Chapter 1: Whole Numbers

Transcription

1 1 Chapter 1: Whole Numbers Prep Test a and D; b and E; c and A; d and B; e and F; f and C. 5. fifty Go Figure Section 1.1 On the first trip, the two children row over. The second trip, one child returns with the boat. The third trip, one adult rows to the other side. The fourth trip, one child returns with the boat. At this point, one adult has crossed the river. Repeat the first four trips an additional four times, one time for each adult. After completing the fifth time, there have been twenty trips taken, and the only people waiting to cross the river are the two children. On the twenty-first trip, the two children cross the river. So the minimum number of trips is twenty-one. Objective A Exercises 1. is greater than is units to the left of is 3 units to the right of is 7 units to the left of < < > ,761 < 3, ,61 >, ,5 < 8,5 27. Yes , 1, 16, 21, , 8, 72, 8, , 9, 77, 9, , 399, 662, 736, , 37, 377, 3,77, 3,7 Objective B Exercises 39. comma; three 1. five hundred eight 3. six hundred thirty-five 5. four thousand seven hundred ninety 7. fifty-three thousand six hundred fourteen 9. two hundred forty-six thousand fifty-three 51. three million eight hundred forty-two thousand nine hundred five , , , ,12, ,5, , , + 3, + 2, , , , + 2, ,, tens

2 2 Chapter 1: Whole Numbers Objective C Exercises 79. greater Given place value 81. 7,18 8> 5 7,18 rounded to the nearest ten is 7,11. Given place value 83.,962 6 > 5,962 rounded to the nearest hundred is 5,. Given place value ,551 5 = 5 28,551 rounded to the nearest hundred is 28,6. Given place value 87. 6,88 8 > 5 6,89 rounded to the nearest thousand is 7,. Given place value ,825 8 > 5 93,825 rounded to the nearest thousand is 9,. Given place value ,513 5 = 5 629,513 rounded to the nearest thousand is 63,. Given place value ,876 2 < 5 352,876 rounded to the nearest ten-thousand is 35,. 95. sometimes true 97. never true 99. blue Objective D Exercises 11. Strategy To find the person with the greater number of stolen bases, compare the numbers 892 and 937. Solution 892 < 937 Billy Hamilton had the greater number of stolen bases. 13. Strategy To find the greater number of performances, compare the numbers 2,8 and 3,22. Solution 2,8 < 3,22 Fiddler on the Roof was performed the greater number of times. 13. Strategy To find the food which contains more calories, compare the numbers 19 and 11. Solution 19 > 11 Two tablespoons of peanut butter contain more calories. 17. Strategy To find the shorter distance, compare the two numbers 1,892 and 1,833. Solution 1,892 > 1,833 The shorter distance is from St. Louis to San Diego. 19. Strategy To find the smaller planet, compare the two numbers 32,2 and 3,8. Solution 32,2 > 3,8 Neptune is the smallest planet Strategy To find the estimate of the speed of light, round the speed (299,8 to the nearest thousand. Solution 299,8 rounded to the nearest thousand is 3,. To the nearest thousand, the speed of light is 3, km/s Strategy To find the land area to the nearest ten-thousand acres, round 161,56 to the nearest ten-thousand. Solution 161,56 rounded to the nearest tenthousand is 16,. To the nearest ten-thousand acres, the land area of the Appalachian Trail is 16, acres.

3 Section Strategy a. To determine during which school year enrollment was lowest, use the line graph to find the school year corresponding to the lowest point on the line. b. To determine if enrollment increased or decreased between 1975 and 198, read the graph at 1975 and at 198. Solution a. Student enrollment was lowest during the 1985 school year. b. Enrollment was less in 198 than in Enrollment decreased between 1975 and 198. Critical Thinking The largest three-digit number is 999. (The next largest whole number is 1,, which has four digits. The smallest five-digit number is 1,. (The next smallest whole number if 9,999, which has digits. Section 1.2 Objective A Exercises 1. a. 12; 2; 1 b. 1; 2; 6; 9 c , ,26 1,383, , ,16 6,3 1 1,37 3,32 + 5,169 12, ,39 2, ,5 199, , , 32 97,126 6, 58 78, , , ,51 168, , , ,77 + 9,71 99, ,872 The total number of undergraduates enrolled at the college in 21 was 1, ,72 + 8,298 15, , ,832 1,388, , ,196 7,7 + 98, , x + y ,272 7, + 8, 15, , 31. x + y, , , ,398 12,15 1,, +, 1,, 2, 7, + 1, 37,

