6th Grade - Algebraic Expressions & Properties

Introduction

• 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: $5\left(2^3-1\right)$.
• An algebraic expression involves numbers, variables, and mathematical operators. Example: $2\left(x+1\right)$.

Algebraic Properties

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

• • Commutative law: 

$A+B=B+A$

• • Associative law:

$\left(A+B\right)+C=A+\left(B+C\right)$

$\left(A\times B\right)\times C=A\times \left(B\times C\right)$ 

• • Distributive law:

$A\left(B+C\right)=A\times B+A\times C$

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.

$3+3m-12+9m$

Solution: $3+3m-12+9m$

$=3m+9m+3-12$

$=12m-9$

 

Question 2: Simplify the given algebraic expression.

$2x^3\times x^5$

Solution: $2x^3\times x^5$

$=2x^{3+5}$

$=2x^8$

 

Question 3: Evaluate $\frac{m}{2}+8$ when $m=10$.

Solution: $\frac{m}{2}+8$

$=\frac{\left(10\right)}{2}+8$

$=5+8$

$=13$

 

Question 4: Find the value of $2x-\left(8+y-3\right)÷2$ if $x=4$ and $y=1$.

Solution: $2x-\left(8+y-3\right)÷2$

$=2\times \left(4\right)-\left[8+\left(1\right)-3\right]÷2$

$=8-\left(6\right)÷2$

$=8-3$

$=5$

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.