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

Transcription

1 Built-In Workbooks Prerequisite Skills Etra Practice Mied Problem Solving Preparing for Standardized Tests Skills Trigonometr The Tangent Ratio The Sine and Cosine Ratios Table of Trigonometric Ratios Measurement Conversion Converting Measures of Area and Volume Converting Between Measurement Sstems Reference English-Spanish Glossar Selected Answers Photo Credits Inde Formulas and Smbols 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 our memor about things ou have learned in other math classes. 1 Estimation Strategies Displaing Data on Graphs Converting Measurements within the Customar Sstem 4 Converting Measurements within the Metric Sstem 5 Divisibilit Patterns 6 Prime Factorization 7 Greastest Common Factor 8 Simplifing Fractions 9 Least Common Multiple 10 Perimeter and Area of Rectangles 11 Plotting Points on a Coordinate Plane 1 Measuring and Drawing Angles What If I Need More Practice? The Etra Practice section provides additional problems for each lesson. What If I Have Trouble with Word Problems? The Mied 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 ou tips and practice on how to answer different tpes of questions that appear on tests. What If I Need Practice in Trigonometr and Measurement Conversion? The Trigonometr section gives ou 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 customar sstems. What If I Forget a Vocabular Word? The English-Spanish Glossar provides a list of important, or difficult, words used throughout the tetbook. 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 our answers to make sure ou understand how to solve all of the assigned problems. What If I Need to Find Something Quickl? The Inde alphabeticall lists the subjects covered throughout the entire tetbook and the pages on which each subject can be found. What If I Forget a Formula? Inside the back cover of our math book is a list of Formulas and Smbols that are used in the book. Student Handbook 599

3 Prerequisite Skills Prerequisite Skills Estimation Strategies Sometimes ou do not need to know the eact answer to a problem, or ou ma want to check the reasonableness of an answer. In those instances, ou can use estimation. There are several different methods of estimation. A common method is to use rounding. Estimate b Rounding Estimate b rounding Round each number to the nearest hundred. Then multipl ,000 The product is about 60, Round each number to the nearest ten. Then add The sum is about 50. You can use clustering to estimate sums. Clustering works best with numbers that all round to approimatel the same number. Estimate b Clustering Estimate b clustering All of the numbers are close to 15. There are four numbers. The sum is about 4 15 or All of the numbers are close to 100. There are five numbers. The sum is about or 500. Compatible numbers are numbers that are eas to compute with mentall. Estimate b Using Compatible Numbers Estimate b using compatible numbers is close to 75, and 4.7 is close to The quotient is about. The fractions 8 and are close to (7 1 0) or 40 The sum is about Prerequisite Skills

4 Astrateg that works well for some addition and subtraction problems is front-end estimation. This strateg involves adding or subtracting the left-most column of digits. Then, add or subtract the net column of digits. Anne zeros for the remaining digits. Use Front-End Estimation Use front-end estimation to find an estimate. 5,8,64 5,8 5, ,64, , The sum is about 8,800. The difference is about 61. Prerequisite Skills Eercises Estimate b rounding Estimate b clustering Estimate b using compatible numbers Estimate b using front-end estimation ,456 8, Use an method to estimate , , ,715. 1, MNEY MATTERS At an arts and crafts festival, Lena selected items priced at $5.98, $7.5, $.5, $8.75, $9.85, $.50, and $7.5. 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 Prerequisite Skills Displaing Data in Graphs Statistics involves collecting, analzing, and presenting information, called data. Graphs displa data to help readers make sense of the information. Bar graphs are used to compare the frequenc of data. The bar graph below compares the average number of vacation das given b countries to their workers. Double bar graphs compare two sets of data. The double bar graph below shows the percent of men and women 65 and older who held jobs in various ears. Average Number of Das (Per Year) Vacation Time Ital France Canada Japan United States Number of People lder Workers Year Source: The World Almanac Men Women Source: The World Almanac Line graphs usuall show how values change over time. The line graph below shows the number of people per square mile in the U.S. from 1800 through 000. U.S. Population Densit Double line graphs, like double bar graphs, show two sets of data. The double line graph below compares the amount of mone spent b both domestic and foreign U.S. travelers. Tourism in U.S. People per Square Mile Source: The World Almanac Year Billions of Dollars Spent Source: The World Almanac Foreign travelers Domestic travelers Year Stem-and-leaf plots are a sstem used to condense a set of data where the greatest place value of the data is used for the stems and the net greatest place value forms the leaves. Each data value can be seen in this tpe of graph. The stem-and-leaf plot below contains this list of mathematics test scores: The least number has 6 in the tens place. Stem Leaf The greatest number has 9 in the tens place The stems are 6, 7, 8, and The leaves are ordered from least to greatest Prerequisite Skills 6 6

