Use of Variables
Variables are used to frame rules to find the perimeter of a polygon. The perimeter of a polygon can be obtained by adding the lengths of its sides.   The following are some simple rules for the properties of numbers using variables. Commutative property of addition: This property states that two numbers can be added in any order. If a and b represent any two numbers, then a + b = b + a. Commutative property of multiplication: This property states that two numbers can be multiplied in any order. If a and b represent any two numbers, then a x b = b x a. Associative property of addition: This property states that three numbers can be added in any order.  If a, b and c represent any three numbers, then (a + b) + c = a + ( b + c). Associative property of multiplication: This property states that three numbers can be multiplied in any order.  If a, b and c represent any three numbers, then (a x b) x c = a x ( b x c). Distributive property of multiplication over addition: This property states that if a, b and c represent any three numbers, then a x ( b + c) = a x b + a x c. Expressions with variables 1)  5 added to y can be expressed as y + 5. 2) a multiplied by 8 can be expressed as 8a. 3) x divided by 3 can be expressed as $\frac{\text{x}}{\text{3}}$ 4) First z multiplied by 2, then 5 substracted from the product can be expressed as 2z - 5. Using expression practically 1) Saritha has 15 more pens than ameena. let ameena have x pens then Saritha has x + 15 pens. 2) Raghu's father's age is 2 years more than 3 times Raghu's age. Let Raghu's age be t years then Raghu's father's age is (3t + 2) years.

#### Summary

Variables are used to frame rules to find the perimeter of a polygon. The perimeter of a polygon can be obtained by adding the lengths of its sides.   The following are some simple rules for the properties of numbers using variables. Commutative property of addition: This property states that two numbers can be added in any order. If a and b represent any two numbers, then a + b = b + a. Commutative property of multiplication: This property states that two numbers can be multiplied in any order. If a and b represent any two numbers, then a x b = b x a. Associative property of addition: This property states that three numbers can be added in any order.  If a, b and c represent any three numbers, then (a + b) + c = a + ( b + c). Associative property of multiplication: This property states that three numbers can be multiplied in any order.  If a, b and c represent any three numbers, then (a x b) x c = a x ( b x c). Distributive property of multiplication over addition: This property states that if a, b and c represent any three numbers, then a x ( b + c) = a x b + a x c. Expressions with variables 1)  5 added to y can be expressed as y + 5. 2) a multiplied by 8 can be expressed as 8a. 3) x divided by 3 can be expressed as $\frac{\text{x}}{\text{3}}$ 4) First z multiplied by 2, then 5 substracted from the product can be expressed as 2z - 5. Using expression practically 1) Saritha has 15 more pens than ameena. let ameena have x pens then Saritha has x + 15 pens. 2) Raghu's father's age is 2 years more than 3 times Raghu's age. Let Raghu's age be t years then Raghu's father's age is (3t + 2) years.

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