Page 170 - ArithBook5thEd ~ BCC

The reason for replacing letters with their assigned values in parentheses is to avoid pitfalls such as
the ones highlighted in the next two examples.
2
Example 208. Evaluate x if x = −4.

2
2
Solution. Forgetting parentheses, we would write x = −4 = −16, which is wrong, since the square of
any nonzero number is positive. The correct evaluation is
2
2
x =(−4) =16.

Example 209. Evaluate ab if a =3 and b = −4.

Solution. Without parentheses, we might think ab =3−4= −1, mistakenly turning multiplication into
subtraction. The correct evaluation is

ab =(3)(−4) = −12.

To evaluate complicated expressions consistently, we must follow the order of operations,which is
restated below for convenience.

1. operations within grouping symbols first;

2. exponents and roots next;

3. multiplications and divisions (in order of appearance) next;

4. additions and subtractions (in order of appearance) last.

Recall that “in order of appearance” means in order from left to right, and that grouping symbols
include parentheses, brackets, braces (curly brackets), the square root symbol, and the fraction bar.
1
Example 210. Evaluate the expression x − 3y if x =4 and y = − .
2

Solution. Substituting the assigned values, and multiplying first according to the order of operations,
" #
1
x − 3y =(4) − 3 −
2
3
=4 +
2
8 3 11 1
= + = = 5 .
2 2 2 2

Example 211. Evaluate a − b − c and a − (b − c)if a =2, b = −11 and c =10.

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