6 Choose a Displa Shonn is writing a research paper about the lmpics 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. Prerequisite Skills Eercises Determine whether a bar graph, double bar graph, line graph, double line graph, or stem-and-leaf plot is the best wa to displa each of the following sets of data. Eplain our reasoning. 1. how the income of households has changed from 1950 through 000. the income of an average household in si different countries. the prices for a loaf of bread in twent different supermarkets 4. the number of bos and the number of girls participating in si different school sports Refer to the bar graph, double bar graph, line graph, double line graph, and stem-and-leaf plot on page Write several sentences to describe the data shown in the graph titled Vacation Time. Include a comparison of the das worked for Canada and the U.S. 6. Write several sentences to describe the data shown in the graph titled lder Workers. What other tpe or tpes of graphs could ou use to displa this data? Eplain our reasoning. 7. Write several sentences to describe the data shown in the graph titled Tourism in U.S. What other tpe or tpes of graphs could ou use to displa this data? Eplain our reasoning. 8. Write several sentences to describe the data shown in the graph titled U.S. Population Densit. What other tpe or tpes of graphs could ou use to displa this data? Eplain our 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 tpe of graph? For Eercises 10 14, use the stem-and-leaf plot at the right that shows the number of stories in the tallest buildings in Dallas, Teas. 10. How man buildings does the stem-and-leaf plot represent? Stem 11. How man stories are there for the shortest building in the stem-and-leaf plot? the tallest building? 1. What is the median number of stories for these buildings? 1. What is the mean number of stories for these buildings? 14. Eplain how the stem-and-leaf plot is useful in displaing the data. Leaf Prerequisite Skills 60

7 Prerequisite Skills Converting Measurements within the Customar Sstem The units of length in the customar sstem are inch, foot, ard, and mile. The table shows the relationships among these units. To convert from larger units to smaller units, multipl. To convert from smaller units to larger units, divide. Customar Units of Length 1 mile (mi) 5,80 feet 1 foot (ft) 1 inches (in.) 1 ard (d) feet Larger Units Smaller Units Smaller Units Larger Units 7 ft in. 108 in ft 4 mi 4 5,80 1,10 ft 15 ft 15 5 d There will be a greater number of smaller units than larger units. There will be fewer larger units than smaller units. Convert Customar Units of Length Complete each sentence. 8 d? ft 144 in.? ft 7.5 mi? ft 8 d (8 ) ft 144 in. (144 1) ft 7.5 mi (7.5 5,80) ft 4 ft 1 ft 9,600 ft The units of weight in the customar sstem 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, multipl. To convert from smaller units to larger units, divide. Customar Units of Weight 1 pound (lb) 16 ounces (oz) 1 ton (T),000 pounds Convert Customar Units of Weight Complete each sentence. 1,400 lb? T 9 oz? lb 1,400 lb 1,400,000 or 6. T 9 oz 9 16 or 5.75 lb Capacit is the amount of liquid or dr substance a container can hold. Customar units of capacit are fluid ounces, cup, pint, quart, and gallon. The relationships among these units are shown in the table. Customar Units of Capacit 1 cup (c) 8 fluid ounces (fl oz) 1 pint (pt) cups 1 quart (qt) pints 1 gallon (gal) 4 quarts Convert Customar Units of Capacit Complete each sentence. 64 fl oz? c 4.4 gal? qt 64 fl oz 64 8 or 8 c 4.4 gal or 17.6 qt 604 Prerequisite Skills

8 Convert Customar Units Using Two Steps 1 pt? gal 1 pt (1 ) qt First, change pints 6 qt (6 4) gal 6 qt to quarts. 1.5 gal So, 1 pints 1.5 gallons. Then, change quarts to gallons. Prerequisite Skills 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) 4 hours 1 da 7 das 1 week 5 weeks 1 ear 65 das 1 ear Convert Units of Time Complete each sentence. 84 h? das 5 weeks? das 84 h 84 4 or.5 das 5 weeks 5 7 or 5 das Adding Mied Measures Find the sum of 4 feet 7 inches and 5 feet 10 inches. Simplif. 4 ft 7 in. Line up like units and add. 5ft10in. 9 ft 17 in. 9 ft (1 in. 5 in.) Separate 17 in. into 1 in. and 5 in. 10 ft 5 in. Replace 1 in. with 1 ft and add like units. Eercises Complete each sentence. 1. mi? ft. 48 oz? lb. 10 min? h T? lb 5. 5 das? h 6. 6,60 ft? mi ft? d 8. 5 gal? qt fl oz? c weeks? das c? gal ,080 in.? mi 1. 5 T? oz h? das oz? lb pt? gal mi? d gal? c ,080 d? mi das? weeks 1. 1 da? s Find each sum.. 15 ft in.. 5 gal 1 qt 4. 1 h 15 min ft 7 in. 10 gal qt 7 h55min lb 14 oz 6. 4 d ft 7. 1 das 7 h 6 lb 1 oz 16 d 1 ft 44 das 0 h Prerequisite Skills 605

