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Algebraic Notation & Vocabulary

Algebraic Notation

What is algebraic notation?

  • When writing expressions in algebra (as opposed to sums in numbers) there are conventions and symbols that are used that take on a particular meaning
    • This is what we mean by algebraic notation
  • In number work, for adding and subtracting, we use + and –
    • In algebra, we still do!
      • Examples:
        a + b
        c + d – e
  • However for multiplication, no symbol is used, and for division, fractions are used
    • Examples:
      ab (means a × b)
      a over b (means a ÷ b)
      3ab (means 3 × a × b)
  • We can have combinations of these of course
    • Examples:
      a b plus c over 3 (means a×b + c÷3)
      The order of operations still apply in algebra so a×b and c÷d would happen before the addition
  • Powers (indices) and roots are used the same way as with numbers
    • Examples:
      a2 means a × a
      4a2 means 4 × a2
      With the order of operations, a2 will happen before multiplying by 4
  • Brackets also work in the same way as with numbers
    • Examples
      3 left parenthesis a space plus space b right parenthesis means 3 space cross times space left parenthesis a space plus space b right parenthesis but with brackets taking priority, when known, a space plus space b would be worked out first, then we would multiply by 3
      5 x left parenthesis 2 x space plus space 3 right parenthesis means 5 space cross times space x space cross times space left parenthesis 2 space cross times space x space plus space 3 right parenthesis, again with the brackets worked out first

How will I need to use algebraic notation?

  • Algebraic expressions are used in many parts of the course
    • You need to be able to understand their meaning and work with them
      • e.g. for rearranging a formula
    • You may be given a situation in words that you then have to write in algebra
      • Which could lead to an equation you may then have to solve

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