Built-In Workbooks. Skills. Reference. Prerequisite Skills Extra Practice Mixed Problem Solving

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(1)Built-In Workbooks Prerequisite Skills . . . . . . . . . . . . . . . . . . . . . . . . . . 600 Extra Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616 Mixed Problem Solving . . . . . . . . . . . . . . . . . . . . 648 Preparing for Standardized Tests . . . . . . . . . . . . 660. Skills Trigonometry The Tangent Ratio . . . . . . . . . . . . . . . . . . . . . 678 The Sine and Cosine Ratios . . . . . . . . . . . . . . 681 Table of Trigonometric Ratios . . . . . . . . . . . . 685 Measurement Conversion Converting Measures of Area and Volume . . . 686 Converting Between Measurement Systems . . 689. Reference English-Spanish Glossary . . . . . . . . . . . . . . . . . . . . 692 Selected Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . 719 Photo Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744 Formulas and Symbols . . . . . . . . . . . Inside Back Cover How To Cover Your Book . . . . . . . . . . . Inside Back Cover. 598 Peter Read Miller/Sports Illustrated.

(2) A Student Handbook is the additional skill and reference material found at the end of books. The Student Handbook can help answer these questions.. What If I Forget What I Learned Last Year? Use the Prerequisite Skills section to refresh your memory about things you have learned in other math classes. 1 Estimation Strategies 2 Displaying Data on Graphs 3 Converting Measurements within the Customary System 4 Converting Measurements within the Metric System 5 Divisibility Patterns 6 Prime Factorization 7 Greastest Common Factor 8 Simplifying Fractions 9 Least Common Multiple 10 Perimeter and Area of Rectangles 11 Plotting Points on a Coordinate Plane 12 Measuring and Drawing Angles. What If I Need More Practice? The Extra Practice section provides additional problems for each lesson. What If I Have Trouble with Word Problems? The Mixed Problem Solving pages provide additional word problems that use the skills in each chapter. What If I Need Help on Taking Tests? The Preparing for Standardized Tests section gives you tips and practice on how to answer different types of questions that appear on tests.. What If I Need Practice in Trigonometry and Measurement Conversion? The Trigonometry section gives you more instruction and practice on the sine, cosine, and tangent ratios. The Measurement Conversion section gives instruction and practice on converting measures between the metric and customary systems. What If I Forget a Vocabulary Word? The English-Spanish Glossary provides a list of important, or difficult, words used throughout the textbook. It provides a definition in English and Spanish as well as the page number(s) where the word can be found. What If I Need to Check a Homework Answer? The answers to the odd-numbered problems are included in Selected Answers. Check your answers to make sure you understand how to solve all of the assigned problems. What If I Need to Find Something Quickly? The Index alphabetically lists the subjects covered throughout the entire textbook and the pages on which each subject can be found. What If I Forget a Formula? Inside the back cover of your math book is a list of Formulas and Symbols that are used in the book. Student Handbook. 599.

(3) Prerequisite Skills. Prerequisite Skills Estimation Strategies Sometimes you do not need to know the exact answer to a problem, or you may want to check the reasonableness of an answer. In those instances, you can use estimation . There are several different methods of estimation. A common method is to use rounding .. Estimate by Rounding Estimate by rounding. 1 5. 2 3. 189.2 ⫻ 315.6. 453ᎏᎏ ⫹ 68ᎏᎏ. Round each number to the nearest hundred. Then multiply.. Round each number to the nearest ten. Then add.. →. 189.2 315.6. →. 1 5 2 68 3. 453. 200 300 60,000. The product is about 60,000.. → →. 450 70 520. The sum is about 520. You can use clustering to estimate sums. Clustering works best with numbers that all round to approximately the same number.. Estimate by Clustering Estimate by clustering. 1 4. 2 5. 5 6. 3 8. 13ᎏᎏ ⫹ 16ᎏᎏ ⫹ 14ᎏᎏ ⫹ 15ᎏᎏ. 99.6 ⫹ 97.83 ⫹ 102.18 ⫹ 100.101 ⫹ 99.90. All of the numbers are close to 15. There are four numbers.. All of the numbers are close to 100. There are five numbers.. The sum is about 4 15 or 60.. The sum is about 5 100 or 500.. Compatible numbers are numbers that are easy to compute with mentally.. Estimate by Using Compatible Numbers Estimate by using compatible numbers. 76.36 ⫼ 24.73 76.36 is close to 75, and 24.73 is close to 25. 3 24.7376.3 6 257 5 The quotient is about 3. 600 Prerequisite Skills. 3 8. 2 3 3 2 1 The fractions and are close to . 8 3 2 1 1 1 1 7 12 20 (7 12 20) 2 2 2 2. 7ᎏᎏ ⫹ 12 ⫹ 20ᎏᎏ. . 39 1 or 40 The sum is about 40.. .

(4) Prerequisite Skills. A strategy that works well for some addition and subtraction problems is front-end estimation . This strategy involves adding or subtracting the left-most column of digits. Then, add or subtract the next column of digits. Annex zeros for the remaining digits.. Use Front-End Estimation Use front-end estimation to find an estimate. 5,283 ⫹ 3,634 5,283 3,634 8. 118.1 ⫺ 57.5 5,283 3,634 8,800. →. 118.1 57.5 6. The sum is about 8,800.. →. 118.1 57.5 61.0. The difference is about 61.. Exercises Estimate by rounding. 1 3. 3 4. 1. 42 59. 2. 78.26 90.1 18.5. 4. 51.68 72.31. 5. 18 32 53. 3 4. 2 3. 1 8. 3. 425 10. 2 5. 6. 96.88 31.98. Estimate by clustering. 1 3. 7. 19.9 17.63 21.45 20.17 18.75. 1 2. 2 3. 2 5. 3 4. 8. 353 349 347 351. 3 5. 9. 74 72 77 76. 10. 3.12 2.75 2.89 3.25 2.9 3.05. Estimate by using compatible numbers. 2 3. 1 2. 11. 105 26. 3 5. 1 2. 14. 2 7 15. 2 5. 1 3. 12. 69.3 34.5. 13. 85 14. 15. 85.1 22.3. 16. 12.4 19 35.6. Estimate by using front-end estimation. 17. 109.67 25.88. 5 8. 1 3. 18. 4,456 8,703. 3 7. 20. 34 56 62. 3 8. 1 2. 19. 625.28 400.35. 21. 99 15. 22. 628 547 432. 23. 752.6 50.1. 24. 69.5 32. 25. 88 2. 26. 99.6 18.25. 27. 700.45 2.1. 28. 1,065.6 200.8. 29. 390 52. 30. 9.5 2.3. 31. 77 55. 32. 1,208.85 399.1. 33. 80 9. Use any method to estimate.. 1 5. 1 3. 2 3. 1 3. 3 8. 2 3. 34. 1,715.3 1,399.9. 35. MONEY MATTERS At an arts and crafts festival, Lena selected items. priced at $5.98, $7.25, $3.25, $8.75, $9.85, $2.50, and $7.25. She has $50 in cash. How could she use estimation to see if she can use cash or if she needs to write a check? Prerequisite Skills. 601.

(5) Statistics involves collecting, analyzing, and presenting information, called data . Graphs display data to help readers make sense of the information.. • Bar graphs are used to compare the. • Double bar graphs compare two sets of. frequency of data. The bar graph below compares the average number of vacation days given by countries to their workers.. data. The double bar graph below shows the percent of men and women 65 and older who held jobs in various years. Older Workers Number of People. 45 40 35 30 25 20 15 10 5 0. 35 30 25 20 15 10 5 0. Men Women. 60 70 80 90 00 19 19 19 19 20 Year. Ita ly Fra nc e Ca na da Jap an Un i Sta ted tes. Average Number of Days (Per Year). Vacation Time. Source: The World Almanac. Source: The World Almanac. • Line graphs usually show how values. • Double line graphs , like double bar graphs,. change over time. The line graph below shows the number of people per square mile in the U.S. from 1800 through 2000.. show two sets of data. The double line graph below compares the amount of money spent by both domestic and foreign U.S. travelers.. U.S. Population Density 90 80 70 60 50 40 30 20 10 0. Tourism in U.S. Billions of Dollars Spent. People per Square Mile. Prerequisite Skills. Displaying Data in Graphs. 79.6 21.5 6.1. 1800 1850 1900 1950 2000. Year. 500 450 400 350 300 250 200 150 100 50 0. Domestic travelers Foreign travelers. ’97. ’98. ’99. Year Source: The World Almanac Source: The World Almanac. • Stem-and-leaf plots are a system used to condense a set of data where the greatest place value of the data is used for the stems and the next greatest place value forms the leaves . Each data value can be seen in this type of graph. The stem-and-leaf plot below contains this list of mathematics test scores: 95 76 64 88 93 68 99 96 74 75 92 80 76 85 91 70 62 81 The least number has 6 in the tens place. The greatest number has 9 in the tens place. The stems are 6, 7, 8, and 9. The leaves are ordered from least to greatest. 602 Prerequisite Skills. Stem 6 7 8 9. Leaf 2 4 8 0 4 5 6 6 0 1 5 8 1 2 3 5 6 9 6 | 2 62. ’00. ’01.

(6) Choose a Display Prerequisite Skills. Shonny is writing a research paper about the Olympics for her social studies class. She wants to include a graph that shows how the times in the 400-meter run have changed over time. Should she use a line graph, bar graph, or stem-and-leaf plot? Since the data would show how the times have changed over a period of time, she should choose a line graph.. Exercises Determine whether a bar graph, double bar graph, line graph, double line graph, or stem-and-leaf plot is the best way to display each of the following sets of data. Explain your reasoning. 1. how the income of households has changed from 1950 through 2000 2. the income of an average household in six different countries 3. the prices for a loaf of bread in twenty different supermarkets 4. the number of boys and the number of girls participating in six different. school sports Refer to the bar graph, double bar graph, line graph, double line graph, and stem-and-leaf plot on page 602. 5. Write several sentences to describe the data shown in the graph titled. “Vacation Time.” Include a comparison of the days worked for Canada and the U.S. 6. Write several sentences to describe the data shown in the graph titled. “Older Workers.” What other type or types of graphs could you use to display this data? Explain your reasoning. 7. Write several sentences to describe the data shown in the graph titled. “Tourism in U.S.” What other type or types of graphs could you use to display this data? Explain your reasoning. 8. Write several sentences to describe the data shown in the graph titled. “U.S. Population Density.” What other type or types of graphs could you use to display this data? Explain your reasoning. 9. Write several sentences to describe the data shown in the stem-and-leaf. plot of mathematics test scores. What is an advantage of showing the scores in this type of graph? For Exercises 10–14, use the stem-and-leaf plot at the right that shows the number of stories in the tallest buildings in Dallas, Texas. 10. How many buildings does the stem-and-leaf plot represent? 11. How many stories are there for the shortest building in the. stem-and-leaf plot? the tallest building? 12. What is the median number of stories for these buildings? 13. What is the mean number of stories for these buildings?. Stem 2 3 4 5 6 7. Leaf 7 9 9 0 1 1 1 3 3 4 4 6 6 7 0 2 2 5 9 0 0 0 0 2 5 6 8 0 2 2 | 7 27. 14. Explain how the stem-and-leaf plot is useful in displaying the data. Prerequisite Skills. 603.

