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Study Guide6th GradeLevel 2 · Standard

Free 6th Grade Order of Operations (PEMDAS)

Explains the PEMDAS rule 6th grade students use to work out calculations with more than one operation: parentheses first, then exponents (powers), then multiplication and division left to right, then addition and subtraction left to right. Four fully worked examples target the tie-break rule that causes most errors.

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Grade
6th Grade
Subject
Math
Topic
Order of Operations
Difficulty
Level 2 · Standard
Estimated time
15 minutes
Curriculum
Texas grade levels (TEKS)
Answers
Not applicable
Format
PDF (A4) + print

Students will practice

  • understanding what each letter of PEMDAS stands for
  • understanding that multiplication and division (and addition and subtraction) are worked left to right
  • evaluating expressions with parentheses and powers
  • spotting when parentheses change the answer

Curriculum: Texas grade levels (TEKS). We show specific outcome codes only where they have been verified against the official curriculum document.

What's next?

Completed: Order of Operations (PEMDAS)

  1. 16th Grade Order of Operations (PEMDAS) Worksheet — Level 1
  2. 26th Grade Order of Operations (PEMDAS) Worksheet — Level 2
  3. 36th Grade Order of Operations (PEMDAS) Worksheet — Level 3
  4. 46th Grade Ratio Worksheet — Level 1
Study guide

How to use this study guide

  1. Read it together first, pausing at each worked example to try the step before reading the answer.
  2. Attempt the "Check yourself" questions at the end without looking back.
  3. Then practice with a worksheet from the pathway above and finish with the topic test.

Common questions

Who is this study guide for?

6th Grade students (typically ages 11–12) working on order of operations. It is pitched at level 2 · standard.

Are the answers included?

This is a study guide, so there is no separate answer sheet; the 'Check yourself' questions include answers.

How long does it take?

About 15 minutes. Short, regular sessions work best: two or three a week beats one long one.

Do I need to sign up to download?

No. Click Download Free PDF and it opens immediately. It is free for personal, classroom and homeschool use.

What should we do next?

Try 6th Grade Order of Operations (PEMDAS) Worksheet — Level 1.

Preview

Success TutoringWorksheets6th Grade · Mathematics · Order of Operations

Order of Operations (PEMDAS)

What you need to know

When a calculation has more than one operation, everyone needs to do it in the same order or we would get different answers. That order is called PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Some people remember the order with the sentence "Please Excuse My Dear Aunt Sally".

LetterMeaningExample
PParentheses first(2 + 3) × 4 = 5 × 4 = 20
EExponents: powers and square roots32 = 9, so 32 + 1 = 10
M and DMultiplication and division, left to right12 ÷ 3 × 2 = 4 × 2 = 8
A and SAddition and subtraction, left to right10 − 4 + 3 = 6 + 3 = 9

The most important detail: M and D are a tie, and A and S are a tie. Division does not beat multiplication and addition does not beat subtraction. When you reach that level, simply work from left to right.

7 + 3 × 4

  1. No parentheses, no powers. Multiplication comes before addition.
  2. 3 × 4 = 12.
  3. 7 + 12 = 19. (Not 40: you do not add first just because the + comes first.)

(7 + 3) × 4

  1. Parentheses first: 7 + 3 = 10.
  2. 10 × 4 = 40.
  3. Same numbers as the last example, but the parentheses change the answer.

20 − 8 ÷ 2 + 32

  1. Exponents first: 32 = 9. The expression becomes 20 − 8 ÷ 2 + 9.
  2. Division next: 8 ÷ 2 = 4. Now it is 20 − 4 + 9.
  3. Addition and subtraction, left to right: 20 − 4 = 16, then 16 + 9 = 25.

36 ÷ (4 + 2) × 3

  1. Parentheses first: 4 + 2 = 6. Now it is 36 ÷ 6 × 3.
  2. Division and multiplication are a tie, so go left to right: 36 ÷ 6 = 6.
  3. Then 6 × 3 = 18. (Not 36 ÷ 18 = 2, which is what you get if you multiply first.)
Common mistake: doing all the multiplication before any division, or all the addition before any subtraction. 36 ÷ 6 × 3 = 18, not 2, and 10 − 4 + 3 = 9, not 3. Ties are worked left to right.
Common mistake: adding parentheses that are not there. 7 + 3 × 4 = 19. If the question wanted 40, it would have been written (7 + 3) × 4.

Check yourself

  1. 5 + 6 × 2 = ?
  2. (5 + 6) × 2 = ?
  3. 24 ÷ 6 × 2 = ?
  4. 18 − 2 × 3 + 4 = ?
  5. 42 − (9 − 5) × 2 = ?
  6. 50 − (3 + 2)2 ÷ 5 = ?

Answers: 1. 17 2. 22 3. 8 (24 ÷ 6 = 4, then 4 × 2) 4. 16 (18 − 6 + 4) 5. 8 (16 − 4 × 2 = 16 − 8) 6. 45 (50 − 25 ÷ 5 = 50 − 5)

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    Evaluate expressions using the correct order of operations. A challenge set for students ready to stretch further. This 6th Grade…

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Created by
Success Tutoring
Last reviewed
1 October 2026
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