4 Chapter 1: Whole Numbers 33. x + y 38, , , ,671 89,9 35. a + b + c , a + b + c, , ,38 1 2,938 2, ,38 1, a + b + c 12, ,75 + 7, ,897 36,75 + 7,38 56, 1 1. The Commutative Property of Addition 3. The Associative Property of Addition 5. The Addition Property of Zero = ( + 17 = ( = Commutative Property of Addition = n = 2 Yes, 38 is a solution of the equation 2 = n h = No, 13 is not a solution of the equation 2 + h = = x = 32 Yes, 3 is a solution of the equation 32 = x + 2. Objective B Exercises 61. a. ; b. 8; 12; c. 2; ; / 3 / / 6 / / 5 / / / 7 / , 8 / 1 / / 3,257 3, /, / / / 2,16 2, /, / / / 1,963 1, / /, / / / 9,856 2, /, 5 / 3 / 6 / 918 1, / 2 /, 8 / / / 5,26 7,378

5 Section / 5 /, / 2 / 3 / 67,875 17, / / The difference between the maximum heights is 15 ft ,355 5,219 2, ,126 2,83 38, ,287 5, 92 31, ,196 98, , x y / / x y / 1 / x y / / / , 5, 2, 6, 2,,, 5, 35, 11. x y 8,672 3,61 8,672 3,61 5, x y 1, /, 6 / / 5 / , 1, 1, 15. x y 23,9 5, / 3 /, / / 9 5,178 18, = 53 y = 29 Yes, 2 is a solution of the equation 29 = 53 y. 19. t 16 = No, is not a solution of the equation t 16 = z= = 55 Yes, 27 is a solution of the equation 82 z = 55. Objective C Exercises 113. addition 115. Strategy To find the sum of the whole numbers less than 21, add the numbers to 2. Solution = 21 The sum of the numbers is Strategy To find the difference, subtract 99 (the largest two-digit number from 1, (the smallest four-digit number. 1, Solution The difference is Strategy To find the number of calories, add the number of calories in one apple (8, one cup of cornflakes (95, one tablespoon of sugar (5, and one cup of milk (15. Solution = 37 The breakfast contained 37 calories.

6 6 Chapter 1: Whole Numbers 121. Strategy To find the perimeter of a rectangle, replace L with 2 and W with 15 in the given formula and solve for P. Solution P = L + W + L + W P = P = 78 The perimeter is 78 m Strategy To find the perimeter of a triangle, replace a, b, and c with 16, 12, and 15 in the given formula and solve for P. Solution P = a + b + c P = P = 3 The perimeter is 3 in Strategy To find the difference in the number of orbits, subtract the number of orbits made by Apollo- Saturn 7 (163 from the number of flights made by Gemini-Titan 7 (26. Solution Gemini-Titan 7 made 3 more orbits than Apollo-Saturn Strategy To find the difference in seating capacity, subtract the seating capacity of Fenway Park (36,298 from the seating capacity of SAFECO Field (7,116. Solution 7,116 36,298 1,818 The difference in seating capacity is 1,818 seats Strategy To find the total cost of the computer system, add the cost of the operating system (83, the monitor (25, the keyboard (175, and the printer (395. Solution ,65 The total cost of the computer system is $1, Strategy To find the estimate of the number of miles driven: Round the two readings of the odometer. Subtract the rounded reading from the beginning of the year from the rounded reading at the end of the year. Solution 77, ,376 8, 6, 2, The car was driven approximately 2, mi during the year Strategy To determine between which two months car sales increased the most, find the difference, if there was an increase, between sales for January and February, February and March, and March and April for 25. Solution Between January and February, 25: = 2 Between February and March, 25: = 2 Between March and April, 25: not an increase Car sales increased the most between January and February of 25. The increase was 2 cars Strategy To find the value of the investment, replace P by 12,5 and I by 775 in the given formula and solve for A. Solution A = P + I A = 12, = 13,275 The value of the investment is $13, Strategy To find the mortgage loan, replace S by 29, and D by 29, in the given formula and solve for M. Solution M = S D M = 29, 29, = 261, The mortgage loan on the home is $261, Strategy To find the ground speed, replace a by 375 and h by 25 in the given formula and solve for g. Solution g = a h g = = 35 The ground speed of the airplane is 35 mph.

