1.4 BEDMAS

Fortunately, there is an easy way to remember the correct order in which arithmetic operations should be carried out. The rules are neatly summed up in the mnemonic BEDMAS. The letters in BEDMAS stand for Brackets, Exponents, Division, Multiplication, Addition and Subtraction, and the order of the letters gives the order in which the operations should be carried out. In other words, you should work out the brackets first, then the exponents (otherwise known as indices or powers), then any divisions and multiplications, and finally the additions and subtractions. You may see BIDMAS (where the ‘I’ stands for ‘Indices’) or BODMAS written instead of BEDMAS; the three expressions are equivalent.

There is one final point to make about the order in which arithmetic should be done. When faced with a calculation that includes a series of multiplications and divisions (or a series of additions and subtractions), then you should work through the calculation from left to right in the order in which it is written.

Question 1.4

To practise the BEDMAS rules, try the following calculations both in your head and with your calculator.

    • a. 26 minus 12 plus four
  • Working from left to right gives

    equation sequence part 1 26 minus 12 plus four equals part 2 14 plus four equals part 3 18
    • b. 16 plus 12 multiplication two
  • The multiplication should be done before the addition, so

    equation sequence part 1 16 plus 12 multiplication two equals part 2 16 plus 24 equals part 3 40
    • c. left parenthesis 16 plus 12 right parenthesis multiplication two
  • The bracket should be evaluated first, so

    equation sequence part 1 left parenthesis 16 plus 12 right parenthesis multiplication two equals part 2 28 multiplication two equals part 3 56
    • d. 35 minus seven multiplication two
  • The multiplication should be done before the subtraction, so

    equation sequence part 1 35 minus seven multiplication two equals part 2 35 minus 14 equals part 3 21
    • e. left parenthesis 35 minus seven right parenthesis multiplication two
  • The bracket should be evaluated first, so

    equation sequence part 1 left parenthesis 35 minus seven right parenthesis multiplication two equals part 2 28 multiplication two equals part 3 56
    • f. 180 division 10 multiplication three
  • Working from left to right gives

    equation sequence part 1 180 division 10 multiplication three equals part 2 18 multiplication three equals part 3 54
    • g. 180 division left parenthesis 10 multiplication three right parenthesis
  • The bracket should be evaluated first, so

    equation sequence part 1 180 division left parenthesis 10 multiplication three right parenthesis equals part 2 180 division 30 equals part 3 six
    • h. left parenthesis four multiplication three right parenthesis squared
  • The bracket should be evaluated first, so

    equation sequence part 1 left parenthesis four multiplication three right parenthesis squared equals part 2 12 squared equals part 3 144
    • i. four multiplication three squared
  • The term including an exponent, 32, should be evaluated first, so

    equation sequence part 1 four multiplication three squared equals part 2 four multiplication nine equals part 3 36
    • j. left curly bracket left parenthesis 10 plus five right parenthesis multiplication left parenthesis three plus one right parenthesis right curly bracket plus four
  • The innermost brackets should be evaluated first, so

    multiline equation row 1 left curly bracket left parenthesis 10 plus five right parenthesis multiplication left parenthesis three plus one right parenthesis right curly bracket plus four equals left curly bracket 15 multiplication four right curly bracket plus four row 2 Blank equals 60 plus four row 3 Blank equals 64
Next : 1.5 Alternative ways of writing calculations 
1.5 Alternative ways of writing calculations