6 CHAPTER 1 Critical Thinking Skills Exercises Warm Up Exercises In Exercises 1–8, fill in the blank with an appropriate word, phrase, or symbol(s). 1. Another name for the counting numbers is the ________ numbers. Natural 2. If a b ÷ has a remainder of 0, then a is ________ by b. Divisible 3. A specific case that satisfies the conditions of a conjecture but shows the conjecture is false is called a ________. Counterexample 4. A belief based on specific observations that has not been proven or disproven is called a conjecture or ________. Hypothesis 5. The process of reasoning to a general conclusion through observation of specific cases is called ________ reasoning. Inductive 6. The process of reasoning to a specific conclusion from a general statement is called ________ reasoning. Deductive 7. The type of reasoning used to prove a conjecture is called ________ reasoning. Deductive 8. The type of reasoning generally used to arrive at a conjecture is called ________ reasoning. Inductive Practice the Skills In Exercises 9–12, use inductive reasoning to predict the next line in the pattern. 9. × = × = × = × = 5 1 5 5 2 10 5 3 15 5 4 20 5 5 25 × = 10. × = × = × = × = 15 10 150 16 10 160 17 10 170 18 10 180 19 10 190 × = 11. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 12. = = = = 10 10 100 10 1000 10 10,000 10 1 2 3 4 100,000 105 = In Exercises 13–16, draw the next figure in the pattern (or sequence). 13. , , , . . . * 14. , , , , , , . . . * 15. , , , , . . . * 16. , , , , , . . . * In Exercises 17–24, use inductive reasoning to predict the next three numbers in the pattern (or sequence). 17. … 1, 3, 5, 7, 9, 11, 13 18. … 4, 7, 10, 13, 16, 19, 22 19. − − … 1, 2, 4, 8, 16, 32, 64 − 20. 3, 9, 27, 81, − − … 243 − 21. … 1, 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 1 7 22. 1 2 , 3 4 , 5 6 , 7 8 ,… 9 10 , 11 12 , 13 14 23. 1, 1, 2, 3, 5, 8, 13, 21,… 34, 55, 89 24. … 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199 Problem Solving In Exercises 25–28, choose several pairs of appropriate numbers to determine the sum or product indicated. Use these results to form a conjecture. See Example 1. 25. The Product of Two Odd Numbers If two odd numbers are multiplied together, is the product an even number or an odd number? The product of two odd numbers is an odd number. 26. The Product of an Even Number and an Odd Number If an even number is multiplied by an odd number, is the product an even number or an odd number? The product of an even number and an odd number is an even number. 27. The Sum of Two Even Numbers If two even numbers are added together, is the sum an even number or an odd number? The sum of two even numbers is an even number. 28. The Sum of Two Odd Numbers If two odd numbers are added together, is the sum an even number or an odd number? The sum of two odd numbers is an even number. 29. Products of 10 a) Select some natural numbers and multiply the numbers by 10. Answers will vary b) Observe the ones digit (the rightmost digit) of the products from part (a). Use inductive reasoning to make a conjecture regarding products involving 10 and natural numbers. Products involving 10 and natural numbers will have a ones digit 0. SECTION 1.1 R R R R R R *See Instructor Answer Appendix
RkJQdWJsaXNoZXIy NjM5ODQ=