Algebra I in Simple English/Introduction to Basic Algebra Ideas/Order of Operations
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(Note to contributors: Please use the ^ symbol to designate exponents when you enter them in the wikibook. I will format them on the student-user interface.--HSTutorials 00:42, 17 July 2006 (UTC)
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[edit] Vocabulary
Order of Operations
PEMDAS
Parenthesis Exponents Multiplication Division Addition Subtraction
[edit] Lesson
Evaluate the expression 3 + 4 * 5.
If you add first, it is 7 * 5 and evaluates to 35.
If you multiply first, it is 3 + 20 and evaluates to 23.
Is the first or second answer true?
With no order of operations, both answers are true. If an expression evaluates to more than one answer, math does not work. For math to work there is only one order of operations to evaluate a mathematical expression.
The order of operations is Parenthesis, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This can be remembered in two ways: "Please Excuse My Dear Aunt Sally" or PEMDAS.
The following list from top to bottom is the order of operations in Algebra. Operations at the top of the list are completed first, operations on the same line are completed from left to right.
- Parenthesis ( )
- Exponent ^
- Multiply *, Divide /
- Add +, Subtract -
Parenthesis is a special operation that has the most precedence. You use the ( and ) signs to make a separate expression from a group of terms. You evaluate an expression in parenthesis first. You use parenthesis if you need to do an operation with less precedence first.
[edit] Example Problems
Let's evaluate these expressions.
5 + x3 where x=2
5 + 23
5 + (2 * 2 * 2)
5 + 8
13
(5 + x)3 where x=2
(5 + 2)3
73
343
6 / x + 3 where x=3
6 / 3 + 3
2 + 3
5
6 / (x + 3) where x=3
6 / (3 + 3)
6 / 6
1
8 - x + 2 where x = 3
8 - 3 + 2
5 + 2 (we evaluate the - operation first, since - and + have the same precedence, and - is on the left)
7
8 - (x + 2) where x = 3
8 - (3 + 2)
8 - 5
3
Back to the first problem: Evaluate the expression 3 + 4 * 5.
There is only one answer, 23, because we multiply first.
If we want to add first, we can use parentheses.
If we write (3 + 4) * 5, then we add first, and get 35.
[edit] Practice Games
put links here to games that reinforce these skills
[edit] Practice Problems
62 * (8 - 6) = (72)
8 + 6 * 32 = (63)
32 / 23 + 4 = (8)
8 + 32 / 16 = (10)
6 +(4 / 2)2 * 8 = (38)
