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1-3 Properties of Numbers CCSS: A.SSE.1b, A.SSE.2, N.Q.3 Vocabulary Using your textbook, define the following: • Equivalent Expressions • Additive Identity • Multiplicative Identity • Multiplicative Property of Zero • Multiplicative Inverse/Reciprocal • Commutative Property • Associative Property • Equivalent Expressions- expressions that represent the same number • Additive Identity- The sum of any number and zero is equal to the number • Multiplicative Identity- The product of any number and 1 is equal to the number • Multiplicative Property of Zero- The product of any number and zero is equal to zero • Multiplicative Inverse/Reciprocal- Two numbers whose product is 1 • Commutative Property- The order in which you add or multiply numbers does not change their sum or product • Associative Property- The way you group three or more numbers when adding or multiplying does not change their sum or product Properties of Equality Property Words Symbols Examples Reflexive Property Any quantity is equal to itself a=a Symmetric Property If one quantity equals a second quantity, then the second quantity equals the first If a=b, then b=a 5=5 4+7=4+7 8=2+6 then 2+6=8 Transitive Property If one quantity equals a second quantity and a second quantity equals a third quantity, then the first quantity equals the third quantity If a=b, b=c, then a=c If 6+9=3+12 and 3+12=15, then 6+9=15 Substitution Property A quantity may be substituted for its equal in any expression If a=b then a may be replaced by b If n=11, then 4n=4*11 Example 1: Evaluate Using Properties 1 Evaluate 7(4 3) 1 5 5 Name the Property used in each step 2 3 (4 2 8) 2 3 (8 8) 2 3 (0) 60 6 Example 2: Real World Item Eric makes a list of items that he needs to buy for a party and Balloons their costs. Find the total cost of these Decorations items Food Beverages Cost ($) 6.75 14.00 23.25 20.50 Example 3: Use Multiplication Properties Name the property used in each step 5 7 4 25 2 7 4 (5 2) (7 4) 10 28 280 Example 4: Common Core A traveler checks into a hotel on Friday and checks out the following Tuesday morning. Use the table to find the total cost of the room including tax Day Mon.-Fri. Room Charge $72 Sat.-Sun. $63 Sales tax $5.40 $5.10 Example 5: Common Core The table shows prices on children’s clothing. a. Interpret the expression 5(8.99)+2(2.99)+7(5.99) b. Write and evaluate three different expressions that represent 8 pairs of shorts and 8 tops c. If you buy 8 shorts and 8 tops you receive a discount of 15%. Find the greatest and least amount of money you can spend on the 16 items at the sale Shorts Shirts Tank Tops $7.99 $8.99 $6.99 $5.99 $4.99 $2.99 Example 6: Accuracy a. Elan has $13 that he wants to divide among his 6 nephews. When he types 13/6 into his calculator, the number that appears is 2.166666667. Where should Elan round? Example 7: Accuracy Dante’s mother brings him a dozen cookies, but before she leaves she eats one and tells Dante he has to share with his two sisters. Dante types 11/3 into his calculator and gets 3.66666667. Where should Dante round? Accuracy: Practice 1. Jessica wants to divided $23 six ways. Her calculator shows 3.833333333. Where should she round? 2. Ms. Harris wants to share 2 pizzas among 6 people. Her calculator shows 0.33333333. Where should she round? 3. The measurements of an aquarium are 12.9, 7.67, and 4.11 inches. Where should the number be rounded?