Class 6 Maths Algebra | Use of Variables in Common Rules |

__Use of Variables in Common Rules__

__Now, we will see some examples how Algebra is used in other branches of Mathematics.__

__Geometry__

__Perimeter of a square__: The perimeter of a square 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

Let each side of a square be *l.*

Perimeter = *l+ l+ l+ l*

* = *4* l*

Here the variable ‘ *l’ *is used to write the formula*.*

__Perimeter of a rectangle__: Similar to a square, the perimeter of a rectangle is the sum of its sides. Let the length of a rectangle be denoted by* l *the breath be denoted by b

Perimeter = *l+l+b+b*

Perimeter = 2*l + *2*b*

Here two variables and *b* have been used to write the formula.

__Arithmetic__

__Commutativity of addition of two numbers__: Commuting means changing the order. In addition the commutative property holds since changing the order of numbers does not change the sum. Thus, 2+3 = 3+2 =5.

Let *a *and *b *be two variables which can take any number value.

Then, we can write the commutative property as: *a *+ *b *= *b *+ *a.*

__Commutativity of multiplication of two numbers__: Commutative property holds true for multiplication of two numbers also. Changing the order of number does not lead to a change in the product of numbers. Thus, 2*3 =3*2 = 6.

Let *a *and *b *be two variables which can take any number value.

Then, we can write the commutative property as: *a*b *= *b*a.*

__Distributivity of numbers__: In this case, a number is broken down to make the calculation easier. For eg : 8* 105

= 8(100+5)

= 8*100 + 8*5

= 800 + 40

=840

This property is true for any three numbers. This can be written using variables in the following way :

= a*z

Now let z be broken down as z = b+ c. We get:

= a (b+ c)

=ab + ac.

Some of the examples related to the above concepts are as follows:

__Problem: A cube is a three-dimensional figure as shown in Fig 11.11. It has six faces and all of them are identical squares. The length of an edge of the cube is given by __*l*. Find the formula for the total length of the edges of a cube.

Solution:

Length of one side of a cube = *l*

Since the sides of a cube are of equal length, all are of size *l.*

There are 12 sides of a cube.

Hence, the total length = 12*l*

.