Sequence of Operations - Basic Mathematics for Water and Wastewater Operators - page 89

3 Sequence of Operations
PEDMAS: P arentheses, E xponents, M ultiplication, D ivision, A ddition, S ubtraction, or
P lease E xcuse M y D ear A unt S ally
Mathematical operations such as addition, subtraction, multiplication, and division
are usually performed in a certain order or sequence. Typically, multiplication and
division operations are done prior to addition and subtraction operations. In addition,
mathematical operations are also generally performed from left to right using this
hierarchy. The use of parentheses is also common to set apart operations that should
be performed in a particular sequence.
Note: It is assumed that the reader has a fundamental knowledge of basic arithme-
tic and math operations; thus, the purpose of the following section is to provide a
brief review of the mathematical concepts and applications frequently employed
by wastewater operators.
SEQUENCE OF OPERATIONS RULES
r ule 1
In a series of additions, the terms may be placed in any order and grouped in any
way; thus, 4 + 3 = 7 and 3 + 4 = 7; (4 + 3) + (6 + 4) = 17, (6 + 3) + (4 + 4) = 17, and
[6 + (3 + 4)] + 4 = 17.
r ule 2
In a series of subtractions, changing the order or the grouping of the terms may
change the result; thus, 100 - 30 = 70, but 30 - 100 = -70, and (100 - 30) - 10 = 60,
but 100 - (30 - 10) = 80.
r ule 3
When no grouping is given, the subtractions are performed in the order written,
from left to right; thus, 100 - 30 - 15 - 4 = 51 (by steps, it would be 100 - 30 = 70,
70 - 15 = 55, 55 - 4 = 51).
r ule 4
In a series of multiplications, the factors may be placed in any order and in any
grouping; thus, [(2 × 3) × 5] × 6 = 180 and 5 × [2 × (6 × 3)] = 180.
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