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ACTIVITY I Identify the property described and give an example for each property. If I am multiplying I can group numbers in a product in any way I want. Property: Example: If I am adding I can do it in any order I want. Property: Example: If I am multiplying the sum of two numbers by a given number I can either add first, and then multiply or multiply each of them by the given number, and then add. Property: Example: If I am adding I can group numbers in a sum in any way I want Property: Example: If I multiply three numbers I can either multiply the first times the second, and then the third or multiply the second times the third and then by the first. Property: Example: If I multiply a given number by 1 the product is equal to the given number Property: Example: If I add zero to any given number I always get the given number back Property: Example: If I multiply a given number by its reciprocal I always get 1 Property: Example: If I multiply zero by a given number I always get zero Property: Example: Division of Mathematics, Science, and Advanced Academic Programs Algebra I Page 3 of 12 Session 3 ACTIVITY II With your team, respond to each of the following in complete sentences. Give specific numeric examples to illustrate each. 1. Does the commutative property of addition hold if you take a difference of two numbers? 2. Does the commutative property of multiplication hold for the division of two numbers? 3. Does the associative property of addition work if one or more of the operations is a difference? 4. Does the associative property of multiplication work if one or more of the operations is a division? 5. Can you use the distributive property to properly distribute (2+3)×(4+5)? Division of Mathematics, Science, and Advanced Academic Programs Algebra I Page 4 of 12 Session 3 ACTIVITY III PRACTICE YOUR SKILLS With your team, name the property or properties illustrated by each statement. 1. 3x + 2 = 3x + 2 2. If 5 + b = 13, then b = 8 3. If 2x = 3y and 3y = -4, then 2x = -4 4. If f – g = n. then f = n + g 5. If 14 = + 10, then + 10 = 14 6. If j + 3 = 10, then 4(j + 3) = 4(10) 7. Given: m = n m= 75 Conclusion: n = 75 8. Given: 7x = 63 Conclusion: x = 9 9. Given: 2x + y = 70 y = 3x Conclusion: 2x + 3x = 70 Division of Mathematics, Science, and Advanced Academic Programs Algebra I Page 5 of 12 Session 3 Activity IV PRACTICE YOUR SKILLS Work with your team to complete each of the following. Identify which property of real numbers is being used. 1. x (yz) = x (zy) 2. 2 (x + y) = 2x + 2y 3. (x + y) + z = (y + x) + z 4. 2 [x (a + d)] = [2x] (a + d) 5. 5a + (-5a ) = 0 6. 2 +5 = (2 + 5) 7. (2 )( ) = 2 8. 3 =1 Justify each step using the properties of real numbers and the properties of equality. An example is given. Example: Given: 15y + 7 = 12 - 20y Conclusion: y = Statement Reason 15y + 7 = 12 - 20y Given 35y + 7 = 12 Addition Property of Equality 35y = 5 y = Subtraction Property of Equality Division Property of Equality Division of Mathematics, Science, and Advanced Academic Programs Algebra I Page 6 of 12 Session 3 1. Given: 27 = -9(y + 5) Conclusion: y = -8 Statement Reason 27 = -9(y + 5) 27 = -9y - 45 72 = -9y -8 = y y = 2. Given: Conclusion: b = Statement Reason 3. Given: Conclusion: x = -2 Statement Reason - b= 2– 12b = 1 -12b = -1 b= -6 -6(x + 3) = 6 -6 - 6x -18 = 6x -6x – 24 = 6x -24 = 12x -2 = x x = -2 Division of Mathematics, Science, and Advanced Academic Programs Algebra I Page 7 of 12 Session 3 Activity V End-of-Instruction Assessment 1. A student tried to solve the following equation but made a mistake. Step 1: 9 − 5(2x + 1) = −28 Step 2: 4(2x + 1) = −28 Step 3: 8x + 4 = −28 Step 4: 8x = −32 Step 5: x = −4 a) In which step did the mistake first appear? b) Correct the mistake and find the value of x. 2. Complete the missing steps. State the name of the properties used. Reasons Step 1. 5(6x + 4) + 1 = −39 Step 2. ________________ ___________________________ Step 3. 30x + 21 = −39 ___________________________ Step 4. ________________ ___________________________ Step 5. x = −2 ___________________________ 3. Perform the indicated operation: -6(a -7). State the name of the property used. 4. Write the additive inverse of the expression a – b. 5. Use the Associative Law of Multiplication to rewrite the expression 6x(4 6. Use the Commutative Law of Addition to rewrite the expression 7x + 5 Division of Mathematics, Science, and Advanced Academic Programs Algebra I Page 8 of 12 Session 3 7. If -10x + 12 = 9, then -5x + 6 = ______________ 8. Is the equation 3(2 x− 4) =−18 equivalent to 6x−12 = −18? A. Yes, the equations are equivalent by the Associative Property of Multiplication. B. Yes, the equations are equivalent by the Commutative Property of Multiplication. C. Yes, the equations are equivalent by the Distributive Property of Multiplication over Addition. D. No, the equations are not equivalent. 9. What is the multiplicative inverse of ? A. −2 B. C. D. 10. 2 If 2n = 6, what property of equality justifies writing p + 2n = 4p + 15 as p + 6 = 4p + 15 A. B. C. D. 11. Which property justifies rewriting 3x – 5x as (3 – 5)x A. B. C. D. 12. Addition property Transitive property Symmetric property Substitution property Associative property of multiplication Distributive property Commutative property of multiplication Associative property of addition The statement “If A. B. C. D. x = 6, then x = 18” is justified by the __________ Associative property of multiplication Commutative property of multiplication Multiplication property of equality Addition property of equality Division of Mathematics, Science, and Advanced Academic Programs Algebra I Page 9 of 12 Session 3

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