7 Section Strategy a. To determine how many drivers were traveling at 7 mph or less, add the numbers traveling 66 7 mph (3,717, mph (2,98, and less than 61 mph (2,87. b. To determine how many drivers were traveling at 76 mph or more, add the numbers traveling 76 8 mph (2,53 and more than 8 mph (1,78. Solution a. 3, ,98 + 2,87 = 9,571 9,571 drivers were traveling at 7 mph or less. b. 2,53 + 1,78 =,211,211 drivers were traveling at 76 mph or more. 13. Strategy To determine whether more people are driving at or below the posted speed limit of 7 mph or driving above the posted speed limit: Find the total number of cars traveling at or below the posted speed limit by adding the numbers traveling at 66 7 mph (3,717, mph (2,98, and less than 61 mph (2,87. Find the total number of cars driving above the posted speed limit by adding the numbers traveling mph (3,651, 76 8 mph (2,53, and more than 8 mph (1,78. Compare the two sums. Solution 3, ,98 + 2,87 = 9,571 3, ,53 + 1,78 = 7,862 9,571 > 7,862 More cars were traveling at or below the posted speed limit. Critical Thinking If you roll two ordinary dice, the possible sums are the numbers 2 (rolling two 1 s through 12 (rolling two 6 s. Therefore there are 11 different sums possible. (The numbers 2, 3,, 5, 6, 7, 8, 9, 1, 11, and a. Substituting any whole number for a in a = a will result in a true equation. The statement is always true. Section 1.3 b. Substituting any whole number for a in a a = will result in a true equation. The statement is always true. Objective A Exercises 1. Students should note that there are five 6's. Therefore, the addition can be written as 5 times 6: a. ; 12; 2; b. 2; 6; 6; 1; 7 c ,92 3 3, , 3 6,7 7 2, , , , , ,32, = 2, = 1, 21. f g = fg

8 8 Chapter 1: Whole Numbers 23. 3, , 3, = 1,2,653 3, = 1,2, , 26 29, 3 39,26 29 = 1,138,13, 3 = 1,2, = 6, = 2, 29. 8, , 7 8, = 6,91,166 9, 7 = 6,3, 31. ab = 1, a 7 65 = 3, xyz = 6 3 = 1, xy = = 3, For example, 5 and 2 1. The Multiplication Property of One 3. The Commutative Property of Multiplication = = 9. x = 2 6 ( 2 2 = 2 Yes, 6 is a solution of the equation x = = 3z 96 3( No, 23 is not a solution of the equation 96 = 3z y = ( = 38 Yes, 19 is a solution of the equation 2y = 38. Objective B Exercises 55. a. 3; b. 3; 3; 3; 3; = = c c = c x x x y y y = x 3 y = = =1,, = ( ( 5 5= 8 25 = = ( = 9 1, = 9, ( = ( ( 6 6 = 36 = = ( = 5 27 = 2 27 = = = 1 ( = = 6 8 = a 83. x 3 y = ( = 8 3 = ab 6 ( = = 5 6 = c 2 d = ( 3 3 ( 5 5 = 9 25 = a. 6 2; 12 b. 6 2 ; 6