(7) Prerequisite Skills. Converting Measurements within the Customary System The units of length in the customary system are inch, foot, yard, and mile. The table shows the relationships among these units.. Customary Units of Length 1 mile (mi) 5,280 feet 1 foot (ft) 12 inches (in.) 1 yard (yd) 3 feet. • To convert from larger units to smaller units, multiply. • To convert from smaller units to larger units, divide. Smaller Units. Larger Units. Smaller Units. 7 ft 7 12 84 in.. Larger Units. 108 in. 108 12 9 ft. 4 mi 4 5,280 21,120 ft. 15 ft 15 3 5 yd. There will be a greater number of smaller units than larger units.. There will be fewer larger units than smaller units.. Convert Customary Units of Length Complete each sentence. 8 yd ⫽ ? ft. 144 in. ⫽. 8 yd (8 3) ft. 144 in. (144 12) ft. 7.5 mi (7.5 5,280) ft. 24 ft. 12 ft. 39,600 ft. ?. 7.5 mi ⫽. ft. The units of weight in the customary system are ounce, pound, and ton. The table at the right shows the relationships among these units. As with units of length, to convert from larger units to smaller units, multiply. To convert from smaller units to larger units, divide.. ?. ft. Customary Units of Weight 1 pound (lb) 16 ounces (oz) 1 ton (T) 2,000 pounds. Convert Customary Units of Weight Complete each sentence. 12,400 lb ⫽ ? T. 92 oz ⫽. 12,400 lb 12,400 2,000 or 6.2 T. 92 oz 92 16 or 5.75 lb. ?. lb. Capacity is the amount of liquid or dry substance a container can hold. Customary units of capacity are fluid ounces, cup, pint, quart, and gallon. The relationships among these units are shown in the table.. Customary Units of Capacity 1 cup (c) 8 fluid ounces (fl oz) 1 pint (pt) 2 cups 1 quart (qt) 2 pints 1 gallon (gal) 4 quarts. Convert Customary Units of Capacity Complete each sentence. 64 fl oz ⫽ ? c. 4.4 gal ⫽. 64 fl oz 64 8 or 8 c. 4.4 gal 4.4 4 or 17.6 qt. 604 Prerequisite Skills. ?. qt.

(8) Convert Customary Units Using Two Steps ?. Prerequisite Skills. 12 pt ⫽. gal. 12 pt (12 2) qt First, change pints. 6 qt (6 4) gal. to quarts.. 6 qt. 1.5 gal. Then, change quarts to gallons.. So, 12 pints 1.5 gallons.. Units of time can also be converted. The table shows the relationships between these units. Units of Time 60 seconds (s) 1 minute (min) 60 minutes 1 hour (h) 24 hours 1 day. 7 days 1 week 52 weeks 1 year 365 days 1 year. Convert Units of Time Complete each sentence. 84 h ⫽ ? days. 5 weeks ⫽. 84 h 84 24 or 3.5 days. 5 weeks 5 7 or 35 days. ?. days. Adding Mixed Measures Find the sum of 4 feet 7 inches and 5 feet 10 inches. Simplify. 4 ft 7 in. 5 ft 10 in. 9 ft 17 in. 9 ft (12 in. 5 in.) 10 ft 5 in.. Line up like units and add. Separate 17 in. into 12 in. and 5 in. Replace 12 in. with 1 ft and add like units.. Exercises Complete each sentence. 1. 2 mi ? ft 4. 8.5 T 7. 150 ft . ?. lb. ?. yd ? days. 10. 20 weeks 13. 5 T 16. 10 pt . ?. oz ?. gal 19. 14,080 yd ? mi. ?. 2. 48 oz . ?. 5. 5 days 8. 5 gal . 3. 120 min . ?. h. 6. 63,360 ft . ?. mi. qt. 9. 128 fl oz . ?. c. lb h. ?. 11. 24 c . ?. gal. 12. 190,080 in. . 14. 36 h . ?. days. 15. 12 oz . 17. 1 mi . ?. yd ? weeks. 18. 12 gal . ?. c. 21. 1 day . ?. s. 20. 49 days . ?. ?. mi. lb. Find each sum. 22.. 15 ft 2 in. 32 ft 7 in.. 23.. 5 gal 1 qt 10 gal 2 qt. 24.. 12 h 15 min 27 h 55 min. 25.. 45 lb 14 oz 62 lb 12 oz. 26.. 4 yd 2 ft 16 yd 1 ft. 27.. 12 days 7 h 44 days 20 h Prerequisite Skills. 605.

(9) Prerequisite Skills. Converting Measurements within the Metric System All units of length in the metric system are defined in terms of the meter (m). The diagram below shows the relationships between some common metric units. 1,000. kilometer km. 100. meter m. 10. centimeter cm. 1,000. 100. Comparing Metric and Customary Units of Length. millimeter mm. 1 mm 0.04 inch (height of a comma) 1 cm 0.4 inch (half the width of a penny) 1 m 1.1 yards (width of a doorway) 1 km 0.6 mile (length of a city block). 10. • To convert from larger units to smaller units, multiply. • To convert from smaller units to larger units, divide. Converting From Larger Units to Smaller Units There will be a greater number of smaller units than larger units.. Converting From Smaller Units to Larger Units. 1 km 1 1,000 1,000 m 1 m 1 100 100 cm 1 cm 1 10 10 mm. 1 mm 1 10 0.1 cm 1 cm 1 100 0.01 m 1 m 1 1,000 0.001 km. There will be fewer larger units than smaller units.. Convert Metric Units of Length Complete each sentence. 7 km ⫽ ? m. 123 cm ⫽. 7 km (7 1,000) m. 123 cm (123 100) m. 38.9 cm (38.9 10) mm. 7,000 m. 1.23 m. 389 mm. ?. 38.9 cm ⫽. m. ?. mm. The basic unit of capacity in the metric system is the liter (L). A liter and milliliter (mL) are related in a manner similar to meter and millimeter. 1,000. Comparing Metric and Customary Units of Capacity. 1 L 1,000 mL. 1 mL 0.03 ounce (drop of water) 1 L 1 quart (bottle of ketchup). 1,000. Convert Metric Units of Capacity Complete each sentence. 14.5 L ⫽ ? mL. 750 mL ⫽. 14.5 L 14.5 1,000 or 14,500 mL. 750 mL 750 1,000 or 0.75 L. ?. The mass of an object is the amount of matter that it contains. The basic unit of mass in the metric system is the kilogram (kg). Kilogram, gram (g), and milligram (mg) are related in a manner similar to kilometer, meter, and millimeter. 1 kg 1,000 g 606 Prerequisite Skills. 1 g 1,000 mg. L. Comparing Metric and Customary Units of Mass 1 g 0.04 ounce (one raisin) 1 kg 2.2 pounds (six medium apples).

(10) Convert Metric Units of Mass 4,500 g ⫽. 53 kg 53 1,000 or 53,000 g. 4,500 g 4,500 1,000 or 4.5 kg. ?. Prerequisite Skills. Complete each sentence. 53 kg ⫽ ? g. kg. Sometimes you need to perform more than one conversion to get the desired unit.. Convert Metric Units Using Two Steps Complete each sentence. 35,000 cm ⫽ ? km. ?. 4.5 kg ⫽. mg. 35,000 cm 35,000 100 m. 4.5 kg 4.5 1,000 g. 350 m. 4,500 g. 350 m 350 1,000 km. 4,500 g 4,500 1,000 mg. 0.35 km. 4,500,000 mg. So, 35,000 cm 0.35 km.. So, 4.5 kg 4,500,000 mg.. Exercises State which metric unit you would probably use to measure each item. 1. mass of an elephant. 2. amount of juice in a pitcher. 3. length of a room. 4. distance across a state. 5. mass of a small stone. 6. length of a paper clip. 7. height of a large tree. 8. amount of water in a medicine dropper. 9. width of a sheet of paper. 10. diameter of the head of a pin. 11. mass of a truck. 12. cruising altitude of a passenger jet. Complete each sentence. 13. 45 mm ? cm 16. 7 L . ?. 19. 25 kg . ?. 22. 8.25 kg 25. 79 m . g g. ?. km 28. 82,500 cm ? km 31. 8 L ? mL 34. 0.625 km . ?. m. 20. 450 cm . ?. 23. 655 mL . ?. 29. 5 km . ?. 32. 72.6 cm . mm m. cm ? mm. 35. 425,000 mg . 21. 6.4 m . kg. km m. ?. cm ?. 24. 982 cm . L. ?. ?. 18. 10 km . g. ?. 26. 4,000 mm . ?. 15. 5,000 m . kg ?. 17. 8,000 mg . mL ?. ?. 14. 2,500 g . 27. 60,000 mg . m ? kg. 30. 12 kg . ?. mg. 33. 0.45 L . ?. mL. 36. 1 km . ?. mm. 37. RACES Priscilla is running a five-kilometer race. How many meters long. is the race? 38. MEDICINE A large container of medicine contains 0.5 liter of the drug.. How many 25-milliliter doses of the drug are in this container? Prerequisite Skills. 607.

(11) Prerequisite Skills. Divisibility Patterns If a number is a factor of a given number, you can also say the given number is divisible by the factor. For example, 144 is divisible by 9 since 144 9 16, a whole number. A number n is a factor of a number m if m is divisible by n. A number is divisible by:. • • • • • • •. 2 if the ones digit is divisible by 2. 3 if the sum of the digits is divisible by 3. 4 if the number formed by the last two digits is divisible by 4. 5 if the ones digit is 0 or 5. 6 if the number is divisible by both 2 and 3. 8 if the number formed by the last three digits is divisible by 8. 9 if the sum of the digits is divisible by 9.. • 10 if the ones digit is 0.. Use Divisibility Rules Determine whether 2,418 is divisible by 2, 3, 4, 5, 6, 8, 9, or 10. 2: Yes; the ones digit, 8, is divisible by 2. 3: Yes; the sum of the digits, 2 4 1 8 15, is divisible by 3. 4: No; the number formed by the last two digits, 18, is not divisible by 4. 5: No; the ones digit is not 0 or 5. 6: Yes; the number is divisible by 2 and 3. 8: No; 418 is not divisible by 8. 9: No; the sum of the digits, 15, is not divisible by 9. 10: No; the ones digit is not 0. So, 2,418 is divisible by 2, 3, and 6, but not by 4, 5, 8, 9, or 10.. Exercises Determine whether each number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10. 1. 48. 2. 153. 3. 2,470. 4. 56. 5. 165. 6. 323. 7. 918. 8. 1,700. 9. 2,865 13. 199. 10. 12,357. 11. 16,084. 12. 50,070. 14. 999. 15. 808,080. 16. 117. 17. Is 3 a factor of 777?. 18. Is 5 a factor of 232?. 19. Is 6 a factor of 198?. 20. Is 795 divisible by 10?. 21. Is 989 divisible by 9?. 22. Is 2,348 divisible by 4?. 23. The number 87a,46b is divisible by 6. What are possible values of a and b? 24. FLAGS Each star in the U.S. flag represents a state. If another state joins. the Union, could the stars be arranged in a rectangular array? Explain. 608 Prerequisite Skills.

