Whole Numbers

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WHOLE NUMBERS

OBJECTIVES

  • understand the meaning of whole numbers
  • identify the natural number series and whole number series
  • represents whole numbers on number lines
  • list the properties of natural numbers and whole numbers
  • learn the pattern of whole numbers.

CONCEPTS

  • whole numbers and its meaning
  • representation of whole numbers on the number line
  • closure property under addition and multiplication on whole numbers
  • commutative property under addition and multiplication on whole numbers
  • associative property under addition and multiplication on whole numbers.
  • additive identity ,multiplicative identity of whole numbers
  • distributive property under addition and multiplication.
  • pattern of whole numbers

MEANING OF WHOLE NUMBERS;(01-period)

natural numbers are the representation of existing object i.e 1,2,3,4,5,6,............etc.is there any indicator in natural numbers used to represent non existing objects . Counting numbers are natural numbers ,when there is no object then it is represented as zero but it is not a natural number . if this zero includes with existing objects like 0,1,2,3,4,5,6,..........etc this set of numbers is called as whole numbers. Zero is the smallest whole number . So whole numbers starts from zero and it is infinite set.

ACTIVITY Identify which one of the following is a whole number a)5.6 b)13 c)5/4 d)-12 Enrichment for students to know the meaning of whole numbers use the hyperlink below p://www.mathsisfun.com/whole-numbers.html

REPRESENTING WHOLE NUMBERS ON NUMBER LINE

No Fractions!


whole numbers on number line which begins with zero.click the link to know more about number line. www.mathsisfun.com/whole-numbers.html

PROPERTIES OF WHOLE NUMBERS

to know the closure property under addition we see the properties shown by whole numbers

  • the sum of two whole numbers is always a whole number

5+6=11,5+9=14 Example 1 = With the given whole numbers 4 and 9, Explain Closure Property for addition of whole numbers. Answer= Find the sum of given whole numbers 4 + 9 = 13 As we know that 13 is also a whole number, So, we can say that whole numbers are closed under addition.

Example 2 = With the given whole numbers 13 and 0, Explain Closure Property for addition of whole numbers. Answer= Find the sum of given whole numbers 13 + 0 = 13 As we know that 13 is also a whole number, So, we can say that whole numbers are closed under addition. ACTIVITY SL NO a b a+b Closure propety is satisfied or not Marks 08 1 14 56


02 2 12 -23


02 3 15 76


02 4 -45 23


02

http://www.algebraden.com/closure_property_addition_whole_numbers.htm


COMMUTATIVE PROPERTY UNDER ADDITION Explanation :- Addition is Commutative for Whole Numbers, this means that even if we change the order of numbers in addition expression, the result remains same. This property is also known as Commutativity for Addition of Whole numbers

Commutative Property for Addition of Whole Numbers can be further understood with the help of following examples :-

Example 1 = Explain Commutative Property for addition of whole numbers 5 & 7 in addition expression ? Answer = Given Whole Numbers = 5, 7 and their two orders are as follows :- Order 1 = 5 + 7 = 12 Order 2 = 7 + 5 = 12 As, in both the orders the result is same i.e 12 So, we can say that Addition is Commutative for Whole Numbers.

Example 2 = Explain Commutative Property for addition of whole numbers 23 & 43 in addition expression ? Answer = Given Whole Numbers = 23, 43 and their two orders are as follows :- Order 1 = 23 + 43 = 66 Order 2 = 43 + 23 = 66 As, in both the orders the result is same i.e 66 So, we can say that Addition is Commutative for Whole Numbers.

Example 3 = Explain Commutative Property for addition of whole numbers 20 & 4. Answer = Given Whole numbers = 20, 4 and their two orders are as follows :- Order 1 = 20 + 4 = 24 Order 2 = 4 + 20 = 24 As, in both the orders the result is same i.e 24, So, we can say that Addition is Commutative for Integers.

a+b = b+a there is no imprtance to the order of the numbers in commutative property ACTIVITY 3 Sl no a b a+b b+a Commutative property is hold good Marks alloted( 10) 1 14 15


2 2 23 -54


2 3 21 22


2 4 45 40


2 5 12 13


2

ASSOCIATIVE PROPERTY UNDER ADDITION When whole numbers are added irrespective of their group sum doesnot changes.this is known as associative property under addition. Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. That is, rearranging the paranthesis in such an expression will not change its value. Consider, for instance, the following equations:

(a+b)+c = a+(b+c) Activity 1: Step 1: The "Associative Laws" say that it doesn't matter how you group the numbers (i.e. which you calculate first) ... ... when you add: (a + b) + c = a + (b + c)


(this activity is from www.mathsisfun.com)

ACTIVITY2 : Check the associative property for the set of following whole numbers 1.(5,9,8)

2.(11,12,13) 3.(11,8,10)

Properties under multiplication on whole numbers Closure property: The product of two whole numbers is always a whole number. i.e 2*3=6, 5*5=25, 3*9=27 0*9=0 (the product of any whole number with zero is always a zero)

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