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Lesson ID: 183

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PEMDAS: Order of Operations

Mathematics, Algebra and Function, Operations (+, -, x, /, etc.), Problem Solving

Grade 5- 8



Objective

Students learn about the order of operations.

Directions

In algebra, there is a specific order in which operations are performed when evaluating an expression or solving equations.
This is the algebraic order of operations:
  1. Do any work within parentheses ( ) or other grouping symbols [ ] first.
  2. Do any work with exponents (powers) or roots.
  3. Do any multiplication or division in order from left to right.
  4. Do any addition and subtraction in order from left to right.
The acronym for this order of operations is PEMDAS.
Parentheses Exponents Multiplication Division Addition Subtraction

A popular expression for remembering this is: Please Excuse My Dear Aunt Sally.
Sample A
Read the problem.
42 + (9 - 3) = ?
Do the work in the parentheses first.
42 + 6 = ?
Do the exponents next.
42 = 4 x 4 = 16, so16 + 6 = ?
Finally, add the numbers together.
16 + 6 = 22
Write your answer.
42 + (9 - 3) = 22
Sample B
Read the problem.
52 - (4 x 3) + 9 / 3 x 4 = ?
Do work in the parentheses first.
52 - 12 + 9 / 3 x 4 = ?
Do exponents next.
52 = 5 x 5 = 25, so25 - 12 + 9 / 3 x 4 = ?
Multiply and divide in order from left to right.
25 - 12 + 3 x 4 = ?
9 divided by 3 is 3, and 3 times 4 equals 12.
25 - 12 + 12 = ?
Add and subtract in order from left to right.
13 + 12 = ?
25 minus 12 is 13 and 13 plus 12 equals 25.
13 + 12 = 25
Write down your answer.
52 - (4 x 3) + 9 / 3 x 4 = 25
Using the Calculator
Many calculators are designed to follow the algebraic order of operations. You can use the following problem to see if your calculator is programmed to follow the algebraic order of operations.
8 x 4 / 2 + 3 x 8 / 4 = ?
If your calculator answer was 22, it follows the order of operations. (Unprogrammed calculators get an incorrect answer of 38.)

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