how to write properties of whole numbers under four fundamental operations with one example
Answers
Answer:
WHOLE NUMBERS
Now if we add zero (0) in the set of natural numbers, we get a new set of numbers called the whole numbers. Hence the set of whole numbers consists of zero and the set of natural numbers. It is denoted by W. i.e., W = {0, 1, 2, 3, . . .}. Smallest whole number is zero.
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Absolute Value
Properties of whole numbers
All the properties of numbers satisfied by natural numbers are also satisfied by whole numbers. Now we shall learn some fundamental properties of numbers satisfied by whole numbers.
Properties of Addition
(a) Closure Property: The sum of two whole numbers is always a whole number. Let a and b be two whole numbers, then a + b = c is also a whole number.
This property is called the closure property of addition
Example: 1 + 5 = 6 is a whole number.
closure-property
(b) Commutative Property: The sum of two whole numbers remains the same if the order of numbers is changed. Let a and b be two whole numbers, then
a + b = b + a
This property is called the commutative property of addition.
commutative-property
(c) Associative Property: The sum of three whole numbers remains the same even if the grouping is changed. Let a, b, and c be three whole numbers, then
(a + b) + c = a + (b + c)
This property is called the associative property of addition.
Associative-Property
(d) Identity Element: If zero is added to any whole number, the sum remains the number itself. As we can see that 0+a=a=a+0 where a is a whole number.
Identity-Element
Therefore, the number zero is called the additive identity, as it does not change the value of the number when addition is performed on the number.
Properties of Subtraction
(a) Closure Property: The difference of two whole numbers will not always be a whole number. Let a and b be two whole numbers, then a – b will be a whole number if a > b or a = b. If a < b, then the result will not be a whole number. Hence, closure property does not hold good for subtraction of whole numbers.
Examples
17 – 5 = 12 is a whole number.
5 – 17 = – 12 is not a whole number
Step-by-step explanation:
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Answer:
Properties of whole numbers help us to understand the numbers better. Moreover, they make calculations under certain operations like addition,subtraction,multiplication and division very simple. The different types of properties of whole numbers are are follows:
1) Closure for addition and multiplication.
2) Commutative property for addition and multiplication.
3) Associative property for addition and multiplication.
4) Distributive property of multiplication over addition.
5) Identity for addition and multiplication.
Closure property :
5 + 6 = 11
9 + 8 = 17
36 + 0 = 36
9 x 8 = 72
6 x 11 = 66
0 x 84 = 0
From the example we can conclude that when we add or multiply any two whole numbers we get a whole number.
Whole numbers are closed under addition and multiplication.
Note : Division by zero is not defined.
Commutative property for addition and multiplication
You can add whole nos. in any order. We can say that addition is commutative for whole numbers. This property is known as commutativity for addition.
5 + 11 = 11 + 5
16 = 16
You can multiply two whole numbers in any order. Thus we say multiplication is commutative for whole nos.
Multiply 8 and 6 in different orders, you will get the same answer.
8 x 6 = 48
6 x 8 = 48
∴ 8 x 6 = 6 x 8
Note : Subtraction is not commutative. ( 6 – 5 ≠ 5 – 6).
Division is not commutative. ( 4 ÷ 2 ≠ 2 ÷ 4).
Associative of addition and multiplication :
Observe the following examples :
1) (5 + 7 ) + 3 = 12 + 3 = 15
2) 5 + ( 7 + 3) = 5 + 10 = 15
In the 1st , you can add 5 and 7 first and then add 3 to the sum and in 2nd , you can add 7 and 3 first and then add 5 to the sum. The result in both the cases are same.
This property is generally used to do the addition is easy and fast way.
Oberve the following example :
234 + 197 + 203
In the above example, if we add 197 and 203 first then it will be more easier as unit (ones) digit has become zero.
234 + (197 + 203)
= 234 + 400
= 634
For Multiplication :
Multiplication is true for associative property.
8 x 125 x 1294
Here , if you multiply 125 and 1294 then it will be hard and time consuming. So we will multiply 8 and 125 and then with 1294.
( 8 x 125) x 1294
= 1000 x 1294
= 1,294,000 This arrangement of number is known as associative property.
Distributive of multiplication over addition
35 x ( 98 + 2 ) = 35 x 100 = 3500
65 x (48 + 2) = 65 x 50 = 3250
297 x 17 + 297 x 3 = 297 x (17 + 3) = 297 x 20 = 5940
All the above are the examples of distributive property of multiplication over addition.
Example :
854 x 102
To make this multiplication simpler, write 102 as 100 + 2 and then use distributive property.
854 x (100 + 2)
= 854 x 100 + 854 x 2 ------( distributive property)
= 85,400 + 1,708
= 87,108
Identity (for addition and multiplication
The collection of whole numbers is different from the collection of natural numbers because of just the presence of zero.This number zero has a special role in addition.
When you add zero to any whole number, the same whole number again.
Zero is called an Identity for addition of whole numbers or additive identity for whole numbers.
Zero has a special role in multiplication too. Any number when multiplied by zero becomes zero !
86 x 0 = 0
0 x 125 = 0
You came across an additive identity for whole numbers, a number remains unchanged when added zero to it. Similar case for multiplicative identity for whole numbers. A number remains unchanged when we multiply by 1. So 1 is called identity for multiplication of whole numbers or multiplicative identity for whole numbers.
Step-by-step explanation: