Can u please explain me the commutative and closure property
Easily
Thank you
Can u please explain me the commutative and closure property
Easily
Thank you
definition and solved examples of closure property and commutative property are given below.Read and understand it.
Commutative Property The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2. Any time they refer to the Commutative Property, they want you to move stuff around; any time a computation depends on moving stuff around, they want you to say that the computation uses the Commutative Property.
- Use the Commutative Property to restate "3×4×x" in at least two ways.
They want me to move stuff around, not simplify. In other words, my answer should not be "12x"; the answer instead can be any two of the following:
4 × 3 × x
4 × x × 3
3 × x × 4
x × 3 × 4
x × 4 × 3
Closure property for addition :
If a and b are two whole numbers and their sum is c, i.e. a + b = c, then c is will always a whole number.
For any two whole numbers a and b, (a + b) is also a whole number. This is called the Closure-Property of Addition for the set of W.
Whole number + whole number = Whole number
Some solved examples :
1) 3 + 4 = 7
Here 3 and 4 are whole numbers.
The addition of 3 and 4 which is 7 is also a whole number.
So, property of closure is true for addition.
2) 4 - 3 = 1
Here, 4 and 3 are whole numbers and 1 is also a whole number.
So the property is true.
But 3 - 4 = -1
Here 3 and 4 are whole numbers.
The subtraction of 3 and 4 is -1 which is not a whole number.
So the property of closure for subtraction is not always true.
3) 12 + 0 = 12
Here, 12 and 0 both are whole numbers.
The addition of them which is 12 again is also a whole number.
So the property of closure is true.
Closure property for multiplication :
If a and b are whole numbers then their multiplication is also a whole number.
For any two whole numbers a and b, (a x b) is also a whole number.This is called the property of closure for Multiplication for the set of W.
Whole number x whole number = whole number
Some solved examples :
1) 30 x 7 = 210
Here 30 and 7 are whole numbers.
The multiplication of 30 and 7 which is 210 is also a whole number.
So property of closure for multiplication is true.
2) 40 x 0 = 0
Here 40 and 0 both are whole numbers.
Their multiplication 0 which is the smallest whole number.
Note : Property of closure is not always true for division.
Example : 45 ÷ 0 = not defined
As division with zero is not possible.
Commutative Property
The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2. Any time they refer to the Commutative Property, they want you to move stuff around; any time a computation depends on moving stuff around, they want you to say that the computation uses the Commutative Property.
- Use the Commutative Property to restate "3×4×x" in at least two ways.
They want me to move stuff around, not simplify. In other words, my answer should not be "12x"; the answer instead can be any two of the following:
4 × 3 × x
4 × x × 3
3 × x × 4
x × 3 × 4
x × 4 × 3
Closure property for addition :
If a and b are two whole numbers and their sum is c, i.e. a + b = c, then c is will always a whole number.
| For any two whole numbers a and b, (a + b) is also a whole number. This is called the Closure-Property of Addition for the set of W. |
Whole number + whole number = Whole number
Some solved examples :
1) 3 + 4 = 7
Here 3 and 4 are whole numbers.
The addition of 3 and 4 which is 7 is also a whole number.
So, property of closure is true for addition.
2) 4 - 3 = 1
Here, 4 and 3 are whole numbers and 1 is also a whole number.
So the property is true.
But 3 - 4 = -1
Here 3 and 4 are whole numbers.
The subtraction of 3 and 4 is -1 which is not a whole number.
So the property of closure for subtraction is not always true.
3) 12 + 0 = 12
Here, 12 and 0 both are whole numbers.
The addition of them which is 12 again is also a whole number.
So the property of closure is true.
Closure property for multiplication :
If a and b are whole numbers then their multiplication is also a whole number.
| For any two whole numbers a and b, (a x b) is also a whole number.This is called the property of closure for Multiplication for the set of W. |
Whole number x whole number = whole number
Some solved examples :
1) 30 x 7 = 210
Here 30 and 7 are whole numbers.
The multiplication of 30 and 7 which is 210 is also a whole number.
So property of closure for multiplication is true.
2) 40 x 0 = 0
Here 40 and 0 both are whole numbers.
Their multiplication 0 which is the smallest whole number.
Note : Property of closure is not always true for division.
Example : 45 ÷ 0 = not defined
As division with zero is not possible.
