Multiplication and Division Property

Introduction on multiplication and division property:

           Multiplication: One of the fundamental mathematical operations is called multiplication. The multiplication is the method of scaling one number with another number. It creates the product of numbers. It is denoted by a symbol "×".

           Division: One of the fundamental arithmetic operations is called division. It is the inverse product of multiplication. It is denoted by a symbol ÷.

Multiplication and Division Property: Multiplication

          Multiplication is denoted by a×b.

• Commutative property
• Associative property
• Distributive property
• Identity element
• Zero element

Commutative property: When changing the order of two numbers it does not reflect in result. That is it does not change the result when we are changing the order of two numbers. The commutative property is as follows.

                x.y=y.x

Ex: x=10 y=22

Then         10.22=220

                22.10=220

That is      10.22=22.10

Associative property: The associative property states that the grouping of numbers does not modify the result. The associative property is as follows.

                (x.y).z=x(y.z)

Ex:

                x=5,y= 7 and z=10

Then,        (5.7)10=5(7.10)

                35(10)=5(70)

                350=350

Distributive property:The distributive property is as follows

                x.(y+z)=x.y+x.z

Ex:

                5.(3+2)=5.3+5.2

                5.(5)=15+10

                25=25

Identity element:An identity element is 1. When a number is multiplied by an identity element 1, then the answer is same as the number.

                x.1=x

Ex:

                x=77

Then         77.1=77

Zero element: When a number is multiplied by zero then the prodoct is zero.

                x.0=0

Inverse element:When a number is multiplied by its reciprocal number then the answer is 1.

                x.(1/x)=1

Ex:

                X=100

Then         100.(1/100)=1

Negation: When there is one negative then the negative property is

                (-1).x=(-x)

Ex:

                (-1).8=-8

When there is two negative then the negative property is

                (-1).(-1)=1

Multiplication and Division Property : Division

           The division is a/b=c. here a-dividend, b-divisor and c-quotient.

• Inverse of multiplication
• The result is zero when a number is divided by itself.
• Zero property:
• a/b is not an integer forever.
• The result is undefined when a number is divided by 0.

Inverse of multiplication:

           The following equation represents the inverse of multiplication property.

                              x.y=z

                              x=y/z

Ex:  x=8 y=4 then x.y=8.4=32

For division 8=32/4

Result of a number when it is divided byitself is 1:

                              a / a = 1

Ex: 10/10=1

Zero property:

              When the dividend is zero then the output is always zero. 0/a=0

Ex: 0/99=0

Result is undefined:

              When a number is divided by 0 then the result of division cannot be determined.

Ex: 0/55=undefined

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