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General algebra

Terms in algebra

  • A variable is a term that is used to indicate that the symbol may take various values.
    • Usually a letter of the alphabet is used to represent a variable.
    • It is most important that the meaning of variables is understood.
  • An algebraic expression might involve variables, numbers and symbols \( (+, \ -, \ \times,\ \div, \ \sqrt{\hspace{5pt}}, \ \ldots)\) but no equals sign.
  • An equation contains an equals sign \((=)\) and indicates that two expressions are equal. Formulas are examples of equations.


Formulas in algebra

  • A formula is a rule connecting different variables. For example, the area of a rectangle is found by multiplying its length by its width, that is, \( A = lw\).
  • The subject of the formula is the variable on its own, usually on the left hand side, e.g. \(A\) is the subject of the Area formula.
  • Sometimes we know the value of the subject but not that of one of the other variables. In such cases, we need to rearrange the formula so that the unknown variable becomes the subject of the formula.
  • Use substitution to replace the variable with a numeric value and then calculate the answer.

    For example: Substituting \(x=2.5\) into \(4 (x+3)\) gives \begin{eqnarray} 4(x+3) &=& 4(2.5 + 3)\ \\ &=& 4 \times 5.5\ \\ &=& 22\ \end{eqnarray}