9 Section Objective C Exercises ; , r , r , r , , , , r r , r , r , c d , 72, ,72 7 = 776, 5 = , 8 76, 8 389,8 76 = 5,129, 8 = 5, , 98 79, 8 38,98 79 = 93 r37, 8 = , 219 3, 2 332, 219 = 1,516 3, 2 = 1,5

10 1 Chapter 1: Whole Numbers x y 8 1 = 8 x y 79 is undefined, because division by zero is undefined. x y 39,2 9,8 39, z = = Yes, 9 is a solution of the equation = x No, 9 is not a solution of the equation. Objective D Exercises 133. factors; 1; 3; 5; = = = 2 The factors of 1 are 1, 2, 5, and = = = 12 = 3 The factors of 12 are 1, 2, 3,, 6, and = = 8 = 2 The factors of 8 are 1, 2,, and is prime number. The factors of 13 are 1 and = = = = 3 The factors of 18 are 1, 2, 3, 6, 9, and = = 5 The factors of 25 are 1, 5, and = = = = = 7 The factors of 56 are 1, 2,, 7, 8, 1, 28, and = = 1 2 = = The factors of 28 are 1, 2,, 7, 1, and = = = 16 8 = = = 6 The factors of 8 are 1, 2, 3,, 6, 8, 12, 16, 2, and = = = = = 6 The factors of 5 are 1, 2, 3, 6, 9, 18, 27, and = = = = 2 2 3

11 Section = = = is a prime number = = = = = = 2 23 Objective E Exercises 175. division 177. Strategy To find the number of calories, multiply the number of calories in one ounce of cheese (115 by the number of ounces (. Solution 115 = 6 Four ounces of cheese contain 6 calories Strategy To find the amount of jet fuel used, multiply the amount of fuel used each hour (865 by the time of flight (5. Solution =,325 The flight used,325 gal of jet fuel Strategy a. To determine the perimeter of a rectangle, substitute 2 for L and 15 for W in the formula below. b. To determine the area of a rectangle, substitute 2 for L and 15 for W in the formula below. Solution a. P = 2L + 2W P = = 78 The perimeter of the rectangle is 78 m. b. A = LW A = 2 15 = 36 The area of the rectangle is 36 m Strategy To find the area of the patio, substitute 9 for s in the area formula below. Solution A = s 2 = 9 2 = 81 The area of the patio is 81 ft Strategy To find the estimate of the total cost: Round the number of suits to hundreds and the cost of each suit to tens. Multiply the rounded numbers. Solution = 16, The total cost of the suits is approximately $16, Strategy To find the total amount paid, replace M by 285 and N by 2 in the given formula and solve for A. Solution A = MN A = = 6,8 The total amount paid on the loan is $6, Strategy To find the time to drive the distance, replace d by 513 and r by 57 in the given formula and solve for t. Solution t = d r t = = 9 It takes 9 h to drive 513 mi.

12 12 Chapter 1: Whole Numbers 191. Strategy To find the value per share, replace C by 1,5, and S by 5, in the given formula and solve for V. Solution V = C S V = 1,5, 5, V = 21 The stock has a value of $21 per share. Critical Thinking There are 7 days in one week. There are 52 weeks in one year = 36 days. There are 36 days in 52 weeks. There are 365 days in one year (366 days in a leap year. 52 weeks in one year is an approximation We need to find the smallest three-digit multiple of 6 that is a palindromic number. The smallest three digit palindromic number is 11; the next is 121; the next is 131. Any three-digit palindromic number that has a 1 in the hundreds place must have a 1 in the ones place. No number that has a 1 in the one s place is divisible by 6. The smallest three-digit palindromic number with a 2 in the hundreds place is 22, which is not divisible by 6. The next smallest is 212, which is not divisible by is the smallest three-digit multiple of 6 that is a palindromic number. Section 1. Objective A Exercises 1. 5; x + 9 = 23 x = 23 9 x + = 1 x = 1 The solution is b = b = b = 25 b = 25 The solution is m = 15 3m 3 = m = 5 m = 5 The solution is = c 52 = c 13 = 1c 13 = c The solution is = w = w = w + 7 = w The solution is = 19 + p = p 9 = + p 9 = p The solution is y = 8 1y 1 = 8 1 1y = 8 y = 8 The solution is = 1d 1 1 = 1d 1 1 = 1d 1 = d The solution is b + 7 = 7 b = 7 7 b + = b = The solution is t = t = t = 76 t = 76 The solution is 76. Objective B Exercises 23. n + 8 = 13

