Geoscience Reference
In-Depth Information
2.3.1
r
ules
For
s
equenCe
oF
o
perations
Rule 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.
Rule 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.
Rule 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, 100 - 30 = 70, 70 - 15 = 55, 55 - 4 = 51).
Rule 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.
Rule 5
In a series of divisions, changing the order or the grouping may change the result; thus, 100 ÷ 10
= 10 but 10 ÷ 100 = 0.1, and (100 ÷ 10) ÷ 2 = 5 but 100 ÷ (10 ÷ 2) = 20. Again, if no grouping is
indicated, the divisions are performed in the order written, from left to right; thus, 100 ÷ 10 ÷ 2 is
understood to mean (100 ÷ 10) ÷ 2.
Rule 6
In a series of mixed mathematical operations, the convention is as follows: Whenever no grouping
is given, multiplications and divisions are to be performed in the order written, then additions and
subtractions in the order written.
2.3.2 e
xamples
oF
s
equenCe
oF
o
perations
In a series of additions, the terms may be placed in any order and grouped in any way:
4 + 6 = 10 and 6 + 4 = 10
(4 + 5) + (3 + 7) = 19, (3 + 5) + (4 + 7) = 19, and [7 + (5 + 4)] + 3 = 19
In a series of subtractions, changing the order or the grouping of the terms may change the result:
100 - 20 = 80, but 20 - 100 = -80
(100 - 30) - 20 = 50, but 100 - (30 - 20) = 90
When no grouping is given, the subtractions are performed in the order written—from left to right:
100 - 30 - 20 - 3 = 47
or by steps:
100 - 30 = 70, 70 - 20 = 50, 50 - 3 = 47
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