Algebra Summary Class 6 Maths Chapter 11

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Algebra

• Algebra is a branch of mathematics that uses letters to represent numbers and show how they are related.

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

• The commutativity of addition means that changing the order of the numbers does not affect the sum. For example, a + b = b + a.
• The commutativity of multiplication means that changing the order of the numbers does not change the product. For example, 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 the variable that satisfies the equation is known as a solution. One way to find a solution is through trial and error: by testing different values for the variable, we check if they satisfy the equation until we find the correct one.

Variables help us express many common rules in geometry and arithmetic in a broad manner. The left-hand side (LHS) of an equation equals the right-hand side (RHS) only for a specific value of the variable.