(12) Prime Factorization Prerequisite Skills. When a whole number greater than 1 has exactly two factors, 1 and itself, it is called a prime number . When a whole number greater than 1 has more than two factors, it is called a composite number . The numbers 0 and 1 are neither prime nor composite. Notice that 0 has an endless number of factors and 1 has only one factor, itself.. Identify Numbers as Prime or Composite Determine whether each number is prime, composite, or neither. 33. 59. The numbers 1, 3, and 11 divide into 33 evenly. So, 33 is composite.. The only numbers that divide evenly into 59 are 1 and 59. So, 59 is prime.. When a number is expressed as a product of factors that are all prime, the expression is called the prime factorization of the number. A factor tree is useful in finding the prime factorization of a number.. Write Prime Factorization Use a factor tree to write the prime factorization of 60. You can begin a factor tree for 60 in several ways. 60. 60. 60. 2 30. 3 20. 6 10. 2 5 6. 3 4 5. 2 5 2 3. 3 2 2 5. 2 3 2 5. Notice that the bottom row of “branches” in every factor tree is the same except for the order in which the factors are written. So, 60 2 2 3 5 or 22 3 5. Every number has a unique set of prime factors. This property of numbers is called the Fundamental Theorem of Arithmetic .. Exercises Determine whether each number is prime, composite, or neither. 1. 45. 2. 23. 3. 1. 4. 13. 5. 27. 6. 96. 7. 37. 8. 0. 9. 177. 10. 233. 11. 507. 12. 511. Write the prime factorization of each number. 13. 20. 14. 49. 15. 225. 16. 32. 17. 25. 18. 36. 19. 51. 20. 75. 21. 80. 22. 117. 23. 72. 24. 4,900 Prerequisite Skills. 609.

(13) Prerequisite Skills. Greatest Common Factor The greatest of the factors common to two or more numbers is called the greatest common factor (GCF) of the numbers. One way to find the GCF is to list the factors of the numbers.. Find the GCF Find the greatest common factor of 36 and 60. Method 1 List the factors.. factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Common factors of 36 and 60: 1, 2, 3, 4, 6, 12. The greatest common factor of 36 and 60 is 12. Method 2 Use prime factorization.. 36 2 2 3 3 60 2 2 3 5. Common prime factors of 36 and 60: 2, 2, 3. The GCF is 2 2 3 or 12.. Find the GCF Find the greatest common factor of 54, 81, and 90. Use a factor tree to find the prime factorization of each number. 54. 81. 90. 6 9. 9 9. 9 10. 2 3 3 3. 3 3 3 3. 3 3 2 5. The common prime factors of 54, 81, and 90 are 3 and 3. The GCF of 54, 81, and 90 is 3 3 or 9.. Exercises Find the GCF of each set of numbers. 1. 45, 20. 2. 27, 54. 3. 24, 48. 4. 63, 84. 5. 40, 60. 6. 32, 48. 7. 30, 42. 8. 54, 72. 9. 36, 144. 10. 3, 51. 11. 24, 36, 42. 12. 35, 49, 84. 13. DESIGN Suppose you are tiling a tabletop with 6-inch square tiles. How. many of these squares will be needed to cover a 30-inch by 24-inch table? 14. SHELVING Emil is cutting a 72-inch-long board and a 54-inch-long board. to make shelves. He wants the shelves to be the same length while not wasting any wood. What is the longest possible length of the shelves? Two or more numbers are relatively prime if their greatest common factor is 1. Determine whether each set of numbers is relatively prime. 15. 9, 19. 610 Prerequisite Skills. 16. 7, 21. 17. 3, 51. 18. 4, 28, 31.

(14) Simplifying Fractions Prerequisite Skills. Fractions, mixed numbers, decimals, and integers are examples of rational numbers . When a rational number is represented as a fraction, it is often expressed in simplest form . A fraction is in simplest form when the GCF of the numerator and denominator is 1.. Simplify Fractions 30 45. Write in simplest form. Method 1 Divide by the GCF.. Method 2 Use prime factorization.. 30 2 3 5 Factor the numerator.. 3 0 235 45 335 235 335. 45 3 3 5 Factor the denominator. The GCF of 30 and 45 is 3 5 or 15. 3 0 30 15 45 45 15 2 3. Divide numerator and denominator by the GCF, 15.. 2 3. Write the prime factorization of the numerator and denominator. Divide the numerator and denominator by the GCF, 3 5. Simplify.. Exercises Write each fraction in simplest form. If the fraction is already in simplest form, write simplest form. 1. . 8 72. 2. . 27 45. 3. . 60 75. 4. . 15 25. 7. . 36 81. 8. . 18 54. 9. . 6. . 15 24. 12. . 48 72. 13. . 45 10 0. 17. . 7 91. 18. . 6 9. 22. . 16 40. 23. . 2 15. 27. . 90 120. 28. . 11. 16. 21. 26. . 99 300. 31. . 50 1,000. 32. . 36 54 14 66. 66 88. 3 9. 5. . 24 54. 10. . 72 98. 24 120. 14. . 15 100. 19. . 15 60. 20. . 64 68. 25. . 6 16. 75 89. 90 6,000. 33. . 24. . 15. . 17 51 30 80. 16 96. 30. . 150 400. 35. . 29. 34. . 133 140. 10 10,000. 36. Both the numerator and the denominator of a fraction are even. Can. you tell whether the fraction is in simplest form? Explain. 37. WEATHER The rainiest place on Earth is Waialeale, Hawaii. Of 365 days. per year, the average number of rainy days is 335. Write a fraction in simplest form to represent these rainy days as a part of a year. 38. OLYMPICS In the 2000 Olympics, Brooke Bennett of the U.S. swam the. 800-meter freestyle event in about 8 minutes. Express 8 minutes in terms of hours using a fraction in simplest form. Prerequisite Skills. 611.

(15) Prerequisite Skills. Least Common Multiple A multiple of a number is the product of that number and any whole number.. List Multiples List the first six multiples of 15. 0 15 0, 1 15 15, 2 15 30, 3 15 45, 4 15 60, 5 15 75 The first six multiples of 15 are 0, 15, 30, 45, 60, 75.. The least of the nonzero common multiples of two or more numbers is called the least common multiple (LCM) of the numbers. To find the LCM of two or more numbers, you can list the multiples of each number until a common multiple is found, or you can use prime factorization.. Find the LCM Find the LCM of 12 and 18. Method 1 List the multiples.. Method 2 Use prime factorization.. multiples of 12: 0, 12, 24, 36, 48, … multiples of 18: 0, 18, 36, 72, 90, …. 12 2 2 3. The LCM of 12 and 18 is 36. Remember that the LCM is a nonzero number.. 18 2 . 33. 2233. Write the prime factorization of each number. Multiply the factors, using the common factors only once.. The LCM is 2 2 3 3 or 36.. Exercises List the first six multiples of each number. 1. 7. 2. 11. 3. 4. 4. 5. 6. 25. 7. 150. 8. 2. 9. 3. 5. 14 10. 6. Find the least common multiple (LCM) of each set of numbers. 11. 8, 20. 12. 15, 18. 13. 12, 16. 14. 7, 12. 15. 20, 50. 16. 16, 24. 17. 2, 7, 8. 18. 2, 3, 5. 19. 4, 8, 12. 20. 7, 21, 5. 21. 8, 28, 30. 22. 10, 12, 14. 23. 35, 25, 49. 24. 24, 12, 6. 25. 68, 170, 4. 26. 45, 10, 6. 27. 10, 100, 1,000. 28. 100, 200, 300. 29. 2, 3, 5, 7. 30. 2, 15, 25, 36. 31. CIVICS In the United States, a president is elected every four years.. Members of the House of Representatives are elected every two years. Senators are elected every six years. If a voter had the opportunity to vote for a president, a representative, and a senator in 1996, what will be the next year the voter has a chance to make a choice for a president, a representative, and the same Senate seat? 612 Prerequisite Skills.

(16) Perimeter and Area of Rectangles Prerequisite Skills. The distance around a geometric figure is called its perimeter . The perimeter P of a rectangle is twice the sum of the length ᐉ and width w, or P 2ᐉ 2w. The measure of the surface enclosed by a figure is its area . The area A of a rectangle is the product of the length ᐉ and width w, or A ᐉw.. Find the Perimeter and Area of a Rectangle Find the perimeter of the rectangle. P 2ᐉ 2w. Write the formula.. .. 27 ft. P 2(27) 2(12) Replace ᐉ with 27 and w with 12. P 54 24. Multiply.. P 78. Add.. 12 ft. The perimeter is 78 feet. Find the area of the rectangle. A ᐉw. Write the formula.. A 27 12 Replace ᐉ with 27 and w with 12. A 324. Multiply.. The area is 324 square feet. A square is a rectangle whose sides are all the same length. The perimeter P of a square is four times the side length s, or P 4s. Its area A is the square of the side length, or A s2.. Estimate the Perimeter and Area of a Square 5 8. Find the approximate perimeter and area of a square with side length 6 inches. P 4s. A s2. Write the formula.. . 5 P 4 6 8. . 5 8. Replace s with 6.. P 4(7) or 28. Write the formula.. 5 2 A 6 8. A 72 or 49. Estimate.. The perimeter is about 28 inches.. 5 8. Replace s with 6. Estimate.. The area is about 49 square inches.. Exercises Find the perimeter and area of each figure. 1.. 2m. 2.. 5 yd. 6m. 3.. 5.5 in.. 7.5 cm 6.5 in.. 8 yd. 4.. 7.5 cm. 5. rectangle: 3 mm by 5 mm. 6. rectangle: 144 mi by 25 mi. 7. square: side length, 75 ft. 8. square: side length, 0.75 yd. 9. rectangle: 4.3 cm by 2.7 cm 11. square: side length of 87 km. 10. square: side length of 625 m 12. rectangle: 875.5 mm by 245.3 mm Prerequisite Skills. 613.

(17) x-coordinate. An ordered pair of numbers is used to locate any point on a coordinate plane. The first number is called the x-coordinate. The second number is called the y-coordinate.. y-coordinate. (4, 3). . Prerequisite Skills. Plotting Points on a Coordinate Plane. ordered pair. Identify Ordered Pairs Write the ordered pair that names point A. Step 1 Start at the origin.. y. A. Step 2 Move left on the x-axis to find the x-coordinate of point A, which is 1.. B. Step 3 Move up along the y-axis to find the y-coordinate which is 4.. x. O. The ordered pair for point A is (1, 4). Write the ordered pair that names point B. The x-coordinate of B is 2. Since the point lies on the x-axis, its y-coordinate is 0. The ordered pair for point B is (2, 0).. Graph an Ordered Pair Graph and label the point C(3, ⫺2) on a coordinate plane.. y. Step 1 Start at the origin. x. O. Step 2 Since the x-coordinate is 3, move 3 units right. Step 3 Since the y-coordinate is 2, move down 2 units. Draw and label a dot.. C (3, ⫺2). Exercises Name the ordered pair for the coordinates of each point on the coordinate plane. 1. Z. 2. X. 3. W. 4. Y. 5. T. 6. V. 7. U. 8. S. 9. Q. 10. R. 11. P. 12. M. y. Z. T X Y W R P. O. U. V S. Graph each point on the same coordinate plane. 13. A(4, 7). 14. C(1, 0). 15. B(0, 7). 16. E(1, 2). 17. D(4, 7). 18. F(10, 3). 19. G(9, 9). 20. J(7, 8). 21. K(6, 0). 22. H(0, 3). 23. I(4, 0). 24. M(2, 7). 25. N(8, 1). 26. L(1, 1). 27. P(3, 3). 614 Prerequisite Skills. Q M. x.

