Kinds of Numbers & Properties
* Natural number * Whole number
* Even numbers. * Odd numbers
* Prime numbers * Integer number. * Composite numbers * Rational number
* Twin prime numbers * Irrational number
* Co-prime numbers
* Comparison of numbers:
* Properties of Odd/Even.
* Properties of Natural numbers
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Natural number:-
Natural numbers are also called counting numbers.
[ 1,2,3,4..etc are all natural numbers.]
[ It is denoted by the letter N.]
[ The smallest natural number is 1.]
Whole number:-
All natural number along with 0 are called whole numbers .
[ 0, 1, 2, 3, 4, 5..... etc are whole numbers.]
[ The set of whole numbers is denoted by the letter W. ]
[ The smallest whole number is 0.]
Even numbers
The numbers which are divisible by 2 are called even numbers. 2, 4, 6, 8, .. are even numbers.
Odd numbers
The numbers which are not divisible by 2 are called odd numbers. 1, 3, 5, 7, ... are odd
numbers.
Prime numbers
The numbers which are divisible by 1 or itself are called prime numbers.
2, 3, 5, 7, ... are prime numbers. 2 is the only even number which is prime.
Composite numbers
The numbers which are greater than 1 and not prime numbers are called composite numbers. 4, 6, 8, 9, 10, ... are composite numbers.
Twin prime numbers
Two prime numbers whose difference is 2 are called twin prime numbers. (3,5), (5, 7), (11, 13), (17, 19), ... are twin prime numbers.
Co-prime numbers
Two numbers which do not have any common factor other than 1 are called co-prime numbers. 3 and 8 have no common factor except 1. So, these are co-prime numbers.
Integer number:
The whole numbers together with the negatives of counting or natural number are known as integers.
[The set of integers is denoted by the letter l.
-3,-2,-1, 0,1,2,3...... etc. are all integers.
1,2,3,4........ etc.are positive integers.
-1,-2,-3,-4,....... etc. are negative integers.
0 is neither positive nor negative.]
Rational number:
A number of the form p/q, where p and q are integers and p≠0, is called a rational number.
[ p is called the numerator and q is called the denominator of the rational number.
Thus, every rational number is the quotient of two integers such that the denominator is non-zero.]
[ the set of rational number is denoted by the letter Q.]
For examples: 1/2, -3/-4, x/y etc.
*Any number which can be express as p/q form.
Irrational number:
Number which when expressed in decimal form are expressible neither in terminating nor in repeating decimals are known as irrational numbers.
[ The symbol used to represent the irrational symbol is “P”]
Numbers & Properties
A digit is any one of these symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
For example, the number 23 is written with two digits, 2 and 3.
Example: The numeral 9 is made up of 1 digit ("9").]
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Comparison of numbers:
Rule I: A number with more digits is always greater than a number with less digits.
Example: Compare 598 and 98.
598 has 3 digit while 98 has 2 digits.
So, 598 is greater than 98.
598 > 98
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Rule II: When the digits of two numbers are the same, we start comparing the digits from the left side until we come to the unequal digits. Example:
Compare 379 and 279.
3 > 2
so, 379 > 279.
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If hundred place digit is equal of the given two numbers then tens place digit will be compared.Example:-
Compare 586 and 567.
5 = 5
8 > 6
Hence, 586 > 567
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Natural numbers are also called counting numbers and All natural number along with 0 are called whole numbers .
[ 1, 2, 3, 4....etc are all natural numbers.]
[ 0, 1, 2, 3, 4, 5.. etc are whole numbers.]
[ Natural number is denoted by the letter N.]
[ The set of whole numbers is denoted by the letter W. ]
[ The smallest natural number is 1 and whole number is 0.]
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Properties of Natural numbers
* Even number: The number which are divisible by 2 are called even number. 0, 2, 4, 6, 8....etc are even numbers.
* Odd number: The number which are not divisible by 2 are called odd numbers. 1, 3, 5, 7, 9, 11, 13, 15, 17... etc are odd numbers.
Property of even number:
When we add (subtract / multiply) even or even numbers the results are alalways:
Even + Even = Even (2+4=6)
Even - Even = Even (4 -2=2)
Even × Even = Even (2×4=8)
Property of odd number:
When we add (subtract / multiply) odd or odd numbers the results are always:
Odd + Odd = Even (3+5=8)
Odd - Odd = Even (5 - 3=2)
Odd × Odd = Odd (3×3=9)
Properties of even and odd numbers:-
When we add (subtract / multiply) even or odd numbers the results are always:
Even + Odd = Odd (2 + 3 = 5)
Odd + Even = Odd (4 + 5 = 9)
Odd - Even = Odd (5 - 2 = 3 )
Even - Odd = Odd (4 - 3 = 1 )
Odd × Even = Even (3 × 2 = 6)
Even × Odd = Even (4 × 5=20)
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When we divide even / odd numbers the results are always:
*Even number is divisible by 2, and leaves the remainder 0.
*An odd number is not completely divisible by 2, and leaves the remainder 1.
*An even number ends with 0, 2, 4, 6, and 8
*An odd number ends with 1, 3, 5, 7, and 9
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[A]. Questions with answers:-
1. Write the followings :
1. The smallest even number.
Ans: 2
2. The smallest odd number.
Ans: 1
3. The first five even numbers.
Ans: 2, 4, 6, 8, 10.
4. The first five odd numbers.
Ans: 1, 3, 5, 7,9.
5. The last five two-digit even numbers.
Ans: 90, 92, 94, 96, 98.
6. The last five two-digit odd numbers.
Ans: 91, 93, 95, 97, 99.
7. Write the even numbers coming between
15 and 25.
Ans: 16, 18, 20, 22, 24.
8. Write the odd numbers coming between
98 and 108.
Ans: 99, 101, 103, 105, 107.
9. Write the even number coming just before
19.
Ans: 18
10. Write the odd number coming just after
72.
Ans: 73.
11. Write the greatest odd number of one
digit.
Ans: 9.
12. Write the smallest even number of two
digits.
Ans: 10.
13. Write the greatest odd number of two
digits.
Ans: 99.
14. Write the smallest even number of three
digits.
Ans: 100.
15. Write the first even number between
41 and 49.
Ans: 42.
16. Write the last odd number between
88 and 100.
Ans: 99.
17. Find whether the number is even or odd:
a. 458. Even.
b. 2983. Odd.
c. 8661. Odd.
d. 33570. Even.
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