Mr. Scandrett's ClassroomOS

Mathematics · Lesson 08

PEMDAS & Order of Operations

Parentheses Exponents Multiply or divide left to right Add or subtract left to right

PEMDAS is the shared agreement mathematicians use so one expression has one answer. In this lesson, students learn the order, practice the tricky left-to-right parts, and check their reasoning with immediate feedback.

Learning Target

I can evaluate numerical expressions using the order of operations.

By the end of the lesson, students should be able to explain why 8 - 2 + 5 is solved left to right, why multiplication does not always happen before division, and why parentheses can change the entire value of an expression.

The PEMDAS Order

PEMDAS names the order, but two pairs share the same priority. Multiplication and division are solved left to right. Addition and subtraction are also solved left to right.

PParenthesesDo grouping symbols first: ( ), [ ], or fraction bars.
EExponentsEvaluate powers such as 32 or 24.
MMultiplySame level as division; move left to right.
DDivideSame level as multiplication; move left to right.
AAddSame level as subtraction; move left to right.
SSubtractSame level as addition; move left to right.
Important rule 1Multiplication and division are a tie. Solve whichever appears first from left to right.
Important rule 2Addition and subtraction are a tie. Solve whichever appears first from left to right.

Worked Example

Evaluate 6 + 3 × (8 - 4)2 / 2.

6 + 3 × (8 - 4)2 / 2
Start with the original expression.
6 + 3 × 42 / 2
Parentheses first: 8 - 4 = 4.
6 + 3 × 16 / 2
Exponents next: 42 = 16.
6 + 48 / 2
Multiply and divide from left to right. First, 3 × 16 = 48.
6 + 24
Then divide: 48 / 2 = 24.
30
Add last: 6 + 24 = 30.

Interactive Check

Choose the correct value. Use the feedback to catch which PEMDAS step needs attention.

18 / 3 × 2
0/0correct this round

Guided Practice

Evaluate each expression. Type the final value only.

5 + 2 × 6
30 - 12 / 3 × 2
(4 + 3)2
2 + 3 × 42 / 4

Exit Ticket

Students answer these in complete sentences or with shown work.

  • Why does 18 / 3 × 2 equal 12 instead of 3?
  • Create two expressions using the numbers 2, 3, and 4. One expression should equal 14, and one should equal 20.
  • Explain one PEMDAS mistake you know how to avoid now.