(18) Measuring and Drawing Angles Prerequisite Skills. Two rays that have a common endpoint form an angle . The common endpoint is called the vertex , and the two rays that make up the angle are called the sides of the angle.. vertex. B side. A circle can be divided into 360 equal sections. Each section is one degree . You can use a protractor to measure an angle in degrees and draw an angle with a given degree measure.. side. A. C. Measure an Angle Use a protractor to measure ⬔FGH.. 90. 100 80. 110 70. 12 0 60. 13 50 0. 15. 0. 0 15 30. 30. 14. 40. 80 100. 0. 50 0 13. 70 110 60 0 12. 0 14 40. ៮៬. Step 2 Use the scale that begins with 0° at GH ៮៬, Read where the other side of the angle, GF crosses this scale.. 170 10. 10 170. 20 160. 160 20. G 130˚ 50 0 13. 70 110 60 0 12. 80 100. 90. 100 80. 110 70. 12 0 60. 13 50 0. 14 30. 15. 0. 0 15 30. 170 10. 10 170. 20 160. 160 20. The measure of angle FGH is 130°. Using symbols, m⬔FGH 130°.. H. 0 14 40. 40. F 0. Step 1 Place the center point of the protractor’s base on vertex G. Align the straight side with ៮៬ so that the marker for 0° is on one of side GH the rays.. F. G. H. Draw an Angle Draw ⬔X having a measure of 75°.. X. Step 1 Draw a ray. Label the endpoint X. 90. 100 80. 110 70. 12 0 60. 0. 60 0 12 50 0 13. 80 100. 13 50 0. 15. 0. 0 15 30. 30. 14. 40. 75˚ 70 110. 0 14 40. Step 2 Place the center point of the protractor’s base on point X. Align the mark labeled 0 with the ray.. 170 10. 10 170. 20 160. 160 20. Step 3 Use the scale that begins with 0. Locate the mark labeled 75. Then draw the other side of the angle.. X. Exercises Use a protractor to find the measure of each angle. 1. ⬔XZY. 2. ⬔SZT. 3. ⬔SZY. 4. ⬔UZX. 5. ⬔TZW. 6. ⬔UZV. V U. W X. T. Use a protractor to draw an angle having each measurement. 7. 40°. 8. 70°. 9. 65°. 10. 110°. 11. 85°. 12. 90°. 13. 155°. 14. 140°. 15. 117°. S. Z. Prerequisite Skills. Y. 615.

(19) Extra Practice Lesson 1-1. (Pages 6–10). Use the four-step plan to solve each problem. 1. Joseph is planting bushes around the perimeter of his lawn. If the. Extra Practice. bushes must be planted 4 feet apart and Joseph’s lawn is 64 feet wide and 124 feet long, how many bushes will Joseph need to purchase? 2. Find the next three numbers in the pattern 1, 3, 7, 15, 31, . . .. 3. At the bookstore, pencils cost $0.15 each and erasers cost $0.25 each.. What combination of pencils and erasers can be purchased for a total of $0.65? 4. Cheap Wheels Car Rental rents cars for $50 per day plus $0.15 per mile.. How much will it cost to rent a car for 2 days and to drive 200 miles? 5. Josie wants to fence in her yard. She needs to fence three sides and the. house will supply the fourth side. Two of the sides have a length of 25 feet and the third side has a length of 35 feet. If the fencing costs $10 per foot, how much will it cost Josie to fence in her yard?. Lesson 1-2. (Pages 11–15). Evaluate each expression. 1. 15 5 9 2. 2. (52 2) 3. 4. 6 3 9 1. 5. (42. 25 (3 4). . 22). 3. 12 20 4 5. 5. 6. 24 8 2. 8. (15 7) 6 2. 7. 2 . 9. 3[15 (2 7) 3]. Evaluate each expression if a 3, b 6, and c 5. bc a. 10. 2a bc. 11. ba2. 14. (2c b) a. 15. . 2(ac)2 b. 12. . 13. 3a c 2b. 16. abc. 17. (3b a)c. Name the property shown by each statement. 18. 2(a b) 2a 2b. 19. 3 5 5 3. 20. (2 6) 5 2 (6 5). 21. 3(4 1) (4 1)3. 22. (7 5)2 7(5 2). 23. 8(2x 1) 8(2x) 8(1). 24. 5(x 2) (x 2)5. 25. (3x 2) 0 3x 2. 26. 5 1 5. Lesson 1-3 Replace each. (Pages 17–21). with , , or to make a true sentence.. 1. 3. 0 5. 8 10 9. 13 12 14 13. 14. 2. 1. 2 6. 6 6 5 10. 2 4 14. 0. Evaluate each expression. 17. 1 18. 92 21. 80 100 22. 0 25. 161 26. 150 616 Extra Practice. 3. 5. 4 7. 11 20 19 11. 13 20 15. 23. 7 8. 8 2 2 12. 6 12 16. 12. 19. 3. 20. 160 32. 23. 7 3. 24. 3 7. 27. 102 2. 28. 116. 4. 6.

(20) Lesson 1-4. (Pages 23–27). Add. 1. 7 (7). 2. 36 40. 3. 18 (32). 4. 47 12. 5. 69 (32). 6. 120 (2). 7. 56 (4). 8. 14 16. 9. 18 11. 11. 13 (11). 12. 95 (5). 13. 120 2. 14. 25 (25). 15. 4 8. 16. 9 (6). 17. 42 (18). 18. 33 (12). 19. 7 (13) 6 (7). 20. 6 12 (20). 21. 4 9 (14). 22. 20 0 (9) 25. 23. 5 9 3 (17). 24. 36 40 (10). 25. (2) 2 (2) 2. 26. 6 (4) 9 (2). 27. 9 (7) 2. 28. 100 (75) (20). 29. 12 24 (12) 2. 30. 9 (18) 6 (3). Lesson 1-5. Extra Practice. 10. 42 29. (Pages 28–31). Subtract. 1. 3 7. 2. 5 4. 3. 6 2. 4. 12 9. 5. 0 (14). 6. 58 (10). 7. 41 15. 8. 81 21. 9. 26 (14). 10. 6 (4). 11. 63 78. 12. 5 (9). 13. 72 (19). 14. 51 47. 15. 99 1. 16. 8 13. 17. 2 23. 18. 20 0. 19. 55 33. 20. 84 (61). 21. 4 (4). 22. 2 (3). 23. 65 (2). 24. 0 (3). 25. 0 5. 26. 2 6. 27. 4 7. 28. 3 (3). 29. 15 6. 30. 5 8. Lesson 1-6. (Pages 34–38). Multiply. 1. 5(2). 2. 11(5). 3. 5(5). 4. 12(6). 5. 2(2). 6. 3(2)(4). 7. (4)(4). 8. 4(21). 9. 50(0). 10. 3(13). 11. 2(2). 12. 2(2). 13. 5(12). 14. 2(2)(2). 15. 6(4). 16. 4 (2). 17. 16 (8). 18. 14 (2). 19. 18 3. 20. 25 5. 21. 56 (8). 22. 81 9. 23. 55 11. 24. 42 (7). 25. 18 (3). 26. 0 (1). 27. 32 8. 28. 81 (9). 29. 18 (2). 30. 21 3. Divide.. Extra Practice. 617.

(21) Lesson 1-7. (Pages 39–42). Write each verbal phrase as an algebraic expression. 1. 12 more than a number. 2. 3 less than a number. 3. a number divided by 4. 4. a number increased by 7. 5. a number decreased by 12. 6. 8 times a number. 7. 28 multiplied by m. 8. 15 divided by a number. Extra Practice. 9. 54 divided by n. 10. 18 increased by y. 11. q decreased by 20. 12. n times 41. 13. 5 less than a number. 14. the product of a number and 15. Write each verbal sentence as an algebraic equation. 15. 6 less than the product of q and 4 is 18.. 16. Twice x is 20.. 17. A number increased by 6 is 8.. 18. The quotient of a number and 7 is 8.. 19. The difference between a number and 12 is 37. 20. The product of a number and 7 is 42.. Lesson 1-8. (Pages 45–49). Solve each equation. Check your solution. 1. g 3 10. 2. b 7 12. 3. a 3 15. 4. r 3 4. 5. t 3 21. 6. s 10 23. 7. 9 n 13. 8. 13 v 31. 9. 4 b 12. 10. z 10 8. 11. 7 x 12. 12. 7 g 91. 13. 63 f 71. 14. a 6 9. 15. c 18 13. 16. 23 n 5. 17. j 3 7. 18. 18 p 3. 19. 12 p 16. 20. 25 y 50. 21. x 2 4. 22. r (8) 14. 23. m (2) 6. 24. 5 q 12. 25. t 12 6. 26. 8 p 0. 27. 12 x 8. 28. 14 t 10. 29. x 5 7. 30. 2 3 x. Lesson 1-9. (Pages 50–53). Solve each equation. Check your solution. 1. 4x 36. 2. 39 3y. 3. 4z 16. t 4. 6 5. 5. 100 20b. 6. 8 . 7. 10a 40. 8. 8. 10. 8k 72. r 7. s 9. 11. 2m 18. w 7. w 8. 9. 420 5s. m 8. 12. 5. 13. 8. 14. 8. 15. 18q 36. 16. 9w 54. 17. 4 p 4. 18. 14 2p. 19. 12 3t. 20. 12. m 4. 21. 6h 12. 22. 2a 8. 23. 0 6r. 24. 6. 25. 3m 15. 26. 10. 27. 6f 36. 28. 81 9w. 29. 6r 42. 30. 15. 618 Extra Practice. c 4. y 12. x 2.

(22) Lesson 2-1. (Pages 62–66). Write each fraction or mixed number as a decimal. 2 5 3 5. 4 5 9. 6. 3 4. 3 11 2 6. 3 3 10. 1 5. 1. . 5 7 1 8. 2 8 12. 9. 3. . 2. 2. 4. . 7 11. 7. . 1 4. 11. 2. 13. 0.5. 14. 0.8 . 15. 0.32. 16. 0.75. 17. 2.2 . 18. 0.3 8. 19. 0.486. 20. 20.08. 21. 9.36. 22. 10.18 . 23. 1.24. 24. 5.7 . Lesson 2-2. (Pages 67–70). with , , or to make a true sentence.. Replace each 1. 5.6. 6 7. 4.2. 2. 4.256. 7 9. 5. . 2 3. 6. . 3 8. 4.25. 2 5. 10. 0.25. 12. 9. 12.56. Extra Practice. Write each decimal as a fraction or mixed number in simplest form.. 3 8. 7. . 0.26. 5 7. 0.23. 3. 0.233. 1 2. 8. . 0.375 1.3 1. 11. 1.31. 2 5. 4. . 3 5. 12. . 0.5 2 3. Order each set of rational numbers from least to greatest. 14. 0.3 , 0.3, 0.34, 0.34, 0.33. 13. 0.24, 0.2, 0.245, 2.24, 0.25. 2 2 2 2 2 5 3 7 9 1. 1 5 2 8 6 2 7 9 9 6 3 3 3 3 3 3 3 18. , , , , , , 10 2 5 1 8 7 4 3 2 1 3 5 20. , , , , 5 3 2 4 6 2 5 22. 7.5, 7, 6, 6.8 3 6. 15. , , , , . 16. , , , , . 253 1,000. 17. 0.25, 0.2, 0.02, 0.251, . 3 2 5 3 4 3 21. , 0.4, 0.44, 9 5 2 1 5 23. , , 0.1, 3 3 6. 33 50. 19. , , 0.61, 0.65, . 24. 0.5, 0.5, 0, 0.35, 0.51. Lesson 2-3. (Pages 71–75). Multiply. Write in simplest form. 2 3 11 4 7 1 8 3 1 8 2 4 1 2 5 6 4 3 1 1 4 3 5 3 1 1 4 1 2 3 4 7 5 6. 78 . 1. . 2. 4 . 5.. 6. . 9. 13. 17. 21. 25.. . . . . . . 3 4. 10. 14. 18. 22. 26.. 4 5 3 8 3 4 9 3 2 8 4 4 5 3 8 4 1 5 3 5 3 7 8 9. . 4 7. . 3 5. 3. . 1 2. 7. 1 . 2 3. 8.. 78 . 12.. 10 21. 11. . 2 3. 15. 6 8. . . 2 1 3 2 1 1 23. 4 1 3 2 3 1 27. 1 2 4 7 19. 3 3. . . 6 7 7 12 5 6 6 7 4 5 1 5 6 3 3 5 5 2 2 5 5 1 5 3 3 1 8 5 4. 4. . . 16. 20. 24. 28. Extra Practice. 619.