13 Section The unknown number: n sixteen added to a number is equal to forty n + 16 = n = 16 n = 2 The number is The unknown number: n five times a number 5n = 3 5n 5 = 3 5 n = 6 The number is 6. is thirty 29. The unknown number: n fifteen is three more than a number 15 = n = n = n The number is Strategy To find the width of the rectangle, write and solve an equation using w to represent the width. Solution the width of a rectangle is 5 in. more than the length 17 = w = w = w The width of the rectangle is 12 in. 33. Strategy To find the distance from Forth Worth to Austin, write and solve an equation using x to represent the distance from Forth Worth to Austin. Solution the distance from Galveston to Austin is 22 miles more than the distance from Forth Worth to Austin 212 = x = x = x The distance from Forth Worth to Austin is 19 mi. 35. Strategy To find the number of payments, replace A by 17,6 and M by 85 in the given formula and solve for N. Solution A = MN 17,6 = 85N 17,6 85 = 85N = N The number of payments is 36.

14 1 Chapter 1: Whole Numbers 37. Strategy To find the time, replace d by 825 and r by 165 in the given formula and solve for t. Solution d = rt 825 = 165t = 165t = t It would take 5 h to travel 825 mi at a speed of 165 mph. Section 1.5 Objective A Exercises 1. to multiply 7 times = = = = =16 3 = (6 3 + = = 15 + = ( = = = ( = = = = = = = = 1 + = (8 5 3 = = = ( 6= = 8 + = = 2 ( = = = = 186 ( (7 = = ( = 6(5 12 = 3 12 = (13 5 = 16 8 = 16 2 = = = = 18 = x 2y = 8 6 = x 2 + 3y = = = x 2 + y x = = + = 8 ( x + x y 8 + ( = = = = x 2 + 3( x y+ z ( = = = = = (8 + 6 = = = (9 5 3= = = 2 Since 2 > 13, 12 + (9 5 3 > 11 + ( ( (7 3 1

15 Chapter Review 15 Critical Thinking ( ( = 15 + (8 3(16 = 15 + (5(16 = = 95 We are looking for the smallest prime number greater than is not prime (for example, it is divisible by is prime. 97 is the smallest prime number greater than ( ( Chapter Review = 1, 3.,27 1,62 2, = ,389 Given place value 6. 38,729 2 < 5 38,729 rounded to the nearest hundred is 38, > , xy = 1 7 = , , ,7 2,359, , = = = = 5 The factors of 5 are 1, 2, 5, 1, 25, and y = = 17 Yes, 7 is a solution of the equation ( = = = = = The Commutative Property of Addition 17. four million nine hundred twenty-seven thousand thirty-six x y 3 5 = = = 675 ( ( 19. Strategy a. To determine by many times more PG- 13 films were released than NC-17 films: Find the number of PG-13 films (112 and the number of NC-17 films (7 from the pie chart. Divide the number of PG-13 films by the number of NC-17 films. b. To determine by many times more R rated films were released than NC-17 films: Find the number of R rated films (27 and the number of NC-17 films (7 from the pie chart. Divide the number of R rated films by the number of NC-17 films. Solution a = There were 16 times more PG-13 films released than NC-17 films. b = There were 61 times more R rated films released than NC-17 films.

