Here's a mnemonic sentence for the order or sequence in which operations are carried out in algebraic and numerical expressions:
" Bless My Dear Aunt Sally! "
(Brackets, Multiplications, Divisions, Additions, Subtractions)
Thus (3*4+4/2-3)*5 is calculated in steps as:
Those who use the term "parentheses" instead of "brackets" may prefer to "Please My Dear Old Sally".
"Extra" brackets or parentheses may be written in for clarity (ie. [[3*4]+[4/2]-2]*5 ), but computer programmers write only the pared-down versions of formulas wherever possible in order to save on computer calculation run-times.
Bruce Nerve of Manchester NH(USA) sent us an alternative (in Apr/00) that expands the mnemonic to include exponents (being quantities of power or indices, such as 32):
" Please Excuse My Dear Aunt Sally! "
(Parentheses, Exponents, Multiplications, Divisions, Additions, Subtractions)
Incidentally the exponent sign E should not be confused with Euler's Constant sign e (used as the base of natural logarithms).
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