9 Prerequisite Skills Converting Measurements within the Metric Sstem All units of length in the metric sstem are defined in terms of the meter (m). The diagram below shows the relationships between some common metric units. 1, kilometer meter centimeter millimeter km m cm mm 1, To convert from larger units to smaller units, multipl. To convert from smaller units to larger units, divide. Comparing Metric and Customar Units of Length 1 mm 0.04 inch (height of a comma) 1 cm 0.4 inch (half the width of a penn) 1 m 1.1 ards (width of a doorwa) 1 km 0.6 mile (length of a cit block) Converting From Larger Units to Smaller Units 1 km 1 1,000 1,000 m 1 m cm 1 cm mm Converting From Smaller Units to Larger Units 1 mm cm 1 cm m 1 m 1 1, km There will be a greater number of smaller units than larger units. There will be fewer larger units than smaller units. Convert Metric Units of Length Complete each sentence. 7 km? m 1 cm? m 8.9 cm? mm 7 km (7 1,000) m 1 cm (1 100) m 8.9 cm (8.9 10) mm 7,000 m 1. m 89 mm The basic unit of capacit in the metric sstem is the liter (L). A liter and milliliter (ml) are related in a manner similar to meter and millimeter. 1,000 1 L 1,000 ml 1,000 Comparing Metric and Customar Units of Capacit 1 ml 0.0 ounce (drop of water) 1 L 1 quart (bottle of ketchup) Convert Metric Units of Capacit Complete each sentence L? ml 750 ml? L 14.5 L ,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 sstem 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 1 g 1,000 mg Comparing Metric and Customar Units of Mass 1 g 0.04 ounce (one raisin) 1 kg. pounds (si medium apples) 606 Prerequisite Skills

10 Convert Metric Units of Mass Complete each sentence. 5 kg? g 4,500 g? kg 5 kg 5 1,000 or 5,000 g 4,500 g 4,500 1,000 or 4.5 kg Sometimes ou need to perform more than one conversion to get the desired unit. Prerequisite Skills Convert Metric Units Using Two Steps Complete each sentence. 5,000 cm? km 4.5 kg? mg 5,000 cm 5, m 4.5 kg 4.5 1,000 g 50 m 4,500 g 50 m 50 1,000 km 4,500 g 4,500 1,000 mg 0.5 km 4,500,000 mg So, 5,000 cm 0.5 km. So, 4.5 kg 4,500,000 mg. Eercises State which metric unit ou would probabl use to measure each item. 1. mass of an elephant. amount of juice in a pitcher. 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 1. cruising altitude of a passenger jet Complete each sentence mm? cm 14.,500 g? kg 15. 5,000 m? km L? ml 17. 8,000 mg? g km? m kg? g cm? mm m? cm. 8.5 kg? g. 655 ml? L cm? m m? km 6. 4,000 mm? m 7. 60,000 mg? kg 8. 8,500 cm? km 9. 5 km? cm 0. 1 kg? mg 1. 8 L? ml. 7.6 cm? mm L? ml km? m 5. 45,000 mg? kg 6. 1 km? mm 7. RACES Priscilla is running a five-kilometer race. How man meters long is the race? 8. MEDICINE Alarge container of medicine contains 0.5 liter of the drug. How man 5-milliliter doses of the drug are in this container? Prerequisite Skills 607

11 Prerequisite Skills Divisibilit Patterns If a number is a factor of a given number, ou can also sa the given number is divisible b the factor. For eample, 144 is divisible b 9 since , a whole number. A number n is a factor of a number m if m is divisible b n. A number is divisible b: if the ones digit is divisible b. if the sum of the digits is divisible b. 4 if the number formed b the last two digits is divisible b 4. 5 if the ones digit is 0 or 5. 6 if the number is divisible b both and. 8 if the number formed b the last three digits is divisible b 8. 9 if the sum of the digits is divisible b if the ones digit is 0. Use Divisibilit Rules Determine whether,418 is divisible b,, 4, 5, 6, 8, 9, or 10. : Yes; the ones digit, 8, is divisible b. : Yes; the sum of the digits, , is divisible b. 4: No; the number formed b the last two digits, 18, is not divisible b 4. 5: No; the ones digit is not 0 or 5. 6: Yes; the number is divisible b and. 8: No; 418 is not divisible b 8. 9: No; the sum of the digits, 15, is not divisible b 9. 10: No; the ones digit is not 0. So,,418 is divisible b,, and 6, but not b 4, 5, 8, 9, or 10. Eercises Determine whether each number is divisible b,, 4, 5, 6, 8, 9, or , ,700 9., , , , , Is a factor of 777? 18. Is 5 a factor of? 19. Is 6 a factor of 198? 0. Is 795 divisible b 10? 1. Is 989 divisible b 9?. Is,48 divisible b 4?. The number 87a,46b is divisible b 6. What are possible values of a and b? 4. 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 arra? Eplain. 608 Prerequisite Skills

