,6,7,8,9,………(Natural Number) Negative Integer: …….-5,-4,-3,-2,-1(Additive inverse of Natural Number) |
How to represent integers on Number Line?
- As shown in above figure,
- Zero is at the center on a number line.
- Positive Integers are the right side of Zero
- Negative Integers are the left side of the Zero.
Natural Numbers, Integers & Whole Numbers representing on Number Line
Additive Inverse Property Of Integer:
| If ‘a’ is an integer then its Additive Inverse is (-a). i.e. {(a) + (-a)=0} |
Multiplicative Inverse Property Of Integer:
| If ‘a’ is an integer then its Multiplicative Inverse is (1/a). i.e. {(a) x (1/a)=1} |
Identity Property Of Integer:
| If ‘a’ is an integer and it is multiplied by ‘1’ and addition to ‘0’. It remains unchanged in its value. i.e. {(a) + 0=a} and {(a) x 1=a} |
We can perform various arithmetical operation on Integer, such as
| # Addition of integers # Subtraction of integers # Multiplication of integers # Division of integers |
There are following funs of two integers via Arithmetical Operation
| # Sum of two positive integers is a positive integer. # Sum of two negative integers is a negative integer. # Sum of a positive integer and a negative integer is either positive or negative integer. # Difference of two positive integers is either negative or positive integer. # Difference of a positive integer and a negative integer is either negative or positive integer. |
| # Product of two positive integers is positive integer. Product of two negative integers is positive integer. # Product of a negative integer and a positive integer is a negative integer. # Product of an integer and its inverse is equal to Zero. # Product of an integer & its reciprocal is always equal to 1. |
Some Important Facts for Integers (Same funs in Multiply & Divide Rules)
| # [(-) x (-) = (+)] {i.e. (-3) x (-4) = [(-) x (-) x (3) x (4)] = {+12} The product of two negative integer always gives a positive integer. Similarly, for divide rules also. |
| # [(+) x (+) = (+)] {i.e. (+5) x (+6) = [(+) x (+) x (5) x (6)] = {+30} The product of two positive integer always gives a positive integer. Similarly, for divide rules also. |
| # [(-) x (+) = (-)] { i.e. (-7) x (+5) = [(-) x (+) x (7) x (5)] = {-35} The product of a negative integer and a positive integer always gives a negative integer. Similarly, for divide rules also. |
Some important funs and facts for Integer in Addition and Subtraction
Addition:-Number System with Funs and Facts
| # (+) + (+) = (+) {(+3) + (+4)} ={ 3 + 4} = {+7} The sum of two positive integers always gives a positive integer. Simply, you can add both integers and take positive sign. |
| # (-) + (-) = (-) {(-5) + (-6)} = {5 + 6} = {-11} The sum of two negative integers always gives a negative integer. Simply you can add both integers and take negative sign. |
| # (+) + (-) = (+) if (+) > (-) ; {(+8) + (-5)} = (8 – 5) = {+3} The sum of a positive integer and a negative integer. If positive integer is greater than negative integer, then Simply, Smaller integer subtract from greater integer. We will get a positive integer. |
| # (+) + (-) = (-) if (+) < (-); {(+5) + (-8)} = (-8 + 5 )= -(8 – 5) = {-3} The sum of a positive integer and a negative integer. If positive integer is smaller than negative integer, then Simply, Smaller integer subtract from greater integer. We will get a negative integer. |
Subtraction:-Number System with Funs and Facts
| # (+) – (+) = (+) {(+7) – (+4)} = {7 – 4} = {+3} if first integer is greater than second integer. We get difference easily subtracting smaller integer from greater integer. Result always positive integer. |
| # (+) – (+) = (-) {(+7) – (+10)} = -(10 – 7) = {-3} if first integer is smaller than second integer. We get difference easily subtracting smaller integer from greater integer. Result always positive integer. |
| # (-) – (-) = (-) {(-5) – (-3)} = -(5 – 3) = {-2} if first integer is greater than second integer. We get difference easily subtracting smaller integer from greater integer. Result always negative integer. |
| # (-) – (-) = (+) {(-3) – (-5)} = (5 – 3) = {+2} if first integer is smaller than second integer. We get difference easily subtracting smaller integer from greater integer. Result always positive integer. |
| # (+) – (-) = (+) {(+8) – (-5) = {8 + 5} = {+13} |
| # (-) – (+) = (-) {(-5) – (+8)} = -(8 + 5) = {-13} |
Even Number:
Even numbers are integers that exactly divisible by 2. The number, exactly divisible by 2. The number is called an even Number. We can say in a simple way, The table of 2 is known as an even number and we can also find the even number in this way, A number, they have ones place 0, 2, 4,6,8. The number is divisible by 2 and It is called Even number.
| Even Number: 2, 4, 6, 8, 10, …………….. |
Odd Number:
Odd numbers are the integers that exactly not divisible by 2. The number, exactly not divisible by 2. The number is called an odd number. We can say in a simple way, A number, they have ones place 1, 3, 5, 7, 9. The number is not divisible by 2 and It is called Odd Number.
| Odd Number: 1, 3, 5, 7, 9, ……………. |
Number System with Funs and Facts
| Q: Is ‘0’ a Positive Number? Ans: No. |
| Q: Is ‘0’ a Negative Number? Ans: No. |
| Q: What is ‘0’? Ans: ‘0’ is Neither Positive Nor Negative. |
| Q: Every Natural Number is Whole Number? Ans: Yes. |
| Q:The sum of two integers is always integer? Ans: 4 + 5 = 9 |
| Q:The difference of two integers is always integer? Ans: 5 – 4 = 1 |
| Q: The product of two integer is always integer? Ans: 3 x 4 = 12 |
| Q: What is the smallest number of one digit? Ans: 0 |
| Q: What is the greatest number of one digit? Ans: 9 |
| Q: What is the smallest number of two digits? Ans: 10 |
| Q: What is the greatest number of two digits? Ans: 99 |
| Q: What is the smallest number of three digits? Ans: 100 |
| Q: What is the greatest number of three digits? Ans: 999 |
| Q: What is the smallest or first even number? Ans: 2 |
| Q: What is the smallest or first odd number? Ans: 1 |
| Q: What is the sum of first-ten natural numbers? Ans: 55 |
| Q: What is the sum of first-ten whole numbers? Ans: 45 |
| Q: What is the sum of first-ten even numbers? Ans: 110 |
| Q: What is the sum of first-ten odd numbers? Ans: 100 |
| Note:- If you know the sum of ten consecutive even number, then you can find the sum of ten odd consecutive numbers easily, by subtracting 10 from the sum of consecutive even numbers. Let 2+4+6+8+10+12+14+16+18+20=110 You can get the sum of ten consecutive odd number = 110 -10 =100 You can check it. 1+3+5+7+9+11+13+15+17+19=100 # Lets check for another: Four Even Consecutive Number: 4+6+8+10 = 24 + 4 = 28 Four Odd Consecutive Number: 3+5+7+9 = 24 ∴(28 – 4 = 24) |
| Q: What is the even prime number? Ans: 2 (only) |
| Q: Is ‘0’ an even number? Ans: Yes. It is divisible by 2. |
| Q: What is the smallest odd prime number? Ans: 3 |
| Q: How many odd numbers between 1 and 100? Ans: 50 |
| Q: How many even numbers between 1 and 100? Ans: 50 |
| Q: What is the sum of first-fifty odd numbers? Ans: 2500 |
| Q: What is the sum of first-fifty even numbers? Ans: 2550 |
| Q: What is the sum of first-hundreds natural numbers? Ans: 5050 |
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