## Ncert Solutions for Class 6 Maths Chapter 11 Algebra Exercise 11.2:-

**Exercise 11.2**Ā Class 6 maths NCERT solutions Chapter 11 Algebra pdf download:-

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### Ncert Solution for Class 6 Maths Chapter 11 Algebra Exercise 11.2 Tips:-

**Use of Variables in Common Rules**

Let us now see how certain common rules in mathematics that we have already

learnt are expressed using variables.

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**Rules from geometry**

We have already learnt about the perimeter of a square and of a rectangle in

the chapter on Mensuration. Here, we go back to them to write them in the

form of a rule.

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**1. Perimeter of a square**

We know that perimeter of

any polygon (a closed figure made up of 3 or more

line segments) is the sum of the lengths of its sides.

A square has 4 sides and they are equal in length

Therefore,

The perimeter of a square = Sum of the lengths of the

sides of the square

= 4 times the length of a side of the square

= 4 Ć l = 4l.

Thus, we get the rule for the perimeter of a square. The use of the variable

l allows us to write the general rule in a way that is concise and easy to

remember.

We may take the perimeter also to be represented by a variable, say p.

Then the rule for the perimeter of a square is expressed as a relation between

the perimeter and the length of the square, p = 4l

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**2. Perimeter of a rectangle**

We know that a rectangle

has four sides. For example, the rectangle ABCD

has four sides AB, BC, CD and DA. The opposite

sides of any rectangle are always equal in length.

Thus, in the rectangle ABCD, let us denote by l, the

length of the sides AB or CD and, by b, the length

of the sides AD or BC. Therefore,

Perimeter of a rectangle= length of AB + length of BC + length of CD+ length of AD

= 2 Ć length of CD + 2 Ć length of BC = 2l + 2b

The rule, therefore, is that the perimeter of a rectangle = 2l + 2b

where l and b are respectively the length and breadth of the rectangle.

Discuss what happens if l = b.

If we denote the perimeter of the rectangle by the variable p, the rule for

the perimeter of a rectangle becomes p = 2l + 2b

*Note:*Here, both l and b are variables. They take on values**independent of each other. i.e. the value one variable takes does not**

**depend on what value the other variable has taken.**

In your studies of geometry you will come across several rules and formulas

dealing with perimeters and areas of plane figures, and surface areas and

volumes of three-dimensional figures. Also, you may obtain formulas for the

sum of internal angles of a polygon, the number of diagonals of a polygon

and so on. The concept of variables which you have learnt will prove very

useful in writing all such general rules and formulas.

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**4. Commutativity of multiplication of two numbers**

We have seen in the chapter on whole numbers that for multiplication of

two numbers, the order of the two numbers being multiplied does not matter.

For example,

4 Ć 3 = 12, 3 Ć 4 = 12

Hence, 4 Ć 3 = 3 Ć 4

This property of numbers is known as commutativity of multiplication

of numbers. Commuting (interchanging) the order of numbers in

multiplication does not change the product. Using variables a and b as in the

case of addition, we can express the commutativity of multiplication of two

numbers as a Ć b = b Ć a

**Note that a and b can take any number value. They are variables. All the**

**special cases like**

4 Ć 3 = 3 Ć 4 or 37 Ć 73 = 73 Ć 37 follow from the general rule.

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**5. Distributivity of numbers**

Suppose we are asked to calculate 7 Ć 38. We obviously do not know the

table of 38. So, we do the following:

7 Ć 38 = 7 Ć (30 + 8) = 7 Ć 30 + 7 Ć 8 = 210 + 56 = 266

This is always true for any three numbers like 7, 30 and 8. This property is

known as distributivity of multiplication over the addition of numbers.

By using variables, we can write this property of numbers also in a general

and concise way. Let a, b and c be three variables, each of which can take any

number. Then, a Ć (b + c) = a Ć b + a Ć c

Properties of numbers are fascinating. You will learn many of them in your

study of numbers this year and in your later study of mathematics. Use of

variables allows us to express these properties in a very general and concise

way.