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Simplifying Numerical Expressions using Number Properties

Learn how to identify and use number properties to simplify numerical expressions. This lesson covers commutative property, associative property, identity property, and distributive property. Practice mental math strategies to simplify expressions.

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Simplifying Numerical Expressions using Number Properties

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  1. Find your seat and be ready for your Do Now Good Morning !!

  2. Do Now Evaluate. 1. 2 + 5  3 – 7 2. 5(3 – 1) ÷ (3 + 2) 3. (4 + 1)2 – 8 ÷ 2 4. 12 ÷ 3  6 – 20 10 2 21 4

  3. Objective: SWBAT identify properties of numbers and use them to simplify numerical expressions.

  4. Vocabulary Commutative Property Associative Property Identity Property Distributive Property

  5. Mental math means “doing math in your head.” Many mental math strategies use number properties that you already know to make equivalent expressions that may be easier to simplify.

  6. Rearranging The Order

  7. Grouping

  8. Adding Zero or Multiplying by 1

  9. Ex. 1: Identifying Properties of Addition and Multiplication Tell which property is represented. A. (2  6)  1 = 2  (6  1) B. 3 + 0 = 3 C. 7 + 9 = 9 + 7 The numbers are regrouped. Associative Property Zero is being added. Identity Property The order of the numbers is switched. Commutative Property

  10. TOYO 1 Tell which property is represented. A. 7  1 = 7 B. 3 + 4 = 4 + 3 C. (5  1)  2 = 5  (1  2)

  11. Ex. 2: Using Properties to Simplify Expressions Simplify each expression. Justify each step. A. 21 + 16 + 9 B. 20  9  5 Commutative Property. 21 + 16 + 9 = 16 + 9 + 21 Associative Property. = 16 + (9 + 21) Add. = 16 + 30 = 46 Commutative Property. 20  9  5 = 20  5  9 Associative Property. = (20  5)  9 Multiply. = 100  9 = 900

  12. Tell which property is represented. 1.) 2.) 3.)

  13. You can use the Distributive Property to multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.

  14. Ex. 3: Using the Distributive Property to Multiply Mentally Use the Distributive Property to find 6(54). Method 1: Method 2: 6(50 + 4) Break apart 54 as 50 + 4. Use the Distributive Property. = (6  50) + (6  4) = 300 + 24 Multiply. = 324 Add. 6(60 – 6) Break apart 54 as 60 – 6. = (6  60) – (6  6) Use the Distributive Property. Multiply. = 360 - 36 Subtract. = 324

  15. TOYO 3 Use the Distributive Property to find 8(19). Use both methods. Method 1: Method 2:

  16. TOYO 4 Use the Distributive Property and choose any method. A.) B.)

  17. Review for Mastery - Communicator Identify the property shown. Identify the property shown and the missing number in each equation. Commutative Property (CP) Associative Property (AP) Identity Property (IP) Distributive Property (DP)

  18. Review for Mastery - Communicator Use the distributive property to find each product. 5(31) (34)6 2(19)

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