12 Prime Factorization When a whole number greater than 1 has eactl 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 onl one factor, itself. Identif Numbers as Prime or Composite Prerequisite Skills Determine whether each number is prime, composite, or neither. 59 The numbers 1,, and 11 divide into evenl. So, is composite. The onl numbers that divide evenl into 59 are 1 and 59. So, 59 is prime. When a number is epressed as a product of factors that are all prime, the epression 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 was Notice that the bottom row of branches in ever factor tree is the same ecept for the order in which the factors are written. So, 60 5 or Ever number has a unique set of prime factors. This propert of numbers is called the Fundamental Theorem of Arithmetic. Eercises Determine whether each number is prime, composite, or neither Write the prime factorization of each number ,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. ne wa to find the GCF is to list the factors of the numbers. Find the GCF Find the greatest common factor of 6 and 60. Method 1 List the factors. factors of 6: 1,,, 4, 6, 9, 1, 18, 6 factors of 60: 1,,, 4, 5, 6, 10, 1, 15, 0, 0, 60 The greatest common factor of 6 and 60 is 1. Common factors of 6 and 60: 1,,, 4, 6, 1 Method Use prime factorization The GCF is or 1. Common prime factors of 6 and 60:,, 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 The common prime factors of 54, 81, and 90 are and. The GCF of 54, 81, and 90 is or Eercises Find the GCF of each set of numbers , 0. 7, 54. 4, , , 60 6., , , , , , 6, , 49, DESIGN Suppose ou are tiling a tabletop with 6-inch square tiles. How man of these squares will be needed to cover a 0-inch b 4-inch table? 14. SHELVING Emil is cutting a 7-inch-long board and a 54-inch-long board to make shelves. He wants the shelves to be the same length while not wasting an wood. What is the longest possible length of the shelves? Two or more numbers are relativel prime if their greatest common factor is 1. Determine whether each set of numbers is relativel prime , , 1 17., , 8, Prerequisite Skills

14 Simplifing Fractions Fractions, mied numbers, decimals, and integers are eamples of rational numbers. When a rational number is represented as a fraction, it is often epressed in simplest form. A fraction is in simplest form when the GCF of the numerator and denominator is 1. Simplif Fractions Write 0 in simplest form. 45 Method 1 Divide b the GCF. 0 5 Factor the numerator Factor the denominator. The GCF of 0 and 45 is 5 or 15. Method Use prime factorization Divide numerator and denominator b the Simplif. GCF, 15. Write the prime factorization of the numerator and denominator. Divide the numerator and denominator b the GCF, 5. Prerequisite Skills Eercises Write each fraction in simplest form. If the fraction is alread in simplest form, write simplest form , 000 6, , Both the numerator and the denominator of a fraction are even. Can ou tell whether the fraction is in simplest form? Eplain. 7. WEATHER The rainiest place on Earth is Waialeale, Hawaii. f 65 das per ear, the average number of rain das is 5. Write a fraction in simplest form to represent these rain das as a part of a ear. 8. LYMPICS In the 000 lmpics, Brooke Bennett of the U.S. swam the 800-meter freestle event in about 8 minutes. Epress 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 an whole number. List Multiples List the first si multiples of , , 15 0, 15 45, , The first si multiples of 15 are 0, 15, 0, 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, ou can list the multiples of each number until a common multiple is found, or ou can use prime factorization. Find the LCM Find the LCM of 1 and 18. Method 1 List the multiples. Method Use prime factorization. multiples of 1: 0, 1, 4, 6, 48, 1 Write the prime factorization multiples of 18: 0, 18, 6, 7, 90, of each number. 18 The LCM of 1 and 18 is 6. Multipl the factors, using the Remember that the LCM is common factors onl once. a nonzero number. The LCM is or 6. Eercises List the first si multiples of each number Find the least common multiple (LCM) of each set of numbers , , , , , , 4 17., 7, 8 18.,, , 8, , 1, , 8, 0. 10, 1, 14. 5, 5, , 1, , 170, , 10, , 100, 1, , 00, 00 9.,, 5, 7 0., 15, 5, 6 1. CIVICS In the United States, a president is elected ever four ears. Members of the House of Representatives are elected ever two ears. Senators are elected ever si ears. If a voter had the opportunit to vote for a president, a representative, and a senator in 1996, what will be the net ear the voter has a chance to make a choice for a president, a representative, and the same Senate seat? 61 Prerequisite Skills

16 Perimeter and Area of Rectangles The distance around a geometric figure is called its perimeter. The perimeter P of a rectangle is twice the sum of the length and width w, or P w. The measure of the surface enclosed b a figure is its area. The area A of a rectangle is the product of the length and width w, or A w. Find the Perimeter and Area of a Rectangle Prerequisite Skills Find the perimeter of the rectangle. P w Write the formula.. P (7) (1) Replace with 7 and w with 1. P 54 4 Multipl. P 78 Add. The perimeter is 78 feet. Find the area of the rectangle. A w Write the formula. A 7 1 Replace with 7 and w with 1. A 4 Multipl. The area is 4 square feet. 1 ft 7 ft 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 s. Estimate the Perimeter and Area of a Square Find the approimate perimeter and area of a square with side length inches. P 4s Write the formula. A s Write the formula. P Replace s with A Replace s with P 4(7) or 8 Estimate. A 7 or 49 Estimate. The perimeter is about 8 inches. The area is about 49 square inches. Eercises Find the perimeter and area of each figure in. 4. m 5 d 6 m 6.5 in. 8 d 7.5 cm 7.5 cm 5. rectangle: mm b 5 mm 6. rectangle: 144 mi b 5 mi 7. square: side length, 75 ft 8. square: side length, 0.75 d 9. rectangle: 4. cm b.7 cm 10. square: side length of 65 m 11. square: side length of 87 km 1. rectangle: mm b 45. mm Prerequisite Skills 61

