Game Development Reference
In-Depth Information
easier to understand, you can employ parentheses:
ð
3
3
Þ
2
¼
9
2
¼
7
ð
3
3
Þ
2
ð
2
2
Þ¼
9
2
4
¼
7
4
¼
3
ð
3
3
Þ
2
ð
2
2
Þ¼
9
2
1
¼
7
1
¼
6
Parentheses override the standard order of operations. When you work with
parentheses, you perform the operations in the innermost parentheses first and
then proceed outward. After calculating the innermost grouping symbols, you
then simplify the exponential expressions. After that, you carry out operations
according to the usual order. Here is an example:
2
3
þ
33
ð
3
þ
4
ð
2
þ
2
ÞÞð
3
3
Þð
3
Þ
¼
2
3
þ
33
ð
3
þ
4
ð
4
ÞÞ ð
9
Þð
3
Þ
¼
2
3
þ
33
ð
3
þ
16
Þð
27
Þ
¼
2
3
þ
33
ð
19
Þð
27
Þ
¼
8
þ
33
ð
19
Þð
27
Þ
¼
8
þð
33
19
Þ
27
¼
8
þ
627
27
¼
635
27
¼
608
Exercise Set 4.2
Here are a few problems involving orders of operation. Reduce the expressions.
a. 4a ð2a þ 6Þ
b. 16b c 5ð33a 2b þ5bÞ
c.
ð3a þ 12bÞ3ð4a 16bÞ
2
d.
ð6 2Þ
2
e.
ðrÞ
f. r
2
