200 Chapter 2 The Integers
Order of operations
1.Perform all calculations within parentheses
and other grouping symbols following the
order listed in Steps 2–4 below, working from
the innermost pair of grouping symbols to
the outermost pair.
2.Evaluate all exponential expressions.
3.Perform all multiplications and divisions as
they occur from left to right.
4.Perform all additions and subtractions as they
occur from left to right.
When grouping symbols have been removed,
repeat Steps 2–4 to complete the calculation.
If a fraction bar is present, evaluate the
expression above the bar (called the numerator)
and the expression below the bar (called the
denominator) separately. Then perform the
division indicated by the fraction bar, if possible.DEFINITIONS AND CONCEPTS EXAMPLES
Evaluate:
Evaluate the exponential
expression.
Do the multiplication.
Use the subtraction rule: Add the
opposite of 40.
Do the addition.Evaluate: 2 Do the division.In the numerator, do the addition.
In the denominator, do the subtraction.14
7
In the numerator, do the multiplication.
In the denominator, evaluate the
exponential expression.6 4(2)
16 (3)^2
6 ( 8 )
16 9
6 4(2)
16 (3)^2
35
75 40
75 (40)
3 (5)^2 (40)3( 25 )(40)
3(5)^2 (40)
Absolute value symbolsare grouping symbols,
and by the order of operations rule, all
calculations within grouping symbols must be
performed first.Evaluate:
Do the addition within the absolute
value symbol.
Find the absolute value of 7.
Do the multiplication.
4 Do the subtraction.10 14
10 2(7)
10 20 8 10 10 20 70
10 20 8 10
When an exact answer is not necessary and
a quick approximation will do, we can use
estimation.Estimate the value of by rounding
each number to the nearest ten.Add the positives and the
negatives separately.
70 Do the addition.170 100
60 ( 70 ) 90 ( 40 ) 10
56 (67) 89 (41) 14
Evaluate each expression.107. 20 2[12( 7 5)^2 ]
4 a 20 2(12 5 2)15
3
b 2312 (89)^270 80 2(3)(4)
2(5)(4) 42 (4)^2
0 90
32
65 8(9)(47) 3(2)^3 16
2 4(6) 7 (2)^2 1
108.
- Round each number to the nearest hundred to
estimate the value of the following expression: - Find the mean (average) of , 4, 7, , 2, 0, ,
and . 4
8 11 6
4,4717,9352,094(3,188)
c 45 a 53 100
4
c 1 a 23 bd100
50
bd3(6) 11 1
42 32
2 5 (6)
3 15
8 60 3 4 50
REVIEW EXERCISESSECTION 2.6 Order of Operations and Estimation