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Name_______________________________________ Date__________________ Period _____ MATH 7 CHAPTER 1 PRACTICE TEST For problem # 1, use both the distributive property and order of operations methods to solve the problem. Explain why the two methods simplify to equal answers. O3 1. Distributive Property 3 (12 - 2 ) 3 (12 - 2) In problems #2 and 3, a) Decide which method (O3 or Distributive Property) would be easiest, b) Explain why it’s easier, then c) SOLVE using ONLY the method that you selected. Remember: Using the Distributive Property BACKWARDS can be one of your choices. 2. 18 ( 40 + 60 ) a) My choice of method: _______________________________ b) Explanation of choice: ___________________________________________________ ________________________________________________________________________ c) Solution using my method (show work below): __________________ 3. 543 (11) a) My choice of method: _______________________________ b) Explanation of choice: ___________________________________________________ ________________________________________________________________________ c) Solution using my method (show work below): __________________ For problems #4 - 6, solve by using the Distributive Property. Simplify if possible. 4. 5. 6. 12 ( y + 2) 5 ( 2 + x + 3) Could you have solved #4 & #5 using order of operations? Why or why not? 7. You just solved a numeric expression by using the Distributive Property. The answer was 30. Now you solve the SAME problem using Order of Operations. What is the answer now? Why? 8. How many counterexamples are there to the Commutative & Associative Properties of Addition, the Commutative & Associative Properties of Multiplication, and Distributive Properties? 9. How many counterexamples do you need to show that division is not Commutative? Why? Justify: 10. 96 + 15 + 4 + 85 = 96 + 4 + 15 + 85 ________________________________ (96 + 4) + (15 + 85) ________________________________ 100 + 100 ________________________________ 200 ________________________________ Simplify: 11) 054 12. 541 13. 154 14. 540 Use the following word bank to help you answer problems #15 – 17. Some answers are NOT in the word bank! constant variable algebraic or variable expression numerical expression coefficient 15. 7 + y is a combination of a constant, a variable, and at least one operation so it is an __________________________________ and should be properly rewritten as _________________. 16. In 7 + 2y, the 7 is the ___________ or a number that never changes, the 2 is the ___________________________, the y is a ______________ or a value that changes based on what you substitute. 17. 7 + 2 is called a _____________________________________, since there are no variables. 18. Algebraically, the expression 2a 3 should be rewritten as ____________. 19. Rewrite the product (y)(5) properly _________ Simplify the following expressions. NO WORK = NO CREDIT! 20. 12 ÷ 2 6 + (4 + 2) 21. 9 + 3 (33) ÷ 9 . 3 22. [40 - (25 + 5)] (5 + 1) - 3 + 8 23. { 5 + [ (7 - 1) ÷ 3] 2 } 24. 12 - 3 2 + 30 0 25. Although generally order of operations should be used to simplify, there are times when you can choose to simplify in a different way. For the following scenarios, please JUSTIFY which mathematical property allows you to change the way you simplify. a. 5 ( 10 + 6) Order of operations states to do the parentheses first, but you decide to do the following: 5(10) + 5(6). JUSTIFY: _________________________________ b. (11 + 7) + (23 + 9) Order of operations states do the parentheses first but you decide to change the problem to this: (11 + 9) + (7 + 23). JUSTIFY: __________________________________________________________ c. (253)(5)(2) For the problem above, use your properties to change the problem TO MAKE THE MATH EASIER: _________________________________________________________ JUSTIFY:_________________________________________________________ 26. Give the FORMAL math word for the answer you get for each operation: a. addition _______________________ b. multiplication _______________________ c. subtraction _______________________ d. division _______________________ 27. Can you evaluate the expression 5 + b? If not, state why. 28. Evaluate the following expressions where x = 5, y = 4, and z = 3. a. xyz b. b-b In problem #30, use the commutative and associative properties to simplify the problem. State which property(ies) you used. 29. (17 + 84) + (83 + 54) + 16 + 46 30. Give your own real life example of the commutative property. 31. Give an example from real life that could not possibly be commutative. 32. Give a counterexample (a math one – not real life!) to prove that subtraction is not commutative. 33. Give a counterexample to prove that division is not commutative. EXTRA CREDIT 1. Give a counterexample to prove that subtraction is not associative. 2. Give a counterexample to prove that division is not associative. 3. Word attack the following (Give the root word that tells you why they make sense): Evaluate Numerical Variable Equation Commutative Associative Distributive 4. (115) (23) = 23 (115) _________________________________ 23 (100 + 15) _________________________________ 23 (100) + 23 (15) _________________________________ 2,300 + 23 (15) _________________________________ 2,300 + 15 (23) _________________________________ 2,300 + 15 (20 + 3) _________________________________ 2,300 + 15 (20) + 15 (3) _________________________________ 2,300 + 300 + 45 _________________________________ (2,300 + 300) + 45 _________________________________ 2,600 + 45 __________________________________ 2,645 __________________________________