The
order
of
operations
The order of operations is a set of rules that all mathematicians use in
order to get the same answer. The order of operations goes like this:
Parentheses and Grouping, Exponents, Multiplication and Division and
Addition and Subtraction. To help students remember the order of
operations, many mathematic courses tell the students to remember
PEMDAS :
•
•
•
•
•
•
•
•
Parentheses
Exponents
Multiplication
and
Division
Addition
and
Subtraction
Some important things to remember about PEMDAS:
Multiplication and Division are done left to right.
Addition and Subtraction are done left to right.
If no Parentheses are present, you start with Exponents. If no
exponents are present, you would start with multiplication and
division. If no multiplication and division are present, you start with
addition and subtraction.
If the problem skips a step, then you would simply go on to the step
after the one skipped
Example: 8x3(7+8)-6
You would evaluate the parentheses first. Because there is no
exponents, you skip to the multiplication. Then you do the
subtraction
Parentheses and Grouping are the same thing. If there is brackets
or another form of grouping, then you it would still go first.
How to do parentheses:
-Do whatever operation is in the parentheses before doing operations
outside parentheses.
-After doing the parentheses, continue with order of operation
How to evaluate an exponent:
An important thing to remember about Powers:
-The smaller number is called an exponent.
-A Power is a way of writing repeated multiplication. For example, 34 is
actually 3x3x3x3. Its just quicker.
How to actually evaluate it:
Example: If it says 43, write down two fours, like this: 4 4 4
-Then put a multiplication sign between the three fours, like this: 4x4x4.
-Multiply the three numbers.
-Exponent answer: 64
-You have then evaluated the Exponent
Multiplication and Division
-Do all multiplication and division symbols left to right
Addition and Subtraction:
-Do all addition and subtraction symbols left to right.
Practice Problems
Test yourself by using these problems to make sure you understand
the concepts taught in this lesson. For problems 1, 3, and 4, figure out
what N equals. For problem 4, do as the directions say.
1. 16÷(32-1)=
2. A package of paper costs $4.00. For every ten packages of
paper that you buy, you receive a discount of $11.00. Write and
evaluate an expression to find the cost of buying 66 packages of
paper.
3. 6+7x4=
4. 36 ÷3x23=
To find the length of a show, use the expression p+2i, where p is the
length in minutes, of the play and I is the length, in minutes, of each
intermission. If the play is 130 minutes long and the intermissions
take 15 minutes each, how long is the show?
---for more practice problems, see text book starting page
17.
Answers
1.
2
2.
$198
3.34
4.
96
5.
160
minutes
long