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Use of Variables

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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.

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.