Order of Operations: Arithmetic Rules

Order of Operations: Arithmetic Rules
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In this lesson, students will learn and practice the order of operations in arithmetic expressions, including using parentheses, exponents, multiplication, division, addition, and subtraction. The lesson covers the rules for simplifying numerical expressions and introduces the acronym PEMDAS to remember the order. Through sample problems, students will apply these rules to find the values of expressions correctly following the order of operations.

  • Arithmetic
  • PEMDAS
  • Order of Operations
  • Exponents
  • Mathematics
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  1. The Order of Operations Unit 1 Lesson 3

  2. The Order of Operations Students will be able to: Perform arithmetic operations, including those involving whole-number exponents, in the conventional order. Key Vocabulary: Parentheses, exponents, multiplication, division, addition subtraction

  3. The Order of Operations When we evaluate expressions, we use one set of rules so that everyone arrives at the same correct answer. The rules used for simplifying numerical expressions are called order of operations.

  4. The Order of Operations These rules are based on doing the most powerful operations first (exponents), then the less powerful ones (multiplication and division, going from left to right), and finally, the least powerful ones last (addition and subtraction, going from left to right). Grouping symbols, like parentheses, tell us to evaluate whatever is inside them before moving on.

  5. The Order of Operations You can remember the order of operations with the acronym PEMDAS. Please Excuse My Dear Aunt Sally Multiplication Parentheses Subtraction Exponents Addition Division P E M D A S

  6. The Order of Operations Expressions with Only Addition, Subtraction, Multiplication, and Division Multiplication and division are evaluated first, from left to right. Addition and subtraction are always evaluated last, from left to right.

  7. The Order of Operations Sample Problem 1: Find the value of each numerical expression. Follow the order of operations when finding each value. a. ?? ?? ? + ? =

  8. The Order of Operations Sample Problem 1: Find the value of each numerical expression. Follow the order of operations when finding each value. a. ?? ?? ? + ? = = ?? ? + ? = = ?? + ? = = ??

  9. The Order of Operations Sample Problem 1: Find the value of each numerical expression. Follow the order of operations when finding each value. b. ??? ?? ?? =

  10. The Order of Operations Sample Problem 1: Find the value of each numerical expression. Follow the order of operations when finding each value. b. ??? ?? ?? = = ?,??? ?? = = ?,???

  11. The Order of Operations Sample Problem 1: Find the value of each numerical expression. Follow the order of operations when finding each value. c. ??? ? ?? ?? ? =

  12. The Order of Operations Sample Problem 1: Find the value of each numerical expression. Follow the order of operations when finding each value. c. ??? ? ?? ?? ? = = ??? ?? ? = = ? ? = = ?

  13. The Order of Operations Expressions with Four Operations and Exponents Exponents are more powerful than multiplication or division. If exponents are present in an expression, they are evaluated before any multiplication or division.

  14. The Order of Operations Sample Problem 2: Find the value of each numerical expression. Follow the order of operations when finding each value. a. ?? ??? ? + ? =

  15. The Order of Operations Sample Problem 2: Find the value of each numerical expression. Follow the order of operations when finding each value. a. ?? ??? ? + ? = = ?? ??? ? + ? = = ?? ?? + ? = = ?? + ? = = ??

  16. The Order of Operations Sample Problem 2: Find the value of each numerical expression. Follow the order of operations when finding each value. b. ??? ?? ??? ?? =

  17. The Order of Operations Sample Problem 2: Find the value of each numerical expression. Follow the order of operations when finding each value. b. ??? ?? ??? ?? = = ??? ?? ??? ?? = = ?,??? ? = = ?,???

  18. The Order of Operations Sample Problem 2: Find the value of each numerical expression. Follow the order of operations when finding each value. c. ??? + ??? ?? ?? ? =

  19. The Order of Operations Sample Problem 2: Find the value of each numerical expression. Follow the order of operations when finding each value. c. ??? + ??? ?? ?? ? = = ??? + ??? ?? ?? ? = = ??? + ? ?? = = ??? ?? = = ??

  20. The Order of Operations Expressions with Parentheses The last important rule in the order of operations involves grouping symbols, usually parentheses. These tell us that in certain circumstances or scenarios, we need to do things out of the usual order. Operations inside grouping symbols are always evaluated first, before exponents and any operations.

  21. The Order of Operations Sample Problem 3: : Find the value of each numerical expression. Follow the order of operations when finding each value. a. ? (?? + ???) =

  22. The Order of Operations Sample Problem 3: : Find the value of each numerical expression. Follow the order of operations when finding each value. a. ? (?? + ???) = = ? ??? = = ???

  23. The Order of Operations Sample Problem 3: : Find the value of each numerical expression. Follow the order of operations when finding each value. b. ??? (?? ? ?? ?) =

  24. The Order of Operations Sample Problem 3: : Find the value of each numerical expression. Follow the order of operations when finding each value. b. ??? (?? ? ?? ?) = = ??? (??? ?) = = ??? ??? = = ???

  25. The Order of Operations Sample Problem 3: : Find the value of each numerical expression. Follow the order of operations when finding each value. c. ? (??? ? ? ?? ?? ?) =

  26. The Order of Operations Sample Problem 3: : Find the value of each numerical expression. Follow the order of operations when finding each value. c. ? (??? ? ? ?? ?? ?) = = ? (??? ? ?? ?) = = ? (??? ?? ?) = = ? (??? ?) = = ? ??? = ???

  27. The Order of Operations Expressions with Parentheses and Exponents

  28. The Order of Operations Sample Problem 4: Find the value of each numerical expression. Follow the order of operations when finding each value. a. ??? (?? ? ? ?? ?) =

  29. The Order of Operations Sample Problem 4: Find the value of each numerical expression. Follow the order of operations when finding each value. a. ??? (?? ? ? ?? ?) = = ??? (?? ? ? ?? ?) = = ??? (?? ? ?) = = ??? ?? ? = = ??? ?? = = ??

  30. The Order of Operations Sample Problem 4: Find the value of each numerical expression. Follow the order of operations when finding each value. b. ??? ??? + (??+ ??? ??) =

  31. The Order of Operations Sample Problem 4: Find the value of each numerical expression. Follow the order of operations when finding each value. b. ??? ??? + (??+ ??? ??) = = ??? ??? + ?? + ??? ?? = = ? + ?? + ? = = ? + ?? = = ??

  32. The Order of Operations Sample Problem 4: Find the value of each numerical expression. Follow the order of operations when finding each value. c. ??? ??? ?? ? ?=

  33. The Order of Operations Sample Problem 4: Find the value of each numerical expression. Follow the order of operations when finding each value. c. ??? ??? ?? ? = ??? ??? ?? ??= = ??? ??? ???= = ??? ???= = ??? ??? = = ?? ?=

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