16 16 Chapter 1: Whole Numbers 67 r , , x y = = = x y 8 6 = = = x 36 = x 9 = x The solution is x + y = (a + b 2 2c = 6 2 = 6 8 = 56 ( 2 2 = Strategy To find the person with the greater number of rebounds, compare the numbers 17, and 16,279. Solution 17, > 16,279 Kareem Abdul-Jabbar had more rebounds. 31. Strategy To find the total cost, multiply the number of square feet of floor space (2,8 by the cost per square feet (65. Solution 2,8 65 = 182, The total cost of the contractor s work will be $182,. 32. Strategy a. To find the perimeter of the rectangle, substitute 25 for L and 12 for W in the formula below. b. To find the area of the rectangle, substitute 25 for L and 12 for W in the formula below. Solution a. P = 2L + 2W P = P = P = 7 The perimeter is 7 m. b. A = LW A = = 3 The area is 3 m Strategy To determine between which decade the number of students enrolled in college increased the most, and the amount of increase, find the amount of increase for each decade. Then compare the numbers. Solution 196 to 197: 8,581, 3,789, =,792, 197 to 198: 12,97, 8,581, = 3,516, 198 to 199: 13,819, 12,97, = 1,722, 199 to 2: 1,889, 13,819, = 1,7,,792, > 3,516, > 1,722, > 1,7, a. The number of students enrolled in college increased the most from 196 to 197. b. The amount of increase was,792, people.

17 Cumulative Review Strategy To find the distance traveled, substitute 3 for t and 1 for r in the given formula and solve for d. Solution d = rt d = 1 3 d = 2 The cyclist traveled 2 mi. 35. Strategy To find the markup, substitute 2,22 for S and 1,775 for C in the given formula and solve for M. Solution M = S C M = 2,22 1,775 M = 9 The markup on the copy machine is $9. Chapter Test 1. 3,297 1 = 329, = 16, 3.,92 873,29. x x x x y y y = x y = p = p = p Yes Given place value 6. 2,961 6 > 5 2,961 rounded to the nearest hundred is 3,. 7. 7,177 < 7, ,9 9. three hundred eighty-two thousand nine hundred four ,36 1, , , ,79, 5 6, 6 = 2,, = = 6 92 = = The factors of 92 are 1, 2,, 23, 6, = = x y 39,21 8,375 = 3, The Commutative Property of Addition 17. x y 3,588 = ( = = 27 1 = = $ = 17 + d 6 17 = 17 + d = d The solution is = t 176 t = t = The solution is x + (x y (8 2 = + 2 = + 16 = 56 The solution is 56.

18 18 Chapter 1: Whole Numbers x = x 12 = 9 12 x = 78 The number is = Strategy First, to find the total cost of the computer system, add the prices of the components. Then, to find the balance of the checking account, subtract the total cost of the computer system from $2,276. Solution = 172 2, = 556 The balance is $ Strategy a. To find the perimeter of the square, substitute 2 for s in the formula below. b. To find the area of the square, substitute 2 for s in the formula below. Solution a. P = s P = 2 = 96 The perimeter is 96 cm. b. A = s 2 A = (2 2 = 576 The area is 576 cm Strategy To find the data processor s take home pay, subtract the sum of his deductions, taxes (85, retirement (272, and insurance (18, from the total salary (5,69. Solution 5,69 ( = 5,69 1,23 =,56 The data processor s take home pay is $, Strategy a. To determine between which two years the number of hybrids sold increased the most, for year there was an increase, find the increase. Then compare the numbers. b. The amount of increase is the largest amount. Solution 21 to 22 35, 2,287 = 1, to 23 7,525 35, = 12, to 2 88, 7,525 =,75 2 to 25 25,79 88, = 117,79 117,79 >,75 > 1,713 > 12,525 a. The number of hybrids sold increased the most from 2 to 25. b. The amount of increase was 117,79 hybrids. 3. Strategy To find the commission earned, substitute 2 for U and 8 for R in the given formula and solve for C. Solution C = U R = 2 8 = 96 The commission earned is $ Strategy To find the value per share of the fund, substitute 5,5, for C and 5, for S in the given formula and solve for V. C 5,5, Solution V = = = 11 S 5, The value per share is $11.