(23) Lesson 2-4. (Pages 76–80). Name the multiplicative inverse of each number. 1. 3. 1 15. 5. . 2 3. 2. 5. 3. . 6. 8. 7. 1. 1 8 4 8. 5 4. 2. 1 3. Divide. Write in simplest form. 2 3 3 4 1 13. 4 3 6 3 17. 7 5 3 21. (6) 8 4 25. 8 1 5 1 29. 8 3 6. Extra Practice. 9. . . 4 5 9 6 1 1 5 2 4 2 1 3 (4) 3 5 1 8 6 2 5 7 3 9 4. 10. 14. 18. 22.. . 26. 30.. . . 3 8. 12. . 15. 6 . 47 . 16. 6 . 1 5 3 12 1 3 23. 4 6 4 4 3 6 27. 5 7 1 11 31. 1 2 2 14. 20. 1. 7 12. 2 9. 5 18. 11. . 3 8. 5 6. 19. 2 7. 1 4. 1 9. 1 1 6 8 8 2 28. 4 2 9 3 1 4 32. 2 4 5 24. 4 3. . Lesson 2-5. . (Pages 82–85). Add or subtract. Write in simplest form.. . . 17 13 21 21 13 9 5. 28 28 17 4 9. 35 35 29 26 13. 9 9 3 7 17. 10 10 5 21. 5 3 7 5 2 25. 4 1 9 9 1. . . . 5 11. . 6 11. 2. . 2 9. 7 9 3 5 8 8 3 3 2 7 5 5 4 9 11 11 5 3 4 8 5 7 2 8 12 12. 6. 1 10. 14. 18. 22. 26.. . 8 11 13 13 15 13 16 16 8 2 15 15 13 5 18 18 1 7 1 8 8 3 6 5 2 7 7 1 3 5 1 4 4. . 7 5 12 12 1 2 2 3 3 4 3 2 7 7 2 6 2 1 7 7 5 7 6 6 3 3 9 2 4 4 1 4 6 2 5 5. 3. . 4. . 7.. 8.. 11. 15. 19. 23. 27.. 12. 16. 20. 24. 28.. Lesson 2-6. . . . . (Pages 88–91). Add or subtract. Write in simplest form. 7 7 12 24 3 5 8 24 2 2 9 3 2 1 3 3 5 4 2 1 3 1 5 3 1 3 2 2 4 3 1 5 8 4 3. 3 7 4 8 3 7 4 12 7 5 15 12 3 4 15 4 1 3 5 8 3 7 2 5 5 3 3 6 3 5 1 3 4 8. 27 3 4 8 5 2 5. 1. . 2. . 3. . 5.. 6.. 7.. 9. 13. 17. 21. 25.. . 620 Extra Practice. 10. 14. 18. 22. 26.. . . . . 3 8. 7 12. 11. . 2 3. 3 4. 15. 1 4. 3 5. 2 3. 19. . 1 7. 1 5. 23. 5 3. 1 2. 5 7. 27. 4 . 56 2 3 8. 15 10 1 1 12. 2 1 4 3 3 5. 4. . 1 1 8 2 1 5 20. 1 2 3 6 1 2 24. 8 1 2 3 2 3 28. 3 9 3 4 16. 2.

(24) Lesson 2-7. (Pages 92–95). Solve each equation. Check your solution. 1. 434 31y. 3 4. 2. 6x 4.2. 3. a 12. 3 4. b 7. 4. 10 . 5. 7.2 c. 7. 2.4n 7.2. 8. 7 d 11.. 13. k 1.18 1.58. 14.. 2 3 g 19. 6 1.2 16. m 22. 17. 20.. 22. a 3.2 6.5. 23.. 1 2. 25. 2.5x . 26.. 1 2 3 1 x 8 2 1 4s 30 2 2 5 g 4 3 6 5 3 z 4 15 8 8 1 2 q 5 3 2 c 3 5 3. 9. n 0.64 5.44. 1 2 2 8 15. f 3 15 1 18. 7 v 3 1 21. 12 j 5. 12. h 14. Extra Practice. t 3. 10. 2. 6. r 0.4 1.4. 24. 3.5z 7. 2 3. 5 6. 27. x . Lesson 2-8. (Pages 98–101). Write each expression using exponents. 1. 4 4 4 4. 2. 3 3. 3. 7 7 7 7 7 7. 4. 4 4 4 4 4 5 5 5 5 5 5 5 5. 5. x y y y y x x x y x. 6. b b b b c c c c c c. 7. 3 2 5 5 5 2 2 2 3 5. 8. a a a b b b a a a b. 9. 6 6 6 6 6 6 6 6. 10. x x x x x x x x x x. 11. a b b b b b b b. Evaluate each expression. 12. 43. 13. 62. 14. 26. 15. 52 62. 16. 3 24. 17. 104 32. 18. 53 19. 19. 22 24. 20. 2 32 42. 21. 73. 22. 22 52. 23. 35 42. 24. 72 34. 25. 33. 26. 24. 27. 52. Lesson 2-9. (Pages 104–107). Write each number in standard form. 1. 4.5 103. 2. 2 104. 3. 1.725896 106. 4. 9.61 102. 5. 1 107. 6. 8.256 108. 7. 5.26 104. 8. 3.25 102. 9. 6.79 105. 10. 3.1 104. 11. 2.51 102. 12. 6 101. 13. 2.15 103. 14. 3.14 106. 15. 1 102. Write each number in scientific notation. 16. 720. 17. 7,560. 18. 892. 19. 1,400. 20. 91,256. 21. 51,000. 22. 0.012. 23. 0.0002. 24. 0.054. 25. 0.231. 26. 0.0000056. 27. 0.000123 Extra Practice. 621.

(25) Lesson 3-1. (Pages 116–119). Find each square root.. 22.. 9 36 961 4 196 16 0.04 0.09 . 25.. 0.36. 1. 4. 7. 10.. Extra Practice. 13. 16. 19.. 2. 5. 8. 11. 14. 17. 20. 23.. 81 169 324 529 729 1,024 2.25 0.49 . 289 10,000 81 29. 64 26.. 49. 28. . 3. 625 6. 9. 12. 15. 18. 21. 24.. 144 225 484 289 0.16 0.01 1.69 . 169 121 25 30. 81 27.. Lesson 3-2. (Pages 120–122). Estimate to the nearest whole number. 1. 4. 7. 10. 13. 16. 19. 22. 25. 28.. 229 27 96 76 137 326 79 117 1.30 25.70 . 2. 5. 8. 11. 14. 17. 20. 23. 26. 29.. 63 333 19 17 540 52 89 410 8.4 1.41 . 3. 6. 9. 12. 15. 18. 21. 24. 27. 30.. 290 23 200 34 165 37 71 47 18.35 15.3 . Lesson 3-3. (Pages 125–129). Name all sets of numbers to which each real number belongs.. 25. 3. 1. 6.5. 2.. 4. 7.2. 5. 0.6 1. 6. . 16 4. 8. 102.1. 9.. 7. . 3.. 1 2. 29. Estimate each square root. Then graph the square root on a number line. 10. 12 . 11.. 13.. 14.. 16.. 10 21. 17.. Replace each 19.. 7. 23 30 202 . 12. 15. 18.. 2 5 10 . with , , or to make a true sentence.. 2.8. 30 212 6.25. 1 3. 20. 2. 22. 5.6. 23. 9.45. 25.. 1 26. 5 3. 622 Extra Practice. 2.3. 21.. 9.4 . 24.. 30. 27.. 11 121 5 2.23 2 4 22 3.

(26) Lesson 3-4. (Pages 132–136). Write an equation you could use to find the length of the missing side of each right triangle. Then find the missing length. Round to the nearest tenth if necessary. 1.. 2.. 3. x ft. 5m. xm. 4 ft. x cm. 6 cm. 8 ft. Extra Practice. 4m 2 cm. 4. a, 6 cm; b, 5 cm. 5. a, 12 ft; b, 12 ft. 6. a, 8 in.; b, 6 in.. 7. a, 20 m; c, 25 m. 8. a, 9 mm; c, 14 mm. 9. b, 15 m; c, 20 m. Determine whether each triangle with sides of given lengths is a right triangle. 10. 15 m, 8 m, 17 m. 11. 7 yd, 5 yd, 9 yd. 12. 5 in., 12 in., 13 in.. 13. 9 in., 12 in., 16 in.. 14. 10 ft, 24 ft, 26 ft. 15. 2 ft, 2 ft, 3 ft. Lesson 3-5. (Pages 137–140). Write an equation that can be used to answer each question. Then solve. Round to the nearest tenth if necessary. 1. How far apart are the. 2. How high does the. boats?. 3. How long is each rafter?. ladder reach? x ft 18 ft. 7 mi. 12 ft. y ft. h ft 6 ft. d mi. 16 ft. 4 ft. 3 mi. Lesson 3-6. (Pages 142–145). Find the distance between each pair of points whose coordinates are given. Round to the nearest tenth if necessary. 1.. y. 2.. (1, 2). O. 3.. y. (1, 4). x. y. (4, 1). (3, 3). O. (0, 4) (7, 1). x. O. x. Graph each pair of ordered pairs. Then find the distance between the points. Round to the nearest tenth. 4. (4, 2), (4, 17). 5. (5, 1), (11, 7). 8. (5, 4), (3, 8). 9. (8, 4), (3, 8). 12. (2, 3), (1, 6). 13. (5, 1), (2, 3). 6. (3, 5), (2, 7). 7. (7, 9), (4, 3). 10. (2, 7), (10, 4). 11. (9, 2), (3, 6). 14. (0, 1), (5, 2). 15. (1, 2), (2, 3) Extra Practice. 623.

(27) Lesson 4-1. (Pages 156–159). Express each ratio in simplest form. 1. 27 to 9. 2. 4 inches per foot. 3. 16 out of 48. 4. 10:50. 5. 40 minutes per hour. 6. 35 to 15. 7. 16 wins to 16 losses. 8. 7 out of 13. 9. 5 out of 50. 10. 3 out of 5. 11. 20 minutes per hour. 12. 6 inches per foot. Extra Practice. Express each rate as a unit rate. 13. 6 pounds gained in 12 weeks. 14. $800 for 40 tickets. 15. $6.50 for 5 pounds. 16. 6 inches of rain in 3 weeks. 17. 20 preschoolers to 2 teachers. 18. 10 inches of snow in 2 days. 19. $500 for 50 tickets. 20. $360 for 100 dinners. Lesson 4-2. (Pages 160–164). For Exercises 1–3, use the following information. Time. 1:00. 2:00. 2:30. 3:00. 3:15. Temperature. 88°F. 89°F. 80°F. 76°F. 76°F. 1. Find the rate of change between 2:00 and 2:30. 2. Find the rate of change between 1:00 and 3:00. 3. Find the rate of change between 3:00 and 3:15. Explain the meaning of. this rate of change.. For Exercises 4–7, use the following information. Time. 6:00. 6:30. 6:45. 7:00. 7:10. 7:30. 8:00. 8:15. 8:30. 2. 32. 77. 137. 139. 140. 142. 142. 142. Number of Tickets Sold. 4. Find the rate of change between 6:45 and 7:00. 5. Was the rate of change between 8:00 and 8:15 positive, negative, or zero? 6. Find the rate of change between 6:00 and 8:30. 7. During which time period was the greatest rate of change?. Lesson 4-3. (Pages 166–169). Find the slope of each line. 1.. 2.. y. 3.. y. y. (2, 3). (0, 3) (2, 1). (2, 1) x. O. (1, 2). x. O. (2, 2). x. O. The points given in each table lie on a line. Find the slope of the line. 4.. x. 0. 1. 2. 3. y. 1. 0. 1. 2. 624 Extra Practice. 5.. x. 0. 2. 4. 6. y. 0. 1. 2. 3. 6.. x. 0. 1. 2. 3. y. 0. 2. 4. 6.

