Algebra I/Content/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)
Order of Operations
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 all of the two answers are true. If an expression evaluates to more than one answer, math does not work. The order of operations says the order you do operations, so there is only one way to evaluate an expression.
You use precedence to make the order of operations in Algebra. All operations have a precedence that is more, less, or the same as an other operation. You do operations with more precedence before you do operations with less precedence. You do operations with the same precedence from left to right.
This list says the order of precedence for operations in Algebra. Operations at the top of the list have more precedence than operations at the bottom of the list. Operations on the same line have the same precedence.
- 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.
Let's evaluate these expressions.
5+x^3 where x=2
(5+x)^3 where x=2
6/x+3 where x=3
6/(x+3) where x=3
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)
8 - (x + 2) where x = 3
8 - (3 + 2)
8 - 5
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.
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