ALGEBRAIC OPERATIONS

ALGEBRAIC OPERATIONS

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:
calculate for brackets first = [3*4+4/2-3] [*5]
multiply within, then divide = [12+2-3] [*5]
add within, then subtract = [11] [*5] = 55

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)

Exponents are also used in "floating point" representation. A floating point number is usually written in the form a x rⁿ, where a is called a mantissa, and r is the number base (ie. 10 for decimal, 2 for binary etc), and n is an integer called the exponent. Thus for example 2 x 10⁴ = 20,000 (the point being shifted 4 places to the right) and 2 x 10^-4 = 0.0002 (the minus indicating 4 places to the left). Decimal numbers are sometimes written exponentially as aEn, whereby 2E04 means 2 x 10⁴ = 20,000.

Incidentally the exponent sign E should not be confused with Euler's Constant sign e (used as the base of natural logarithms).