(28) Lesson 4-4. (Pages 170–173). Determine whether each pair of ratios forms a proportion. 3 5 5 10 6 3 5. , 18 9 2 3 9. , 3 2 1. , . 8 6 4 3 14 12 6. , 21 1 8 2 14 10. , 3 21. 10 5 15 3 4 5 7. , 20 25 1 5 11. , 2 10. 2 1 8 4 9 1 8. , 27 3 3 15 12. , 5 9. 7 c 8 16 5 b 18. 12 5 2 8 22. x 24 0 .3 1.5 26. 0 .2 c. 15. . 3 21 7 d 2 4 19. y 36 y 8 23. 15 60 3 z 27. 10 36. 16. . 2. , . 3. , . 4. , . 2 a 3 12 3 n 17. 5 21 x 14 21. 3 21 27 z 25. 8 4 13. . 14. . Extra Practice. Solve each proportion. 2 18 5 x y 16 20. 8 12 1 a 24. 5 3 2 t 28. 3 4. Lesson 4-5. (Pages 178–182). Determine whether each pair of polygons is similar. Explain your reasoning. 1.. 2.. 5 cm 2 cm. 5.1 m. 4 cm. 4.6 m. 10 cm. 5m. 4m. 2.2 m. 3m. Each pair of polygons is similar. Write a proportion to find each missing measure. Then solve. 3.. 4. 4 cm. x cm. 6 in. 2 in.. 3.5 cm 5 in.. x in.. Lesson 4-6. 7 cm (Pages 184–187). Solve. 1. The distance between two cities on a map is 3.2 centimeters. If the scale. on the map is 1 centimeter 50 kilometers, find the actual distance between the two cities. 2. A scale model of the Empire State Building is 10 inches tall. If the Empire. State Building is 1,250 feet tall, find the scale of this model. 3. On a scale drawing of a house, the dimensions of the living room are. 4 inches by 3 inches. If the scale of the drawing is 1 inch 6 feet, find the actual dimensions of the living room. 4. Columbus, Ohio, is approximately 70 miles from Dayton, Ohio. If a scale. on an Ohio map is 1 inch 11 miles, about how far apart are the cities on the map? Extra Practice. 625.

(29) Lesson 4-7. (Pages 188–191). Write a proportion. Then determine the missing measure. 1. A road sign casts a shadow 14 meters long, while a tree nearby casts a. shadow 27.8 meters long. If the road sign is 3.5 meters high, how tall is the tree? 2. Use the map to find the distance across Catfish. Extra Practice. Lake. Assume the triangles are similar.. Catfish Lake. 3. A 7-foot tall flag stick on a golf course casts a. x km. shadow 21 feet long. A golfer standing nearby casts a shadow 16.5 feet long. How tall is the golfer?. 1.2 km 0.8 km. 4.5 km. 4. A building casts a shadow that is 150 feet. A. tree casts a shadow that is 25 feet. If the tree is 150 feet tall, how tall is the building? 5. A tower casts a shadow that is 120 feet. A pole casts a shadow that is. 5 feet. If the tower is 2,400 feet tall, how tall is the pole?. Lesson 4-8. (Pages 194–197). Find the coordinates of the vertices of triangle ABC after triangle ABC is dilated using the given scale factor. Then graph triangle ABC and its dilation. 1 2. 1. A(1, 0), B(2, 1), C(2, 1); scale factor 2. 2. A(4, 6), B(0, 2), C(6, 2); scale factor . 3. A(1, 1), B(1, 2), C(1, 1); scale factor 3. 4. A(2, 0), B(0, 4), C(2, 4); scale factor . 3 2. In each figure, the green figure is a dilation of the blue figure. Find the scale factor of each dilation, and classify each dilation as an enlargement or as a reduction. 5.. 6.. y. y. 7.. y. x. O O. O. x. x. Lesson 5-1. (Pages 206–209). Write each ratio or fraction as a percent. 1 4. 7 10. 1. 3 out of 5. 2. . 3. . 5. 11 out of 25. 6. 72.5:100. 7. 3 out of 4. 7 20. 9. . 10. 93:100. 11. 2 out of 8. 4. 39:100. 1 2 9 12. 20 8. . Write each percent as a fraction in simplest form. 13. 30%. 14. 4%. 15. 20%. 16. 85%. 17. 3%. 18. 80%. 19. 17%. 20. 55%. 21. 82%. 22. 48%. 23. 32%. 24. 51%. 626 Extra Practice.

(30) Lesson 5-2. (Pages 210–214). Write each percent as a decimal. 1. 2%. 2. 25%. 3. 29%. 4. 6.2%. 5. 16.8%. 6. 14%. 7. 23.7%. 8. 42%. Write each decimal as a percent. 10. 14.23. 11. 0.9. 12. 0.13. 13. 6.21. 14. 0.08. 15. 0.036. 16. 2.34. 21 50 11 23. 20 41 27. 50. 20. . Extra Practice. 9. 0.35. Write each fraction as a percent. 2 5 81 21. 100 33 25. 40. 49 50 2 22. 25 1 26. 50. 17. . 18. . 1 3 9 24. 75 39 28. 100. 19. . Lesson 5-3. (Pages 216–219). Write a percent proportion to solve each problem. Then solve. Round answers to the nearest tenth if necessary. 1. 39 is 5% of what number?. 2. What is 19% of 200?. 3. 6 is what percent of 30?. 4. 24 is what percent of 72?. 1 3. 5. 9 is 33% of what number?. 6. Find 55% of 134.. 7. 8 is what percent of 32?. 8. What is 35% of 215?. 9. 62 is 50% of what number?. 10. 93 is what percent of 186?. 11. 90 is 36% of what number?. 12. 15 is 60% of what number?. 13. What is 15% of 60?. 14. 15 is 20% of what number?. 15. 66 is 75% of what number?. 16. 31 is what percent of 155?. 17. 22 is 25% of what number?. 18. What is 65% of 150?. 19. 6 is 75% of what number?. 20. 27 is what percent of 100?. Lesson 5-4. (Pages 220–223). Compute mentally. 1. 10% of 206. 2. 1% of 19.3. 3. 20% of 15. 4. 87.5% of 80. 5. 50% of 46. 6. 12.5% of 56. 8. 90% of 2,000. 9. 30% of 70. 1 3. 7. 33% of 93. 2 3. 10. 40% of 95. 11. 66% of 48. 12. 80% of 25. 13. 25% of 400. 14. 75% of 72. 15. 37.5% of 96. 16. 40% of 35. 17. 60% of 85. 18. 62.5% of 160. 19. 90% of 205. 20. 1% of 2,364. 21. 20% of 85. 22. 75% of 12. 23. 12.5% of 800. 24. 30% of 90. 25. 1% of 70. 26. 40% of 45. 27. 62.5% of 88 Extra Practice. 627.

(31) Lesson 5-5. (Pages 228–231). Estimate. 1. 33% of 12. 2. 24% of 84. 3. 39% of 50. 4. 19% of 135. 5. 21% of 50. 6. 49% of 121. 7. 72% of 101. 8. 99% of 255. 9. 25% of 41. 10. 11 out of 99. 11. 28 out of 89. 12. 9 out of 20. 13. 25 out of 270. 14. 5 out of 49. 15. 7 out of 57. 16. 2 out of 21. 17. 12 out of 61. 18. 7 out of 15. Extra Practice. Estimate each percent.. Estimate the percent of the area shaded. 19.. 20.. 21.. Lesson 5-6. (Pages 232–235). Solve each equation using the percent equation. 1. Find 5% of 73.. 2. What is 15% of 15?. 3. Find 80% of 12.. 4. What is 7.3% of 500?. 5. Find 21% of 720.. 6. What is 12% of 62.5?. 7. Find 0.3% of 155.. 8. What is 75% of 450?. 9. Find 7.2% of 10.. 10. What is 10.1% of 60?. 11. Find 23% of 47.. 12. What is 89% of 654?. 13. 20 is what percent of 64?. 14. Sixty-nine is what percent of 200?. 15. Seventy is what percent of 150?. 16. 26 is 30% of what number?. 17. 7 is 14% of what number?. 18. 35.5 is what percent of 150?. 19. 17 is what percent of 25?. 20. 152 is 2% of what number?. Lesson 5-7. (Pages 236–240). Find each percent of change. Round to the nearest tenth if necessary. State whether the percent of change is an increase or a decrease. 1. original: 35. 2. original: 550. 3. original: 72. new: 29 4. original: 25 new: 35. new: 425 5. original: 28 new: 19. new: 88 6. original: 46 new: 55. Find the selling price for each item given the cost to the store and markup. 7. golf clubs: $250, 30% markup 9. shoes: $57, 45% markup. 8. compact disc: $17, 15% markup 10. book: $26, 20% markup. Find the sale price of each item to the nearest cent. 11. piano: $4,220, 35% off. 12. scissors: $14, 10% off. 13. book: $29, 40% off. 14. sweater: $38, 25% off. 628 Extra Practice.

(32) Lesson 5-8. (Pages 241–244). Find the simple interest to the nearest cent. 1. $500 at 7% for 2 years. 2. $2,500 at 6.5% for 36 months. 3. $8,000 at 6% for 1 year. 4. $1,890 at 9% for 42 months. 1 2. 5. $760 at 4.5% for 2 years. 6. $12,340 at 5% for 6 months. Find the total amount in each account to the nearest cent. 8. $3,200 at 8% for 6 months. 9. $20,000 at 14% for 20 years. Extra Practice. 7. $300 at 10% for 3 years. 10. $4,000 at 12.5% for 4 years. 1 2. 12. $17,000 at 15% for 9 years. 11. $450 at 11% for 5 years. Lesson 6-1. (Pages 256–260). Find the value of x in each figure. 1.. 2.. 3.. 48˚. x˚. x˚. 125˚ x˚. 107˚. 4.. 5.. 6. x˚. x˚. x˚. 37˚. 55˚. t. For Exercises 7–10, use the figure at the right. 7. Find m⬔6, if m⬔3 42°.. 1 3. 8. Find m⬔4, if m⬔3 71°.. q. 2 4 5 7. 9. Find m⬔1, if m⬔5 128°.. r. 6 8. 10. Find m⬔7, if m⬔2 83°.. Lesson 6-2. (Pages 262–265). Find the value of x in each triangle. 1.. 2.. 3. 101˚. x˚ x˚. x˚. 35˚. 40˚. 59˚. 63˚. Classify each triangle by its angles and by its sides. 4.. 5. 7 in.. 60˚. 60˚. 10 m. 26 m. 7 in. 60˚. 6.. 3 cm 25˚. 130˚. 3 cm 25˚. 24 m. 7 in. Extra Practice. 629.

