CHAPTER P Prerequisites Section P.1 Real Numbers 1. rational 2. Irrational 3. prime 4. variables, constants 5. terms 6. Yes. 52 25 3 3 3 −=−  =− = 7. (c) Commutative Property of Addition:a b b a +=+ 8. (d) Associative Property of Multiplication: () () ab c a bc = 9. (e) Additive Inverse Property: a a +− = ( ) 0 10. (b) Distributive Property: a b c ab ac ( ) += + 11. (f) Associative Property of Addition: () () ab ca bc + +=+ + 12. (a) Multiplicative Identity Property: 1 a a ⋅ = 13. { } 7 2 2 3 −− − − 9, , 5, , 2, 0, 1, 4, 1 (a) Natural numbers: 5, 1 (b) Whole numbers: 5, 0, 1 (c) Integers: − −− 9, 5, 0, 1, 4, 1 (d) Rational numbers: 7 2 2 3 −− − − 9, , 5, , 0, 1, 4, 1 (e) Irrational number: 2 14. { } 7 5 3 4 5, 7, , 0, 3.12, , 2, 8, 3 −− −− (a) Natural number: 3 (b) Whole numbers: 0, 3 (c) Integers: − −− 7, 0, 2, 8, 3 (d) Rational numbers: 7 5 3 4 −− − − 7, , 0, 3.12, , 2, 8, 3 (e) Irrational number: 5 15. {2.01, 0.666 , 13, 0.010110111 , 1, 10, 20} − −   (a) Natural numbers: 1, 20 (b) Whole numbers: 1, 20 (c) Integers: − − 13, 1, 10, 20 (d) Rational numbers: 2.01, 0.666 , 13, 1, 10, 20  − − (e) Irrational number: 0.010110111 16. − − {2.3030030003 , 0.7575, 4.63,  10, 2, 0.3, 8} (a) Natural number: 8 (b) Whole number: 8 (c) Integers: −2, 8 (d) Rational numbers: 0.7575, 4.63, 2, 0.3, 8 − − (e) Irrational numbers: 2.3030030003 , 10  17. { } 1 1 6 332 −− − − − π, , , 2, 7.5, 2, 3, 3 (a) Natural numbers: 6 3 (since it equals 2), 3 (b) Whole numbers: 6 3 , 3 (c) Integers: 6 3 , 2, 3, 3 − − (d) Rational numbers: 1 6 3 3 − −− − , , 7.5, 2, 3, 3 (e) Irrational numbers: 1 2 −π, 2 18. { } 12 1 5 2 25, 17, , 9, 3.12, , 6, 4, 18 − − π − (a) Natural numbers: 25, 9 3, 6, 18 = (b) Whole numbers: 25, 9 3, 6, 18 = (c) Integers: 25, 17, 9, 6, 4, 18 − − (d) Rational numbers: 12 5 25, 17, , 9, 3.12, 6, 4, 18 − − − (e) Irrational number: 1 2 π 19. 5 16 = 0.3125 20. 17 4 = 4.25 21. 41 333 = 0.123 22. 3 7 = 0.428571 23. 100 11 − =−9.09 24. 218 33 − =−6.60