b. Suppose he bought 2 pounds of peaches and 3 pounds of grapes. How much did he spend in total? c. Suppose he spent $15.24 in total. If he only bought one pound of grapes, how many pounds of peaches did he buy? Section 1.2 Class Practice The expression 37P + 32R is called a __________________________________________________ of P and R. Suppose you bought D DVD’s and B Books. If each DVD cost $14.95 and each book you bought off the ‘specials’ table cost $6.95, write an expression that tells how much you spent. 3. On a quiz show, 20 points are given for correct answers to regular questions and 50 points are given for correct answers in the bonus round. Let R represent the number of regular questions answered correctly and B represent the number of bonus questions answered correctly. a. Write an expression that gives the total number of points earned. b. Suppose that a contestant earned 650 points. Write an equation relating R, B, and the number of points earned. c. Give three different possible solutions to the equation you wrote in part b.
Associative Property of Multiplication a(bc) = (ab)c Additive Identity a + 0 = a Multiplicative Identity a·1 = a Additive Inverse Multiplicative Inverse Distributive Property of Multiplication over Addition a(b + c) = ab + ac From the Identity Property, we can say that 0 is the additive identity and 1 is the multiplicative identity. Similarly, from the Inverse Property, is the additive inverse of a and is the multiplicative inverse of a because they both equal the identity for their respective operations. Example Identify the property used in the equations below. a) ___________________________________________________ b) ___________________________________________________ c) ___________________________________________________
Insert the proper operation signs (+,–, x, ÷) and grouping symbols, when needed, to make each sentence true. 9. 5________2________3________3 = -2 10. 6________7________8________2 = 9 Match each example with the property that is illustrated. (a) Additive Identity (b) Additive Inverse (c) Associative Property of Addition (d) Associative Property of Multiplication (e) Commutative Property of Addition (f) Commutative Property of Multiplication (g) Distributive Property of Mult over Addn (h) Multiplicative Identity (i) Multiplicative Inverse 11. __________ 17. 4 3 = 3 4 __________ 12. __________ 18. 4x 1 = 4x __________ 13. __________ 19. __________ 14. __________ 20. __________ 15. __________ 21. __________ 16. __________ 22. __________ 23. Use the Commutative Property of Multiplication to rewrite the given expression. 4 5 6= ______________________________ 24. Use the Distributive Property of Multiplication over Addition. 8x - 24= _______________________________ 25. Is a solution to the equation Show work and explain in words.
1. 2. 10 3. 103 4. 36 5. 6 6. 902 7. 8. 9. 10. 11. e 12. a 13. g 14. i 15. d 16. b 17. f 18. h 19. e 20. c 21. b 22. g 23. 24. 8(x – 3) 25. If were a solution to the equation then Let’s see if it does: -20 – 12 = -32 and -2(-5+21) = -2(16) = -32 Since both sides equal -32, x = -5 is a solution to the equation 4x – 12 = -2(x + 21). 26. cm3 27. = in2 28. = 36 + 72 + 16 124 ft2 29. mg. 30a. 30b. 31. 4x + 5 32. –x + 19 33. 5x + 7 34. 14w2 – 4w 35. simplified already 36. 37. 38. 12x + 3y 39. -123x