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

18 Measuring and Drawing Angles Two ras that have a common endpoint form an angle. The common endpoint is called the verte, and the two ras that make up the angle are called the sides of the angle. Acircle can be divided into 60 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. verte B side side A C Prerequisite Skills Measure an Angle Use a protractor to measure FGH. Step 1 Place the center point of the protractor s base on verte G. Align the straight side with side GH so that the marker for 0 is on one of the ras F G H Step Use the scale that begins with 0 at GH. Read where the other side of the angle, GF, crosses this scale. The measure of angle FGH is 10. Using smbols, mfgh F G H Draw an Angle Draw X having a measure of 75. Step 1 Draw a ra. Label the endpoint X. Step Place the center point of the protractor s base on point X. Align the mark labeled 0 with the ra. X Step Use the scale that begins with 0. Locate the mark labeled 75. Then draw the other side of the angle X Eercises Use a protractor to find the measure of each angle. 1. XZY. SZT. SZY 4. UZX 5. TZW 6. UZV Use a protractor to draw an angle having each measurement. T U V W X S Z Y Prerequisite Skills 615

19 Etra Practice Etra Practice Lesson 1-1 Use the four-step plan to solve each problem. 1. Joseph is planting bushes around the perimeter of his lawn. If the bushes must be planted 4 feet apart and Joseph s lawn is 64 feet wide and 14 feet long, how man bushes will Joseph need to purchase?. Find the net three numbers in the pattern 1,, 7, 15, 1,..... At the bookstore, pencils cost $0.15 each and erasers cost $0.5 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 da plus $0.15 per mile. How much will it cost to rent a car for das and to drive 00 miles? 5. Josie wants to fence in her ard. She needs to fence three sides and the house will suppl the fourth side. Two of the sides have a length of 5 feet and the third side has a length of 5 feet. If the fencing costs $10 per foot, how much will it cost Josie to fence in her ard? (Pages 6 10) Lesson 1- Evaluate each epression (5 ) Etra Practice (Pages 11 15) (4 ) ( 4) 8. (15 7) 6 9. [15 ( 7) ] Evaluate each epression if a, b 6, and c a bc 11. ba 1. b c 1. a c b a 14. (c b) a 15. (a c) 16. abc 17. (b a)c b Name the propert shown b each statement. 18. (a b) a b ( 6) 5 (6 5) 1. (4 1) (4 1). (7 5) 7(5 ). 8( 1) 8() 8(1) 4. 5( ) ( )5 5. ( ) Lesson 1- Replace each with,, or to make a true sentence (Pages 17 1) Evaluate each epression

20 Lesson 1-4 Add (7) () () () (4) (11) (5) (5) (6) (18) 18. (1) (Pages 7) (1) 6 (7) (0) (14). 0 0 (9) (17) (10) 5. () () 6. 6 (4) 9 () 7. 9 (7) (75) (0) (1) 0. 9 (18) 6 () Etra Practice Lesson 1-5 Subtract (14) (10) (14) (4) (9) 1. 7 (19) (61) 1. 4 (4). (). 65 () 4. 0 () () (Pages 8 1) Lesson 1-6 Multipl. 1. 5(). 11(5). 5(5) 4. 1(6) 5. () 6. ()(4) 7. (4)(4) 8. 4(1) 9. 50(0) 10. (1) 11. () 1. () 1. 5(1) 14. ()() 15. 6(4) (Pages 4 8) Divide () (8) () (8) (7) () 6. 0 (1) (9) () 0. 1 Etra Practice 617

21 Etra Practice Lesson 1-7 Write each verbal phrase as an algebraic epression more than a number. less than a number. a number divided b 4 4. a number increased b 7 5. a number decreased b times a number 7. 8 multiplied b m divided b a number divided b n increased b 11. q decreased b 0 1. n times 41 (Pages 9 4) 1. 5 less than a number 14. the product of a number and 15 Write each verbal sentence as an algebraic equation less than the product of q and 4 is Twice is A number increased b 6 is The quotient of a number and 7 is The difference between a number and 1 is The product of a number and 7 is 4. Lesson 1-8 Solve each equation. Check our solution. 1. g 10. b 7 1. a r 4 5. t 1 6. s n v b z g f a c n j p p r (8) 14. m () q 1 5. t p t Lesson 1-9 Solve each equation. Check our solution z 16 t w b s 7. 10a s k m m 8 5 r w q w p p t 0. m h 1 4. a r 4. 6 c 1 5. m f w 9. 6r (Pages 45 49) (Pages 50 5) 618 Etra Practice

