Mathematical Operations (Edexcel GCSE Maths: Foundation)

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Jamie W

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Jamie W

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Mathematical Symbols

What mathematical symbols do I need to know?

  • Starting with the basic four operations
    • plus  Addition, plus, sum, total
    • minus  Subtraction, minus, difference, take away
    • cross times Multiplication, product, times
    • divided by Division, quotient, divide, share
  • Equals signs
    • equals Equal to
      • e.g.  3 x plus 7 equals 19
    • not equal to Not equal to
      • e.g.  2 minus 5 not equal to 5 minus 2
    • almost equal to Approximately equal to
      • e.g.  pi almost equal to 3.14
    • identical to Identical (equivalent) to
      • e.g.  12 x plus 6 identical to 3 left parenthesis 4 x plus 2 right parenthesis
  • Inequality signs
    • greater than Greater than
      • e.g.  5 greater than negative 2
    • less than Less than
      • e.g.  1 half less than 2 over 3
    • greater or equal than Greater than or equal to
    • less or equal than Less than or equal to
  • Other helpful symbols
    • left parenthesis space space right parenthesis  Brackets
      • used to group symbols
      • e.g.  left parenthesis 2 x space plus space 4 right parenthesis space – space 3 left parenthesis x space plus 7 right parenthesis
    • 3 to the power of x  Powers (also called indices, orders, or exponents)
      • repeated multiplication
      • e.g.  3 to the power of 4 equals 3 cross times 3 cross times 3 cross times 3 equals 81
    • square root of blank end root  Square root
      • opposite of squaring
      • e.g.  square root of 81 space equals space 9 is the opposite to 9 squared equals 81
    • plus-or-minus  Plus Minus
      • used to allow for both a positive and negative answer (two distinct answers)
      • a plus-or-minus b is the same as a plus b and a minus b
      • e.g.  x equals 3 plus-or-minus 2.5 is the same as x equals 3 plus 2.5 equals 5.5 and x equals 3 equals 2.5 equals 0.5
    • pi  Pi
      • the ratio of the circumference of a circle to its diameter

Order of Operations (BIDMAS/BODMAS)

What is the order of operations (BODMAS/BIDMAS)?

  • If there is more than one operation in a calculation then they should be done in the following order
    • Brackets: ( )
      • Perform any calculation(s) inside brackets first
    • pOwers or Indices (sometimes Order):  2, 3, √ and similar
      • These include powers, roots, reciprocals
    • Divisions or Multiplications: × or ÷
      • If there are more than one of these then work them out left to right
      • Division includes fractions
    • Additions or Subtractions: + or -
      • If there are more than one of these then work them out left to right
  • The acronym BODMAS or BIDMAS can help you remember the order of operations
  • Modern calculators are programmed to process calculations in this order
    • The calculation can then be typed in to the calculator exactly how it is written on paper
    • Ensure you enter long or complicated calculations carefully, checking if your answer seems sensible
      • Type in extra brackets if needed, to help define which calculation to perform first

In what order should fractions and roots be dealt with?

  • Fractions mean division in calculations (BODMAS/BIDMAS)
  • There may be "invisible brackets" around the numerator and around the denominator
      • e.g.  fraction numerator 2 plus 5 over denominator 7 minus 2 end fraction means open parentheses 2 plus 5 close parentheses divided by open parentheses 7 minus 2 close parentheses
    • Instead of using brackets we extend the fraction line to show exactly what is on the top and what is on the bottom
  • Roots are pOwers (BODMAS/BIDMAS)
  • There may be "invisible brackets" under the root
    • e.g.  square root of 9 plus 16 end root means square root of open parentheses 9 plus 16 close parentheses end root
    • Instead of using brackets we extend the top line on the root symbol to show everything that is to be rooted

Worked example

Work out left parenthesis 5 space – space 3 right parenthesis space plus space 2 space cross times space 7 squared.

Use BODMAS

First calculate anything inside Brackets, 5 minus 3 equals 2, so the question becomes      

2 space plus space 2 space cross times space 7 squared

Then any pOwers, 7 squared equals 49                

2 space plus space 2 space cross times space 49

followed by any Multiplications and Divisions, 2 cross times 49 equals 98

2 plus 98

and finally any Additions and Subtractions, 2 plus 98 equals 100

bold left parenthesis bold 5 bold space bold – bold space bold 3 bold right parenthesis bold plus bold 2 bold cross times bold 7 to the power of bold 2 bold equals bold 100

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Jamie W

Author: Jamie W

Expertise: Maths

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.