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Vocabulary

Learn how to identify and apply addition and multiplication properties, simplify expressions, and use the distributive property to mentally multiply numbers. Practice and sharpen your math skills!

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Vocabulary

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  1. Vocabulary

  2. You can multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.

  3. Example 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 (2  6)  1 = 2  (6  1) The numbers are regrouped. Associative Property One of the addends is 0. 3 + 0 = 3 Identity Property 7 + 9 = 9 + 7 The order of the numbers is switched. Commutative Property

  4. Example 2: Using Properties to Simplify Expressions Simplify each expression. Justify each step. A. 21 + 16 + 9 B. 20  9  5 21 + 16 + 9 = 16 + 9 + 21 Commutative Property = 16 + (9 + 21) Associative Property = 16 + 30 Add. = 46 20  9  5 = 20 59 Commutative Property = 20  (5  9) Associative Property = 20  45 Multiply. = 900

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

  6. Check It Out! 1. Tell which property is represented. (5  1)  2 = 5  (1  2) The numbers are regrouped. Associative Property 2. Simplify each expression. Justify each step. 17 + 14 + 3 17+ 3+ 14 Commutative Property (17+ 3)+ 14 Associative Property Add. = 20 + 14 = 34

  7. Check It Out! Example 3 Use the Distributive Property to find 8(19). Method 1: Method 2: 8(19) = 8(10 + 9) Rewrite 19 as 10 + 9. Use the Distributive Property. = (8  10) + (8  9) = 80 + 72 Multiply. = 152 Add. Rewrite 19 as 20 – 1. 8(19) = 8(20 – 1) = (8  20) – (8  1) Use the Distributive Property. Multiply. = 160 – 8 Subtract. = 152

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