22 Lesson -1 Write each fraction or mied number as a decimal (Pages 6 66) Write each decimal as a fraction or mied number in simplest form Etra Practice Lesson - Replace each with,, or to make a true sentence rder each set of rational numbers from least to greatest , 0., 0.45,.4, , 0., 0.4, 0.4, ,, 7, 9, , 5 7, 9, 8 9, , 0., 0.0, 0.51, 18., 1, , 5, 1, 8, 7, ,, 0.61, 0.65, ,, 1, 4, , 0.4, 0.44, , 7, 65, , 1, 0.1, , 0.5, 0, 0.5, (Pages 67 70) Lesson - Multipl. Write in simplest form (Pages 71 75) Etra Practice 619

23 Lesson -4 Name the multiplicative inverse of each number (Pages 76 80) Etra Practice Divide. Write in simplest form (4) (6) Lesson -5 (Pages 8 85) Add or subtract. Write in simplest form Lesson -6 Add or subtract. Write in simplest form (Pages 88 91) 60 Etra Practice

24 Lesson -7 Solve each equation. Check our solution a 1 4 (Pages 9 95) b c 6. r n d 9. n t h k s f m 17. g v g z j. a q z 7 Etra Practice c Lesson -8 Write each epression using eponents b b b b c c c c c c a a a b b b a a a b a b b b b b b b Evaluate each epression Lesson -9 Write each number in standard form Write each number in scientific notation , , , , (Pages ) (Pages ) Etra Practice 61

25 Etra Practice Lesson -1 Find each square root , , (Pages ) Lesson - Estimate to the nearest whole number Lesson - Name all sets of numbers to which each real number belongs Estimate each square root. Then graph the square root on a number line Replace each with,, or to make a true sentence (Pages 10 1) (Pages 15 19) 6 Etra Practice

26 Lesson -4 Write an equation ou 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 necessar. (Pages 1 16) m 4 m m 6 cm cm 4. a, 6 cm; b, 5 cm 5. a, 1 ft; b, 1 ft 6. a, 8 in.; b, 6 in. 7. a, 0 m; c, 5 m 8. a, 9 mm; c, 14 mm 9. b, 15 m; c, 0 m Determine whether each triangle with sides of given lengths is a right triangle m, 8 m, 17 m d, 5 d, 9 d 1. 5 in., 1 in., 1 in in., 1 in., 16 in ft, 4 ft, 6 ft 15. ft, ft, ft cm ft 8 ft 4 ft Etra Practice Lesson -5 (Pages ) Write an equation that can be used to answer each question. Then solve. Round to the nearest tenth if necessar. 1. How far apart are the. How high does the. How long is each rafter? boats? ladder reach? ft 1 ft ft 7 mi d mi 18 ft h ft 6 ft 16 ft mi 4 ft Lesson -6 Find the distance between each pair of points whose coordinates are given. Round to the nearest tenth if necessar. (Pages ) 1... (1, ) (1, 4) (0, 4) (, ) (4, 1) (7, 1) Graph each pair of ordered pairs. Then find the distance between the points. Round to the nearest tenth. 4. (4, ), (4, 17) 5. (5, 1), (11, 7) 6. (, 5), (, 7) 7. (7, 9), (4, ) 8. (5, 4), (, 8) 9. (8, 4), (, 8) 10. (, 7), (10, 4) 11. (9, ), (, 6) 1. (, ), (1, 6) 1. (5, 1), (, ) 14. (0, 1), (5, ) 15. (1, ), (, ) Etra Practice 6

27 Lesson 4-1 Epress each ratio in simplest form to 9. 4 inches per foot. 16 out of : minutes per hour 6. 5 to wins to 16 losses 8. 7 out of out of out of minutes per hour 1. 6 inches per foot (Pages ) Etra Practice Epress each rate as a unit rate pounds gained in 1 weeks 14. $800 for 40 tickets 15. $6.50 for 5 pounds inches of rain in weeks preschoolers to teachers inches of snow in das 19. $500 for 50 tickets 0. $60 for 100 dinners Lesson 4- For Eercises 1, use the following information. (Pages ) Time 1:00 :00 :0 :00 :15 Temperature 88 F 89 F 80 F 76 F 76 F 1. Find the rate of change between :00 and :0.. Find the rate of change between 1:00 and :00.. Find the rate of change between :00 and :15. Eplain the meaning of this rate of change. For Eercises 4 7, use the following information. Time 6:00 6:0 6:45 7:00 7:10 7:0 8:00 8:15 8:0 Number of Tickets Sold Find the rate of change between 6:45 and 7: 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 8:0. 7. During which time period was the greatest rate of change? Lesson 4- (Pages ) Find the slope of each line (0, ) (, 1) (, 1) (1, ) (, ) (, ) The points given in each table lie on a line. Find the slope of the line Etra Practice

