MAT 060
Order of Operations: Whole Numbers
Objective
a You will be able to simplify expressions containing whole numbers using
the order of operations.
Be sure to do all Practice Problems as you are studying this Supplement!!
It is important that you learn the order in which the operations must be done so you
can correctly simplify expressions. So, make sure that you memorize the following
list:
1. Do all operations inside parentheses or other grouping symbols.
2. Simplify any expressions with exponents and find any square roots.
3. Do multiplications or divisions in the order in which they occur.
4. Do additions or subtractions in the order in which they occur.
Almost everyone seems to do OK with taking care of parentheses first and
exponents and square roots second. However, many people begin to have trouble
with multiplication and division. They incorrectly think that all the multiplications
must be done first, then all the divisions are done afterwards.
It is important to understand that we do the multiplications and divisions in the
order in which they occur.
Example 1 Simplify 12  32  4  4  (5  7) using the order of operations.
12  32  4  4  (5  7)

12  32  4  4  12

12  8  4  12

12  32  12

44  12

56
 Do the operations inside the parentheses.
 There are no expressions with exponents or square
roots, so we move on to multiplication and division.
 Do the multiplications and divisions as they occur.
We come across a division first, so we do it first.
 We finish by multiplying and dividing by doing the
remaining multiplication.
 Do the additions as they occur.
MAT 060
Order of Operations: Whole Numbers
Page 2
Practice Problem 1 Simplify 32  (10  3)  24  4  2 using the order of
operations.
The solution to this Practice Problem may be found on page 5.
As with multiplication and division, many people also the trouble with addition
and subtraction. The incorrectly think that all the additions must be done first, and
then all the subtractions are done afterwards.
It is important to understand that we do the additions and subtractions in the
order in which they occur.
Example 2 Simplify 52  18  3  2  3 using the order of operations.
52  18  3  2  3

25  18  3  2  3

25  6  2  3

25  12  3

13  3

16
 There are no operations in parentheses, so we will
start by simplifying the exponential expression.
 Do the multiplications and divisions as they occur.
We come across a division first, so we do it first.
 We finish multiplying and dividing by doing the
remaining multiplication.
 Do the additions and subtractions as they occur. We
come across a subtraction first, so we do it first.
 Do the remaining addition.
Practice Problem 2 Simplify 30  42  (3  3)  10 using the order of operations.
The solution to this Practice Problem may be found on page 5.
MAT 060
Order of Operations: Whole Numbers
Page 3
Now let’s do an example where all steps of the order of operations are used.
Example 3 Simplify 32  40  4  2  81  (10  6)  7 using the order of
operations.
32  40  4  2  81  (10  6)  7  Do the operations in the parentheses

32  40  4  2  81  4  7

32  40  4  2  9  4  7

32  10  2  9  4  7

32  20  9  4  7

12  9  4  7

3 47

77

0
Practice Problem 3
operations.
 Simplify the square root.
 Do the multiplications and divisions as
they occur. We come across a division
first, so we do it first.
 We finish multiplying and dividing by
doing the remaining multiplication.
 Do the additions and subtractions as they
occur. We come across a subtraction first,
so we do it first.
 Do the remaining additions and
subtractions in the order in which they
occur.
Simplify 70  42  2  3  (3  5)  64 using the order of
The solution to this Practice Problem may be found on page 6.
MAT 060
Order of Operations: Whole Numbers
Page 4
Homework Problems
Simplify each of the following expressions using the order of operations.
1.
23  6  4  (7  4)  25
2.
62  3  2  (4  5)  8  9
3.
15  25  5  3  (3  2)  49
4.
(24  3)  32  10  5  3
5.
54  81  2  3  (36  9)
6.
20  16  3  6  2  (1  4)
7.
30  (5  2)  5  32  6
8.
34  12  (10  8)  3  42
Answers to Homework Problems are on page 6
MAT 060
Order of Operations: Whole Numbers
Page 5
Solutions to Practice Problems
Practice Problem 1 Simplify 32  (10  3)  24  4  2 using the order of
operations.
32  (10  3)  24  4  2  Do the operations inside the parentheses.

3  7  24  4  2
2

9  7  24  4  2

9  7  6 2

9  7  12

 There are no expressions with exponents or square
roots, so we move on to multiplication and division.
 Do the multiplications and divisions as they occur.
We come across a division first, so we do it first.
 We finish by multiplying and dividing by doing the
remaining multiplication.
 Do the additions as they occur.
16  12

28
Practice Problem 2 Simplify 30  42  (3  3)  10 using the order of operations.
30  42  (3  3)  10

30  42  9  10

30  16  9  10

14  9  10

5  10

15
 Do the operations inside the parentheses.
 Simplify the exponent.
 There are no multiplications or divisions, so we will
move on to additions and subtractions.
 Do the additions and subtractions as they occur. We
come across a subtraction first, so we do it first.
 Do the remaining additions and subtractions in the
order in which they occur.
MAT 060
Order of Operations: Whole Numbers
Page 6
Practice Problem 3 Simplify 70  42  2  3  (3  5)  64 using the order of
operations.
70  42  2  3  (3  5)  64  Do the operations inside the parentheses.

70  42  2  3  15  64

70  42  2  3  15  8

70  21  3  15  8

70  63  15  8

7  15  8

22  8

14
 Simplify the exponent.
 There are no multiplications or divisions, so we
will move on to additions and subtractions.
 Do the additions and subtractions as they occur.
We come across a subtraction first, so we do it
first.
 Do the remaining additions and subtractions in
the order in which they occur.
Answers to Homework Problems
1.
26
2.
45
3.
32
4.
71
5.
52
6.
19
7.
12
8.
0