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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
 
\(\begin{aligned} &\space \dfrac{m+n}{x -y} \div \dfrac{(m+n)^2}{x^2 -y^2} \\\\& = \dfrac{\cancel{m+n}}{\cancel{x-y}} \times \dfrac{(x+y)(\cancel{x-y})}{(\cancel{m+n})(m+n)} \\\\& = \dfrac{x+y}{m+n}. \end{aligned}\)
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of pandai.

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
 
\(\begin{aligned} &\space \dfrac{m+n}{x -y} \div \dfrac{(m+n)^2}{x^2 -y^2} \\\\& = \dfrac{\cancel{m+n}}{\cancel{x-y}} \times \dfrac{(x+y)(\cancel{x-y})}{(\cancel{m+n})(m+n)} \\\\& = \dfrac{x+y}{m+n}. \end{aligned}\)
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of pandai.
Chapter : Factorisation and Algebraic Fractions
Topic : Algebraic Expressions and Laws of Basic Arithmetic Operations
Form 2 Mathematics
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