(33) Lesson 6-3. (Pages 267–270). Find each missing length. Round to the nearest tenth if necessary. 1.. 2.. 3. 14 mm. 30˚. b cm. c ft. b ft. c cm. a mm. 30˚ b mm. 45˚ 6 ft. Extra Practice. 4 cm. 4.. 5.. 6. bm. 3m. c in.. 10 in.. cm. 12 m. 30˚ bm. 45˚. cm. 45˚. a in.. Lesson 6-4. (Pages 272–275). Find the value of x in each quadrilateral. 1.. 2.. 100˚ 55˚. x˚. 65˚. x˚. 3.. 110˚. 50˚. 75˚. x˚. 120˚. 120˚. 95˚. Classify each quadrilateral with the name that best describes it. 4.. 5.. 6.. Lesson 6-5. (Pages 279–282). Determine whether the polygons are congruent. If so, name the corresponding parts and write a congruence statement. 1.. 2. A. A D. B. E. 3. K. H. 9 ft. L. S. 4 ft. R. 3 in. 6 in.. B. C. F. E. D. 6 in.. C. N. 4. m⬔A. 7. m⬔H. 630 Extra Practice. 6 ft. Q. E. A. F 55˚. B. 5. BC 6. GH. P. 3 in. G. F. In the figure, quadrilateral ABCD is congruent to quadrilateral EFGH. Find each measure.. M. 6 ft. 7m. C. 35˚ 10 m. D. G. H.

(34) Lesson 6-6. (Pages 286–289). Complete parts a and b for each figure. a. Determine whether the figure has line symmetry. If it does, trace the figure and draw all lines of symmetry. If not write none. b. Determine whether the figure has rotational symmetry. write yes or no. If yes, name the angle(s) of rotation. 2.. 3.. 4.. 5.. 6.. Extra Practice. 1.. Lesson 6-7. (Pages 290–294). Graph the figure with the given vertices. Then graph the image of the figure after a reflection over the given axis, and write the coordinates of its vertices. 1. triangle CAT with vertices C(2, 3), A(8, 2), and T(4, 3); x-axis 2. trapezoid TRAP with vertices T(2, 5), R(1, 5), A(4, 2), and P(5, 2); y-axis. Name the line of reflection for each pair of figures. 3.. y. O. 4.. x. y. O. 5.. y. x O. Lesson 6-8. x. (pages 296–299). Graph the figure with the given vertices. Then graph the image of the figure after the indicated translation, and write the coordinates of its vertices. 1. rectangle PQRS with vertices P(7, 6), Q(5, 6), R(5, 2), and S(7, 2). translated 9 right and 1 unit down 2. pentagon DGLMR with vertices D(1, 3), G(2, 4), L(4, 4), M(5, 3) and R(3, 1). translated 5 units left and 7 units down 3. triangle TRI with vertices T(2, 1), R(0, 3), and I(1, 1) translated 2 units. left and 3 units down 4. quadrilateral QUAD with vertices Q(3, 2), U(3, 0), A(6, 0) and D(6, 2),. translated 3 units left and 1 unit down Extra Practice. 631.

(35) Lesson 6-9. (Pages 300–303). Graph the figure with the given vertices. Then graph the image of the figure after the indicated rotation about the origin, and write the coordinates of its vertices. 1. triangle ABC with vertices A(2, 1), B(0, 1), and C(1, 1); 90°. counterclockwise. Extra Practice. 2. rectangle WXYZ with vertices W(1, 1), X(1, 3), Y(6, 3), and Z(6, 1); 180° 3. quadrilateral QRST with vertices Q(2, 1), R(3, 1), S(3, 3), and T(2, 3);. 90° counterclockwise 4. triangle PQR with vertices P(1, 1), Q(3, 1), and R(1, 4); 90° counterclockwise 5. rectangle ABCD with vertices A(1, 1), B(1, 3), C(4, 3), and D(4, 1); 180° 6. parallelogram GRAM with vertices G(1, 2), R(2, 4), A(2, 3), and. M(1, 1); 90° counterclockwise. 7. triangle DEF with vertices D(0, 2), E(3, 3), and F(3, 1); 180°. Lesson 7-1. (Pages 314–318). Find the area of each figure. 1.. 2. 5m. 5 in.. 3.. 1.6 cm 1.3 cm. 6 in.. 2.3 cm. 8m. 1 2. 4. triangle: base, 2 in.; height, 7 in.. 5. triangle: base, 12 cm; height, 3.2 cm. 6. trapezoid: bases, 5 ft and 7 ft; height, 11 ft. 7. trapezoid: bases, 4 yd and 3 yd; height, 5 yd. 8. parallelogram: base, 15 cm; height, 3 cm. 9. parallelogram: base, 11.2 in.; height, 5 in.. 10. triangle: base, 7 yd; height, 9 yd. 1 4. 1 2. 11. trapezoid: bases, 9 cm and 10 cm; height, 5 cm. Lesson 7-2. (Pages 319–323). Find the circumference and area of each circle. Round to the nearest tenth. 1.. 2.. 3.. 20 mm. 4.. 3.5 m. 5. 4 in.. 7.. 6.. 632 Extra Practice. 2.4 cm. 16 ft. 8. 56 mm. 6 yd. 9. 22.4 m 35 in..

(36) Lesson 7-3. (Pages 326–329). Find the area of each figure. Round to the nearest tenth of necessary. 1.. 2.. 3.. 8m. 3 cm 12 ft. 4m. 6 cm. 8 ft. 4.. 5. 2 yd. 2 yd. 4 in.. 9 yd. 5 yd. 2 in.. 2 in.. 6.. 2 in.. 8 cm 2 cm. 6 in. 5 cm. 6 cm. 2 in.. 6 cm. 5 cm. 7 yd 2 cm. 8 cm. Lesson 7-4. (Pages 331–334). Identify each solid. Name the number and shapes of the faces. Then name the number of edges and vertices. 1.. 2.. 3.. 4.. 5.. 6.. Lesson 7-5. (Pages 335–339). Find the volume of each solid. Round to the nearest tenth if necessary. 1.. 2.. 3.. 6 yd. 5 in.. 3m 10 in.. 3m. 11 yd. 5 in.. 3m. 4.. 26 cm. 5.. 4 in.. 8 cm. 12 in. 18 in.. 6. 7 ft 30 ft Extra Practice. 633. Extra Practice. 4 ft.

(37) Lesson 7-6. (Pages 342–345). Find the volume of each solid. Round to the nearest tenth if necessary. 1.. 5 cm. 2.. 3.. 60 in.. 12 yd. 60 in. 3 cm. Extra Practice. 4 cm. 4.. 3 cm. 7 yd. 60 in.. 5.. 6.. 15 ft. 4 cm. 8 ft. 11 ft. 8 ft. 5 ft. 2 cm. Lesson 7-7. (Pages 347–350). Find the surface area of each solid. Round to the nearest tenth if necessary. 1.. 2 ft. 2.. 3.. 3 ft. 4 cm. 2 ft. 4 ft 8 cm. 2 ft 6 ft. 4.. 8 in.. 5.. 6 cm. 6 in.. 3 cm. 5 cm. 6.. 5.2 cm. 14 cm 3 cm. 10 cm. 6 cm. 6 cm. Lesson 7-8. (Pages 352–355). Find the surface area of each solid. Round to the nearest tenth if necessary. 1.. 2. 12 ft. 3m 6m. 3.. 6m. A 15.6 6m. m2 5 in. 2 in. 2 in.. 4 ft. 4.. 5.. 6.. 10 ft. 6.5 cm 6 in.. 12 ft 3 in.. 3 cm. 634 Extra Practice. 3 in..

(38) Lesson 7-9. (Pages 358–362). Determine the number of significant digits in each measure. 1. 18 min. 2. 7.5 lb. 3. 92.46 m. 4. 7 ft. 5. 0.067 kg. 6. 61.7 cm. 7. 8 mm. 8. 6.02 cm. Find each sum or difference using the correct precision. 9. 9 L 5.7 L 12. 5.612 m 3.1 m. 10. 15.27 in. 3.16 in.. 11. 3.67 ft 2.1 ft. 13. 7.1 mi 5.421 mi. 14. 0.81 kg 5.1 kg. Extra Practice. Find each product or quotient using the correct number of significant digits. 15. 3.257 ft 0.52 ft. 16. 3.25 in 0.2 in. 17. 5.7 mm 3 mm. 18. 7.1 cm 2.1 cm. 19. 18 kg 3.5 kg. 20. 3.7 m 20 m. 21. 1.44 cm 2.2 cm. 22. 500 mL 3.5 mL. 23. 100 mm 73.2 mm. Lesson 8-1. (Pages 374–377). A date is chosen at random from the calendar below. Find the probability of choosing each date. Write each probability as a fraction, a decimal, and a percent. 1. The date is the thirteenth. 2. The day is Friday.. S. M. 3. It is after the twenty-fifth. 4. It is before the seventh. 5. It is an odd-numbered date. 6. The date is divisible by 3.. 6 7 13 14 20 21 27 28. November T W T F 1 2 3 4 8 9 10 11 15 16 17 18 22 23 24 25 29 30. S 5 12 19 26. 7. The day is Wednesday. 8. It is after the seventeenth.. Lesson 8-2. (Pages 380–383). Draw a tree diagram to determine the number of outcomes. 1. A car comes in white, black, or red with standard or automatic. transmission and with a 4-cylinder or 6-cylinder engine. 2. A customer can buy roses or carnations in red, yellow, pink, or white. 3. A bed comes in queen or king size with a firm or super firm mattress. 4. A pizza can be ordered with a regular or deep dish crust and with a. choice of one topping, two toppings, or three toppings.. Use the Fundamental Counting Principle to determine the number of outcomes. 5. A woman’s shoe comes in red, white, blue, or black with a choice of. high, medium, or low heels. 6. Sandwiches can be made with either ham or bologna, American or Swiss. cheese, on wheat, rye, or white bread. 7. Sugar cookies, chocolate chip, or oatmeal raisin cookies can be ordered. either with or without icing. 8. Susan can choose for her outfit a black or tan skirt, a white, pink, or. cream shirt, black or tan shoes, and a red or black jacket. Extra Practice. 635.

(39) Lesson 8-3. (Pages 384–387). Find each value. 1. 8!. 2. 10!. 3. 0!. 4. 7!. 5. 6!. 6. 5!. 7. 2!. 8. 11!. 9. 9!. 10. 4!. 11. P(5, 4). 12. P(3, 3). 14. P(8, 6). 15. P(10, 2). 16. P(6, 4). 13. P(12, 5). Extra Practice. 17. How many different ways can a family of four be seated in a row? 18. In how many different ways can you arrange the letters in the word. orange if you take the letters five at a time? 19. How many ways can you arrange five different colored marbles in a row. if the blue one is always in the center? 20. In how many different ways can Kevin listen to each of his ten CDs once?. Lesson 8-4. (Pages 388–391). Find each value. 1. C(8, 4). 2. C(30, 8). 3. C(10, 9). 4. C(7, 3). 5. C(12, 5). 6. C(17, 16). 7. C(24, 17). 8. C(9, 7). 9. How many ways can you choose five compact discs from a collection. of 17? 10. How many combinations of three flavors of ice cream can you choose. from 25 different flavors of ice cream? 11. How many ways can you choose three books out of a selection of. ten books?. Determine whether each statement is a permutation or a combination. 12. choosing a committee of 3 from a class. 13. placing 6 different math books in a line. Lesson 8-5. (Pages 396–399). Two socks are drawn from a drawer which contains one red sock, three blue socks, two black socks, and two green socks. Once a sock is selected, it is not replaced. Find each probability. 1. P(a black sock and then a green sock). 2. P(a red sock and then a green sock). 3. P(two blue socks). 4. P(two green socks). 5. P(two black socks). 6. P(a black sock and then a red sock). 7. P(a red sock and then a blue sock). 8. P(a blue sock and then a black sock). There are three quarters, five dimes, and twelve pennies in a bag. Once a coin is drawn from the bag it is not replaced. If two coins are drawn at random, find each probability. 9. P(a quarter and then a penny). 10. P(a nickel and then a dime). 11. P(a dime and then a penny). 12. P(two dimes). 13. P(two quarters). 14. P(two pennies in a row). 15. P(a quarter and then a dime). 16. P(a penny and then a quarter). 636 Extra Practice.

