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# 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:

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

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

• Distributive law:

$A\left(B+C\right)=A×B+A×C$

## 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.

$2{x}^{3}×{x}^{5}$

Solution: $2{x}^{3}×{x}^{5}$

$=2{x}^{3+5}$

$=2{x}^{8}$

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: $2x-\left(8+y-3\right)÷2$

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

$=8-\left(6\right)÷2$

$=8-3$

$=5$

## 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.