Algebraic Expressions and Basic Arithmetic Operations

2.3   Algebraic Expressions and Basic Arithmetic Operations
   
Addition and Subtraction of Algebraic Expressions
   
Rules
  • Before adding or subtracting two algebraic fractions, check the denominators first.
  • If they are not the same, you need to express all fractions in terms of common denominators.
   
Examples
   
(i) \(\dfrac{3y}{5} + \dfrac{3y}{5} = \dfrac{6y}{5}\)
   
(ii) \(\begin{aligned} &\dfrac{2}{3} - \dfrac{4s}{9} \\\\&=\dfrac{2\times 3}{3\times 3} - \dfrac{4s}{9} \\\\&= \dfrac{6-4s}{9}. \end{aligned}\)
   
(iii) \(\begin{aligned} &\space \dfrac{1}{2k} - \dfrac{1}{kj} \\\\&= \dfrac{1 \times j}{2k \times j} - \dfrac{1 \times 2}{kj\times 2} \\\\& = \dfrac{j-2}{2kj}. \end{aligned}\)
   
Multiplication and Division
 
  • Factorise expressions before division or multiplication when it is necessary.
 
Example
 
\(\begin{aligned} &\space \dfrac{m+n}{x -y} \div \dfrac{(m+n)^2}{x^2 -y^2} \\\\& = \dfrac{\cancel{m+n}}{\cancel{x-y}} \times \dfrac{(x+y)(\cancel{x-y})}{(\cancel{m+n})(m+n)} \\\\& = \dfrac{x+y}{m+n}. \end{aligned}\)

Algebraic Expressions and Basic Arithmetic Operations

2.3   Algebraic Expressions and Basic Arithmetic Operations
   
Addition and Subtraction of Algebraic Expressions
   
Rules
  • Before adding or subtracting two algebraic fractions, check the denominators first.
  • If they are not the same, you need to express all fractions in terms of common denominators.
   
Examples
   
(i) \(\dfrac{3y}{5} + \dfrac{3y}{5} = \dfrac{6y}{5}\)
   
(ii) \(\begin{aligned} &\dfrac{2}{3} - \dfrac{4s}{9} \\\\&=\dfrac{2\times 3}{3\times 3} - \dfrac{4s}{9} \\\\&= \dfrac{6-4s}{9}. \end{aligned}\)
   
(iii) \(\begin{aligned} &\space \dfrac{1}{2k} - \dfrac{1}{kj} \\\\&= \dfrac{1 \times j}{2k \times j} - \dfrac{1 \times 2}{kj\times 2} \\\\& = \dfrac{j-2}{2kj}. \end{aligned}\)
   
Multiplication and Division
 
  • Factorise expressions before division or multiplication when it is necessary.
 
Example
 
\(\begin{aligned} &\space \dfrac{m+n}{x -y} \div \dfrac{(m+n)^2}{x^2 -y^2} \\\\& = \dfrac{\cancel{m+n}}{\cancel{x-y}} \times \dfrac{(x+y)(\cancel{x-y})}{(\cancel{m+n})(m+n)} \\\\& = \dfrac{x+y}{m+n}. \end{aligned}\)