Algebra Summary Class 6 Maths Chapter 11

Algebra

• Algebra is generalized arithmetic in which numbers are represented by letters, known as literal number of simply literals.

Variable

• A symbol having a fixed numerical value is called a constant. A symbol which takes various numerical values is called a variable. 
• The word variable means something that can vary, i.e., change.
• The value of a variable is not fixed. The length of a square can have any value. But the number of angles of a triangle has a fixed value 3. 
• We use a variable to represent a number and denote it by any letter such as l, m, n, p, x, y, z, etc.
• Variables allow us to express many common rules in both geometry and arithmetic in a general way.

Use of Variable in Common Rules

Rules from Geometry

• Perimeter of a square = Sum of the lengths of the sides of the square = 4 times the length of a side of the square = 41
  Here, the use of variable l allows us to write the general rule in a way that is concise and easy to remember.
• Perimeter of rectangle = Sum of the lengths of its four sides = length + breadth + length + breadth = 2(length + breadth) = 2(l+b)
  Here, both l and b are variables, which take on values independent of each other.

Rules from Arithmetic

• Commutativity of addition of numbers: Commuting (interchanging) the order of numbers in addition does not change the sum.
  a + b = b + a
• Commutativity of multiplication: Interchanging the order of numbers in multiplication does not change the product.
  a×b = b×a

Expressions with variables

• A combination of constants and variables connected by any one or more of the symbol +, –, × and ÷ is called an algebraic expression.
• The several parts of the expression, separated by the sign + or – are called the terms of the expression.
• Equation is an algebraic expression with a variable constants and the sign of equality (=). For example, A number x increased by 9 is 18.  x + 9 = 18.

Solution of an Equation
The value of variable in an equation which satisfies the equation. For getting the solution of an equation, one method is the trial and error method. In this method, we give some value to the variable and check whether it satisfies the equation. We go on giving this way different values to the variable until we find the right value which satisfies the equation.