Sequence of Operations - Basic Mathematics for Water and Wastewater Operators - page 92

Perform addition and subtraction operations from left to right:
2 + 9 - 5 - 8 = -2
There may be cases where several operations will be performed within multiple
sets of parentheses. In these cases we must perform all operations within the inner-
most set of parentheses first and move outward. We must continue to observe the
hierarchical rules throughout the problem. Brackets, [ ], may indicate additional sets
of parentheses.
■ Example 3.3
Problem : Solve the following equation:
[2 × (3 + 5) - 5 + 2] × 3 = ?
Solution: Perform operations in the innermost set of parentheses
3 + 5 = 8
Rewrite the equation:
[2 × 8 - 5 + 2] × 3 = ?
Perform multiplication prior to addition and subtraction within the bracket.
[16 - 5 + 2] × 3 = [11 + 2] × 3 = [13] × 3 = 13 × 3 = 39
■ Example 3.4
Problem : Solve the following equation:
7 + [2(3 + 1) - 1] × 2 = ?
Solution:
7 + [2(4) - 1] × 2 = 7 + [8 - 1] × 2 = 7 + [7] × 2 = 7 + 14 = 21
■ Example 3.5
Problem : Solve the following equation:
[(12 - 4) ÷ 2] + [4 × (5 - 3)] = ?
Solution:
[(8) ÷ 2] + [4 × (2)] = [4] + [8] = 4 + 8 = 12