# These are the multiplication and division properties

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These are the multiplication and division properties of equality Ø If ? = @ , then ? ⋅ A = @ ⋅ A and C = D C . Ø Give examples of this property. . B
Section 2: Equations and Inequalities 33 Try It! 2. The following pairs of equations are equivalent. Determine the property that was used to write the second equation. 1. For each algebraic equation, select the property or properties that could be used to solve it. a. 2 6 + 4 = 14 − 66 and 26 + 8 = 14 − 66 b. 26 + 8 = 14 − 66 and 26 + 8 + 66 = 14 − 66 + 66 c. 26 + 8 + 66 = 14 and 26 + 66 + 8 = 14 d. 86 + 8 = 14 and 86 + 8 − 8 = 14 − 8 e. 86 = 6 and + . ⋅ 86 = + . ⋅ 6 BEAT THE TEST! Algebraic Equation Addition or Subtraction Property of Equality Multiplication or Division Property of Equality Distributive Property Commutative Property ; , = 5 o o o o 26 + 7 = 13 o o o o 46 = 23 o o o o 6 − 3 = −4 o o o o 4(6 + 5) = 40 o o o o 10 + 6 = 79 o o o o −8 − 6 = 19 o o o o 2(6 − 8) + 76 = 9 o o o o Algebra Wall Want some help? You can always ask questions on the Algebra Wall and receive help from other students, teachers, and Study Experts. You can also help others on the Algebra Wall and earn Karma Points for doing so. Go to AlgebraNation.com to learn more and get started!
Section 2: Equations and Inequalities 34 A word problem or situation may require you to write and solve an equation. Jenna is applying to The Citadel, The Military College of South Carolina. Jenna wants to achieve a minimum score on the SAT Reasoning Assessment to be a competitive applicant. Jenna has earned a score of 980 on the SAT and has signed up for a test prep class to help her improve her score. The test prep company claims that each class she attends will increase her score by 10 points. Identify the variable in this situation. Assuming the company’s claim is correct, write an expression to represent Jenna’s SAT score after she attends any given number of classes. The average SAT score for incoming freshman at The Citadel is 1070 . Suppose the test prep company’s claim is correct and her score will increase by 10 points for each class that she attends. Write and solve an equation to determine the number of classes Jenna must take in order to earn the average score. Sarah is an engineer for the Fluor Corporation, an engineering and construction company in Greenville. She needs to calculate how long it will take to remove 6,000 gallons of water from a drainage ditch at a construction site using three water pumps. Used alone, Pump A can remove all of the rain water in four hours, while Pump B will take three hours. Sarah wants to run Pump A, Pump B, and Pump C simultaneously to remove the water in one hour. The equation below models the three pumps working together to remove the water in one hour, where 6 represents the number of hours Pump C will take to remove the rain water by itself. 1 4 + 1 3 + 1 6 = 1 Use the box below to determine the number of hours Pump C will take to remove the rain water by itself. Justify each step. Section 2 – Topic 3 Solving Equations