(40) Lesson 8-6. (Pages 400–403). FOOD For Exercises 1–6, use the survey results at the right.. Favorite Pizza Topping. 1. What is the probability that a person’s favorite pizza topping. Topping. Number. pepperoni. 45. sausage. 25. green pepper. 15. is pepperoni? 2. Out of 280 people, how many would you expect to have pepperoni as. their favorite pizza topping?. mushrooms. 3. What is the probability that a person’s favorite pizza topping is. 5. other. 10. 4. Out of 280 people, how many would you expect to have green pepper. as their favorite pizza topping? 5. What is the probability that a person’s favorite pizza topping is pepperoni. or sausage? 6. Out of 280 people, how many would you expect to have pepperoni or. sausage as their favorite pizza topping?. Lesson 8-7. (Pages 406–409). Describe each sample. 1. To predict who will be the next mayor, a radio station asks their listeners. to call one of two numbers to indicate their preferences. 2. To award prizes at a hockey game, four seat numbers are picked from a. barrel containing individual papers representing each seat number. 3. To evaluate the quality of the televisions coming off the assembly line,. the manufacturer takes one every half hour and tests it. 4. To determine what movies people prefer, people leaving a movie theater. showing an action film are asked to give their preference. 5. To form a committee to discuss how the cafeteria can be improved, one. student is picked at random from each second period class.. Lesson 9-1. (Pages 420–424). ARCHITECTURE For Exercises 1–8, use the histogram at the right. 1. How large is each interval?. Heights of 45 Buildings. 6. How many buildings are less than. 81 –9 0. 71 –8 0. 70. 60. 61 –. 5. How many buildings are taller than 70 feet?. 51 –. of buildings?. 50. 4. Which interval represents the least number. 41 –. of buildings?. 40. 3. Which interval represents the most number. 10 8 6 4 2 0. 31 –. the histogram?. Number of Buildings. 2. How many buildings are represented in. Height (feet). 51 feet tall? 7. What is the height of the tallest building? 8. How does the number of buildings between 61 and 80 feet tall compare to. the number of buildings between 31 and 50 feet tall? Extra Practice. 637. Extra Practice. green pepper?.

(41) Lesson 9-2. (Pages 426–429). Make a circle graph for each set of data.. Extra Practice. 1.. 4.. Sporting Goods Sales. 2.. Energy Use in Home. 3.. Household Income. shoes. 44%. heating/cooling. 51%. primary job. apparel. 30%. appliances. 28%. secondary job. 9%. equipment. 26%. lights. 21%. investments. 5%. other. 4%. Students in North High School. 5.. Number of Siblings. 6.. 82%. Household Expenses. 0. 25%. food. 45%. freshmen. 30%. 1. 45%. housing. 30%. sophomores. 28%. 2. 20%. utilities. 15%. juniors. 24%. 3. 5%. other. 10%. seniors. 18%. 4. 2%. 5. 3%. Lesson 9-3. (Pages 430–433). Choose the most appropriate type of display for each situation. 1. number of televisions in homes compared to the total number of homes. in the survey 2. the amount of sales by different sales people compared to the total sales 3. ages by intervals of amusement park attendees in marketing information. for the park 4. average proficiency test score for five consecutive years 5. numbers of Americans who own motorcycles, boats, and recreational vehicles 6. percent of people who own a certain type of car compared to all car owners 7. a child’s age and his or her height 8. amount of fat grams in intervals in various sandwiches 9. the number of students who have read each of three popular books 10. number of people filing tax returns electronically over the past ten years. Lesson 9-4. (Pages 435–438). Find the mean, median, and mode for each set of data. Round to the nearest tenth if necessary. 1. 2, 7, 9, 12, 5, 14, 4, 8, 3, 10. 2. 58, 52, 49, 60, 61, 56, 50, 61. 3. 122, 134, 129, 140, 125, 134, 137. 4. 36, 41, 43, 45, 48, 52, 54, 56, 56, 57, 60, 64, 65. 5. 3, 9, 14, 3, 0, 2, 6, 11. 6. 6, 3, 1, 8, 7, 2. 7. 11, 15, 21, 11, 6, 10, 11. 8. 21, 20, 19, 20, 18, 21, 23, 25. 9. 1, 3, 2, 1, 1, 2, 2, 2, 3. 10. 23, 35, 42, 26, 27, 29, 31, 29, 27. 11. 32.1, 33.5, 31.5, 37.8. 12. 25.5, 26.7, 20.9, 23.4, 26.8, 24.0, 25.7. 13. 98.6, 97.9, 98.1, 100.1, 100.2. 14. 10.1, 12.3, 11.4, 15.6, 7.3, 10.1. 638 Extra Practice.

(42) Lesson 9-5. (Pages 442–445). Find the range, median, upper and lower quartiles, interquartile range, and any outliers for each set of data. 1. 15, 12, 21, 18, 25, 11, 17, 19, 20. 2. 2, 24, 6, 13, 8, 6, 11, 4. 3. 189, 149, 155, 290, 141, 152. 4. 451, 501, 388, 428, 510, 480, 390. 5. 22, 18, 9, 26, 14, 15, 6, 19, 28. 6. 245, 218, 251, 255, 248, 241, 250. 7. 46, 45, 50, 40, 49, 42, 64. 8. 128, 148, 130, 142, 164, 120, 152, 202 10. 88, 84, 92, 93, 90, 96, 87, 97. 11. 2, 3, 5, 4, 3, 3, 2, 5, 6. 12. 6, 7, 9, 10, 11, 11, 13, 14, 12, 11, 12. 13. 117, 118, 120, 109, 117, 117, 100. 14. 12, 14, 17, 19, 13, 16, 17. Extra Practice. 9. 2, 3, 2, 6, 4, 14, 13, 2, 6, 3. 15. 378, 480, 370, 236, 361, 394, 345, 328, 388, 339 16. 80, 91, 82, 83, 77, 79, 78, 75, 75, 88, 84, 82, 61, 93, 88, 85, 84, 89, 62, 79 17. 195, 121, 135, 123, 138, 150, 122, 138, 149, 124, 149, 151, 152. Lesson 9-6. (Pages 446–449). Draw a box-and-whisker plot for each set of data. 1. 2, 3, 5, 4, 3, 3, 2, 5, 6. 2. 6, 7, 9, 10, 11, 11, 13, 14, 12, 11, 12. 3. 15, 12, 21, 18, 25, 11, 17, 19, 20. 4. 2, 24, 6, 13, 8, 6, 11, 4. 5. 22, 18, 9, 26, 14, 15, 6, 19, 28. 6. 46, 45, 50, 40, 49, 42, 64. 7. 2, 3, 2, 6, 4, 14, 13, 2, 6, 3. 8. 88, 84, 92, 93, 90, 96, 87, 97. 9. 80, 91, 82, 83, 77, 79, 78, 75, 75, 88, 84, 82, 61, 93, 88, 85, 84, 89, 62, 79 10. 195, 121, 135, 123, 138, 150, 122, 138, 149, 124, 149, 151, 152. ZOOS For Exercises 11 and 12, use the following box-and-whisker plot. Area (acres) of Major Zoos in the United States. 0. 100. 200. 300. 400. 500. 600. Source: The World Almanac. 11. How many outliers are in the data? 12. Describe the distribution of the data. What can you say about the areas. of the major zoos in the United States?. Lesson 9-7. (Pages 450–453). Graph B. Students Completing Obstacle Course. Students Completing Obstacle Course. 1. Do both graphs contain the same. information? Explain. 2. Which graph would you use to indicate that many more eighth graders finished the obstacle course than sixth or seventh graders? Explain.. Number of Students. graphs at the right.. 130 120 110 100 90 6th 7th 8th grade grade grade. Number of Students. Graph A. FITNESS For Exercises 1 and 2, use the. 120 100 80 60 40 20 0 6th 7th 8th grade grade grade. Extra Practice. 639.

(43) Lesson 9-8. (Pages 454–457). State the dimension of each matrix. Then identify the position of the circled element. 2 2 6 1. 3 2. 3. [3 4 1 0 1. . Extra Practice. 4.. . . 6 3 2 1 0 1 3 5. . 5.. . . . 6 4 1 9 0 1 2 8 11. 6.. Add or subtract. If there is no sum or difference, write impossible. 7.. . . 9.. . . . 6 5 0 2 3 1 2 1 2 7 8. 2 0 8 6 6 4 1 3. . 2 7 1 2 5 4 6 3 3 9 5 7. 13 11. 7. . . . 8.. . 10.. . 12.. 13 6. 2. . . 10 9 2 8 15 13. 4 12 1 8 6 3. . 8 5 2 1 3 11. 1]. . 6 0 1 0 8 6 2 4 0 7 2 4 1 5 8 0 0 9 5 12. 6 0 15 2. . 7 8 1 2. Lesson 10-1. . (Pages 469–473). Use the Distributive Property to rewrite each expression. 1. 2(x 3). 2. 3(a 7). 3. 3(g 6). 4. 2(a 3). 5. 1(x 6). 6. 4(a 5). 7. 6(x 1). 8. 3(2x 5). 9. 2(3x 1). 10. 1(2x 1). 11. 5(3x 2). 12. 7(2x 2). 13. 3x 2x. 14. 6x 3x. 15. 2a 5a. 16. 5x 6x. 17. 8a 3a. 18. a 4a. 19. 3a 2a 6. 20. 6x 2x 3. 21. 5a 3 2a. 22. 3x 7 5x. 23. x 3 5x. 24. 6x 3x 2. 25. a 2a 5. 26. 6x 2 7x. 27. 5a 7a 2. 28. 4a 2 7a 5. 29. 3a 2 5a 7. 30. 5x 3x 2 5. Simplify each expression.. Lesson 10-2. (Pages 474–477). Solve each equation. Check your solution. x 3. 1. 2x 4 14. 2. 5p 10 0. 3. 5 6a 41. 4. 7 2. 5. 18 6q 24. 6. 18 4m 6. 7. 3r 3 9. 8. 2x 3 5. 9. 0 4x 28. 10. 3x 1 5. 11. 3z 5 14. 12. 3x 15 12. 13. 9a 8 73. 14. 2x 3 7. 15. 3t 6 9. 16. 2y 10 22. 17. 15 2y 5. 18. 3c 4 2. 19. 6 2p 16. 20. 8 2 3x. 21. 4b 24 24. 22. 2x 3x 6 19. 23. 2x 6 14. 24. 3x 9 18. 25. 2a 3a 1 15. 26. 5x 3x 6 10. 27. 3a 5a a 11. 28. 5a 3a 5 1 10. 29. 3 7a 6a 2. 30. 3y 5y 1 15. 640 Extra Practice.

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