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 = 2l + 2b

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 = 12l

.