6th Grade - Algebraic Expressions & Properties


  • An Expression is a mathematical statement comprising variables, numbers, and operators.
  • An expression can be of two types - numerical expression and algebraic expression.
  • A numerical expression involves only numbers and mathematical operators (no variables). Example: 523-1.
  • An algebraic expression involves numbers, variables, and mathematical operators. Example: 2x+1.

Algebraic Properties

  • Below are some of the laws obeyed by the algebraic expressions:
    • Commutative law: 


    • Associative law:



    • Distributive law:


Simplifying/Evaluating Algebraic Expressions

  • To simplify an algebraic expression, perform the following steps as applicable:
    • First, express the given expression in expanded form, if possible.
    • Then, identify and combine like terms to get a simplified expression.
  • An algebraic expression can be evaluated by following the two steps mentioned below:
    • First, replace variables with their respective values.
    • Then, apply the correct order of operations to get the final result.

Solved Examples

Question 1: Simplify the given algebraic expression.


Solution: 3+3m-12+9m




Question 2: Simplify the given algebraic expression.


Solution: 2x3×x5




Question 3: Evaluate m2+8 when m=10.

Solution: m2+8





Question 4: Find the value of 2x-8+y-3÷2 if x=4 and y=1.

Solution: 2x-8+y-3÷2





Cheat Sheet

  • An algebraic expression is a mathematical statement that contains numbers, variables, and mathematical operators.
  • To evaluate an algebraic expression, we replace the variable(s) with the given values and simplify to find the value of the expression.
  • An algebraic expression follows commutative laws, associative laws, and distributive laws.

Blunder Areas

  • When substituting values into algebraic expressions, it is good practice to put the substituted value in parentheses to prevent committing any mistake.