## WHOLE NUMBER - ESSENTIAL POINTS

• Whole numbers are the numbers starting at 0 and counting up forever:
• {0, 1, 2, 3, 4, 5, 6, 7, 8,9,10,11,12...}
• Whole numbers don't include negative numbers, fractions, or decimals.
• Integers are just like whole numbers, but they also include negative numbers:
• {...-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 ...}
• Like whole numbers, integers don't include fractions or decimals.
• Natural numbers are just like whole numbers, but they do not include 0:
• {1, 2, 3, 4, 5, 6 ...}
• The smallest natural number is 1.
• The number 0 is the first and the smallest whole nos.
• There are infinitely many or uncountable number of whole-numbers.
• All natural numbers are whole-numbers.
• All whole-numbers are not natural numbers. For example, 0 is a whole-number but it is not a natural number.
• The different types of properties of whole numbers are are follows:
• Closure for addition and multiplication.
• When we add or multiply any two whole numbers we get a whole number.Whole numbers are closed under addition and multiplication.
• For example 2 + 3 = 5, 5 is a whoole number
• For example 2 x 3 = 6, 6 is a whole number
• Commutative property for addition and multiplication.
• You can add whole numbers in any order. We can say that addition is commutative for whole numbers. This property is known as commutativity for addition. For example 7 + 11 = 11 + 7
• You can multiply two whole numbers in any order. Thus we say multiplication is commutative for whole nos. For example 5 x 9 = 9 x 5
• Subtraction is not commutative. ( 8 – 3 ≠ 3 – 8).
• Division is not commutative. ( 6 ÷ 3 ≠ 3 ÷ 6).
• Associative property for addition and multiplication.
• In the below examples, you can add 5 and 7 first and then add 3 to the sum and in 2nd OR you can add 7 and 3 first and then add 5 to the sum. The result in both the cases are same. This is the associative property for addition
• (5 + 7 ) + 3 = 12 + 3 = 15
• 5 + ( 7 + 3) = 5 + 10 = 15
• Multiplication is true for associative property.
• (8 x 125) x 1294 = (125 x 1294) x 8
• Distributive property of multiplication over addition.
• Examples of Distributive property of multiplication over addition
• 35 x ( 98 + 2 ) = 35 x 100 = 3500
• 65 x (48 + 2) = 65 x 50 = 3250
• Identity for addition and multiplication.
• Zero is called an Identity for addition of whole numbers or additive identity for whole numbers becuase When you add zero to any whole number, the same whole number again.
• 1 is called identity for multiplication of whole numbers or multiplicative identity for whole numbers because A number remains unchanged when we multiply by 1.