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Properties of Operations 1 Glue into your Journal. Commutative Property of Addition: You can add numbers in any order. a+b=b+a Ex. 3 + 5 = 5 + 3 8=8 Ex. 15.3 + 21.7 = 21.7 + 15.3 37 = 37 Ex. ¾ + ¼ = ¼ + ¾ 1=1 Commutative Property of Multiplication: You can multiply numbers in any order. axb=bxa Ex. 3 x 5 x 2 = 2 x 5 x 3 30 = 30 Ex. 15.3 x 21.7 = 21.7 x 15.3 332.01 = 332.01 Ex. ¾ x ¼ = ¼ x ¾ 3/16 = 3/16 Practice: Use the commutative property to solve. (Hint: Group the compatible numbers together.) 1. 32 + 28 = = 2. 2 x 15 x 5 = = 3. ⅓ + 3 ¼ + 1⅔= = 4. 3.4 + 12.3 + 2.6 = = Associative Property of Addition and Multiplication: the order of the numbers do not change, but the grouping symbols do change. Ex. (18 + 13) + 17 = 18 + (13 + 17) 31 + 17 = 18 + 30 48 = 48 Ex. (17 x 5) x 2 = 17 x (5 x 2) 85 x 2 = 17 x 10 170 = 170 Your Turn Now: Use Associative Property to solve. (Hint: Group the compatible numbers together. 1. (23 x 5) x 2 2. (9.5 + 4.9) + 5.1 a.__________________________________________________ ____________________________________________________ b.__________________________________________________ ____________________________________________________ Identity Properties 1. m + 3 = 3 3. 3m = 3 2. m + 0 = 3 4. h x 4 = 0 Tell which property is being illustrated. Then use mental math to evaluate the expression. 1. (10.5 + 5.8) + 6.2 = 10.5 + (5.8 + 6.2) _____________________________________________________ 2. 4.2 + (2.8 + 11.95) = (4.2 + 2.8) + 11.95 _____________________________________________________ 3. 1.5 + (1.74 + 3.5) = 1.5 + (3.5 + 1.74 ) _____________________________________________________ 4. (3.7 + 8.9) + 6.3 = (8.9 + 3.7) + 6.3 _____________________________________________________ 5. 5y = 5 _____________________________________________________ 6. 5r = 0 _____________________________________________________ 7. 7 + 0 = 7 _____________________________________________________ 8. (27 x 2) x 5 = 27 x (2 x 5) _____________________________________________________ 9. 5 x 27 x 2 = 27 x 5 x 2 _____________________________________________________ 10. Solve. Bakery. Find the total cost for a sweet roll that costs $1.30, two hard rolls that cost $1.20 each, and a coffee cake that costs $3.70.