28 Lesson 4-4 Determine whether each pair of ratios forms a proportion. 1. 5, , , , , , , , , 10., , , Solve each proportion. 1. a c d n 5 b a 5. 7 z z c 0 6 t 4 (Pages ) Etra Practice Lesson 4-5 Determine whether each pair of polgons is similar. Eplain our reasoning cm. cm 4 cm 10 cm 5.1 m 4.6 m 4 m 5 m (Pages ). m m Each pair of polgons is similar. Write a proportion to find each missing measure. Then solve in. cm 4 cm in. 5 in. in..5 cm 7 cm Lesson 4-6 Solve. 1. The distance between two cities on a map is. centimeters. If the scale on the map is 1 centimeter 50 kilometers, find the actual distance between the two cities.. A scale model of the Empire State Building is 10 inches tall. If the Empire State Building is 1,50 feet tall, find the scale of this model.. n a scale drawing of a house, the dimensions of the living room are 4 inches b inches. If the scale of the drawing is 1 inch 6 feet, find the actual dimensions of the living room. 4. Columbus, hio, is approimatel 70 miles from Daton, hio. If a scale on an hio map is 1 inch 11 miles, about how far apart are the cities on the map? (Pages ) Etra Practice 65

29 Lesson 4-7 (Pages ) Write a proportion. Then determine the missing measure. 1. A road sign casts a shadow 14 meters long, while a tree nearb casts a shadow 7.8 meters long. If the road sign is.5 meters high, how tall is the tree?. Use the map to find the distance across Catfish Etra Practice Lake. Assume the triangles are similar. Catfish Lake. A 7-foot tall flag stick on a golf course casts a km shadow 1 feet long. A golfer standing nearb casts a shadow 16.5 feet long. How tall is the golfer? 1. km 0.8 km 4.5 km 4. A building casts a shadow that is 150 feet. A tree casts a shadow that is 5 feet. If the tree is 150 feet tall, how tall is the building? 5. A tower casts a shadow that is 10 feet. A pole casts a shadow that is 5 feet. If the tower is,400 feet tall, how tall is the pole? Lesson 4-8 (Pages ) Find the coordinates of the vertices of triangle A B C after triangle ABC is dilated using the given scale factor. Then graph triangle ABC and its dilation A( 1, 0), B(, 1), C(, 1); scale factor. A(4, 6), B(0, ), C(6, ); scale factor. A(1, 1), B(1, ), C( 1, 1); scale factor 4. A(, 0), B(0, 4), C(, 4); scale factor In each figure, the green figure is a dilation of the blue figure. Find the scale factor of each dilation, and classif each dilation as an enlargement or as a reduction Lesson 5-1 (Pages 06 09) Write each ratio or fraction as a percent out of out of : out of : out of : Write each percent as a fraction in simplest form. 1. 0% 14. 4% 15. 0% % 17. % % % 0. 55% 1. 8%. 48%. % 4. 51% 66 Etra Practice

30 Lesson 5- Write each percent as a decimal. 1. %. 5%. 9% 4. 6.% % 6. 14% 7..7% 8. 4% (Pages 10 14) Write each decimal as a percent Write each fraction as a percent Etra Practice Lesson 5- Write a percent proportion to solve each problem. Then solve. Round answers to the nearest tenth if necessar is 5% of what number?. What is 19% of 00?. 6 is what percent of 0? 4. 4 is what percent of 7? 5. 9 is 1 % of what number? 6. Find 55% of is what percent of? 8. What is 5% of 15? 9. 6 is 50% of what number? is what percent of 186? is 6% of what number? is 60% of what number? 1. What is 15% of 60? is 0% of what number? is 75% of what number? is what percent of 155? 17. is 5% of what number? 18. What is 65% of 150? is 75% of what number? 0. 7 is what percent of 100? (Pages 16 19) Lesson 5-4 Compute mentall % of 06. 1% of % of % of % of % of % of % of, % of % of % of % of % of % of % of % of % of % of % of % of, % of % of % of % of % of % of % of 88 (Pages 0 ) Etra Practice 67

31 Lesson 5-5 Estimate. 1. % of 1. 4% of 84. 9% of % of % of % of % of % of % of 41 (Pages 8 1) Etra Practice Estimate each percent out of out of out of out of out of out of out of out of out of 15 Estimate the percent of the area shaded Lesson 5-6 Solve each equation using the percent equation. 1. Find 5% of 7.. What is 15% of 15?. Find 80% of What is 7.% of 500? 5. Find 1% of What is 1% of 6.5? 7. Find 0.% of What is 75% of 450? 9. Find 7.% of What is 10.1% of 60? 11. Find % of What is 89% of 654? (Pages 5) 1. 0 is what percent of 64? 14. Sit-nine is what percent of 00? 15. Sevent is what percent of 150? is 0% of what number? is 14% of what number? is what percent of 150? is what percent of 5? is % of what number? Lesson 5-7 Find each percent of change. Round to the nearest tenth if necessar. State whether the percent of change is an increase or a decrease. 1. original: 5. original: 550. original: 7 new: 9 new: 45 new: original: 5 5. original: 8 6. original: 46 new: 5 new: 19 new: 55 (Pages 6 40) Find the selling price for each item given the cost to the store and markup. 7. golf clubs: $50, 0% markup 8. compact disc: $17, 15% markup 9. shoes: $57, 45% markup 10. book: $6, 0% markup Find the sale price of each item to the nearest cent. 11. piano: $4,0, 5% off 1. scissors: $14, 10% off 1. book: $9, 40% off 14. sweater: $8, 5% off 68 Etra Practice

