Hello Friends,Earlier we have discussed about real numbers examples and in today's session we all are going to discuss about an interesting topic of mathematics which is properties of numbers for

Arithmetic operations on the numbers follow the basic properties

Commutative word originally comes from the word “commute” which refers to move the stuff around. In addition of two numbers, this rule is represented as "p + q = q + p", which means 5 + 9 = 9 + 5. In multiplication of two number, this rule is represented as "p x q = q x p", which means 5 x 9 = 9 x 5. Let’s understand it in this way

Addition of numbers can be done in any order.

For example: 2 + 13 = 13 + 2

p + q = q + p

Multiplication of numbers can be done in any order.

For example: 12 x 6 = 6 x 12

p x q = q x p

Subtraction of numbers can’t be done in any desired order, since it is not commutative

For example: 6 – 2 ≠ 2 – 6

p - q ≠ q – p

Division of numbers can’t be done in any desired order, since it is not commutative

For example: 6 ÷ 2 ≠ 2 ÷ 6

p ÷ q ≠ q ÷ p

Let’s now move to associative property

Associative word originally comes from the word “associate” which refers to the grouping of numbers or objects. In addition of three numbers, this rule is represented as "p + ( q + r ) = ( q + p ) + r", which means 5 + ( 9 + 12 ) = ( 5 + 9 ) + 12. In multiplication of three number, this rule is represented as "p x ( q x r ) = ( p x q ) x r", which means 5 x ( 9 x 12 ) = ( 5 x 9 ) x 12. Let’s understand it in this way

Addition of numbers can be done in any order.

For example: 2 + ( 13 + 9 ) = ( 2 + 13 ) + 9

p + ( q + r ) = ( q + p ) + r

Multiplication of numbers can be done in any order.

For example: 12 x ( 6 x 14 ) = ( 12 x 6 ) x 14

p x ( q x r ) = ( p x q ) x r

Subtraction of numbers can’t be done in any desired order, since it is not associative

For example: 6 – ( 2 – 4 ) ≠ ( 6 – 2 ) - 4

p - ( q - r ) ≠ ( q - p ) - r

Division of numbers can’t be done in any desired order, since it is not commutative

For example: 6 ÷ ( 2 ÷ 4 ) ≠ ( 6 ÷ 2 ) ÷ 4

This is a brief introduction about commutative and associative properties for the grade III students and if anyone want to know about Steps in problem solving then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Probability and Statistics in the next session here.

**grade III**students of gujarat secondary education board. These properties include commutative and**associative properties**. Here I am going to give you the best free math answers and way of understanding these terms.Arithmetic operations on the numbers follow the basic properties

**commutative property**, associative property, distributive property. But here we will only study about two of them. Now start with the Commutative property.Commutative word originally comes from the word “commute” which refers to move the stuff around. In addition of two numbers, this rule is represented as "p + q = q + p", which means 5 + 9 = 9 + 5. In multiplication of two number, this rule is represented as "p x q = q x p", which means 5 x 9 = 9 x 5. Let’s understand it in this way

Addition of numbers can be done in any order.

For example: 2 + 13 = 13 + 2

p + q = q + p

Multiplication of numbers can be done in any order.

For example: 12 x 6 = 6 x 12

p x q = q x p

Subtraction of numbers can’t be done in any desired order, since it is not commutative

For example: 6 – 2 ≠ 2 – 6

p - q ≠ q – p

Division of numbers can’t be done in any desired order, since it is not commutative

For example: 6 ÷ 2 ≠ 2 ÷ 6

p ÷ q ≠ q ÷ p

Let’s now move to associative property

Associative word originally comes from the word “associate” which refers to the grouping of numbers or objects. In addition of three numbers, this rule is represented as "p + ( q + r ) = ( q + p ) + r", which means 5 + ( 9 + 12 ) = ( 5 + 9 ) + 12. In multiplication of three number, this rule is represented as "p x ( q x r ) = ( p x q ) x r", which means 5 x ( 9 x 12 ) = ( 5 x 9 ) x 12. Let’s understand it in this way

Addition of numbers can be done in any order.

For example: 2 + ( 13 + 9 ) = ( 2 + 13 ) + 9

p + ( q + r ) = ( q + p ) + r

Multiplication of numbers can be done in any order.

For example: 12 x ( 6 x 14 ) = ( 12 x 6 ) x 14

p x ( q x r ) = ( p x q ) x r

Subtraction of numbers can’t be done in any desired order, since it is not associative

For example: 6 – ( 2 – 4 ) ≠ ( 6 – 2 ) - 4

p - ( q - r ) ≠ ( q - p ) - r

Division of numbers can’t be done in any desired order, since it is not commutative

For example: 6 ÷ ( 2 ÷ 4 ) ≠ ( 6 ÷ 2 ) ÷ 4

*p ÷( q ÷r ) ≠ ( p ÷q ) ÷r*This is a brief introduction about commutative and associative properties for the grade III students and if anyone want to know about Steps in problem solving then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Probability and Statistics in the next session here.

## No comments:

## Post a Comment