32 Lesson 5-8 Find the simple interest to the nearest cent. 1. $500 at 7% for ears. $,500 at 6.5% for 6 months. $8,000 at 6% for 1 ear 4. $1,890 at 9% for 4 months 5. $760 at 4.5% for 1 ears 6. $1,40 at 5% for 6 months (Pages 41 44) Find the total amount in each account to the nearest cent. 7. $00 at 10% for ears 8. $,00 at 8% for 6 months 9. $0,000 at 14% for 0 ears 10. $4,000 at 1.5% for 4 ears 11. $450 at 11% for 5 ears 1. $17,000 at 15% for 9 1 ears Etra Practice Lesson 6-1 Find the value of in each figure (Pages 56 60) For Eercises 7 10, use the figure at the right. 7. Find m6, if m Find m4, if m Find m1, if m Find m7, if m 8. t q r Lesson 6- (Pages 6 65) Find the value of in each triangle Classif each triangle b its angles and b its sides cm cm 6 m m 7 in. 7 in m 7 in. Etra Practice 69

33 Lesson 6- Find each missing length. Round to the nearest tenth if necessar c ft 0 c cm b ft b cm 45 6 ft 4 cm 14 mm 0 b mm (Pages 67 70) a mm Etra Practice c in. m b m 10 in c m a in. 1 m c m 0 b m Lesson 6-4 (Pages 7 75) Find the value of in each quadrilateral Classif each quadrilateral with the name that best describes it Lesson 6-5 Determine whether the polgons are congruent. If so, name the corresponding parts and write a congruence statement. 1. A D. A B E H. K B In the figure, quadrilateral ABCD is congruent to quadrilateral EFGH. Find each measure. 4. ma 5. BC 6. GH 7. mh C 60 Etra Practice F E D 6 in. in. C F B A in. C 6 in. G 5 10 m N (Pages 79 8) 9 ft L S 4 ft 6 ft M P 6 ft E F 55 7 m D G R H Q

34 Lesson 6-6 (Pages 86 89) Complete parts a and b for each figure. a. Determine whether the figure has line smmetr. If it does, trace the figure and draw all lines of smmetr. If not write none. b. Determine whether the figure has rotational smmetr. write es or no. If es, name the angle(s) of rotation Etra Practice Lesson 6-7 (Pages 90 94) Graph the figure with the given vertices. Then graph the image of the figure after a reflection over the given ais, and write the coordinates of its vertices. 1. triangle CAT with vertices C(, ), A(8, ), and T(4, ); -ais. trapezoid TRAP with vertices T(, 5), R(1, 5), A(4, ), and P(5, ); -ais Name the line of reflection for each pair of figures Lesson 6-8 (pages 96 99) 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, ), and S(7, ) translated 9 right and 1 unit down. pentagon DGLMR with vertices D(1, ), G(, 4), L(4, 4), M(5, ) and R(, 1) translated 5 units left and 7 units down. triangle TRI with vertices T(, 1), R(0, ), and I(1, 1) translated units left and units down 4. quadrilateral QUAD with vertices Q(, ), U(, 0), A(6, 0) and D(6, ), translated units left and 1 unit down Etra Practice 61

35 Etra Practice Lesson 6-9 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(, 1), B(0, 1), and C(1, 1); 90 counterclockwise. rectangle WXYZ with vertices W(1, 1), X(1, ), Y(6, ), and Z(6, 1); 180. quadrilateral QRST with vertices Q(, 1), R(, 1), S(, ), and T(, ); 90 counterclockwise 4. triangle PQR with vertices P(1, 1), Q(, 1), and R(1, 4); 90 counterclockwise 5. rectangle ABCD with vertices A(1, 1), B(1, ), C(4, ), and D(4, 1); parallelogram GRAM with vertices G(1, ), R(, 4), A(, ), and M(1, 1); 90 counterclockwise 7. triangle DEF with vertices D(0, ), E(, ), and F(, 1); 180 (Pages 00 0) Lesson 7-1 Find the area of each figure in cm (Pages 14 18) 5 m 8 m 6 in. 1. cm. cm 4. triangle: base, 1 in.; height, 7 in. 5. triangle: base, 1 cm; height,. cm 6. trapezoid: bases, 5 ft and 7 ft; height, 11 ft 7. trapezoid: bases, d and 1 d; height, 5 d 8. parallelogram: base, 15 cm; height, cm 9. parallelogram: base, 11. in.; height, 5 in. 10. triangle: base, 7 d; height, 9 d 11. trapezoid: bases, 9 cm and 10 cm; height, 5 cm Lesson 7- Find the circumference and area of each circle. Round to the nearest tenth mm.5 m 6 d (Pages 19 ) in. 16 ft.4 cm mm 5 in..4 m 6 Etra Practice