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187 Copyright © Wright Group/McGraw-Hill STUDY LINK 71 Exponents Name Date Time In exponential notation, the exponent tells how many times the base is used as a factor. For example, 6 46  6  6  6 1,296. The base is 6, and the exponent is 4. The product is written as 1,296 in standard notation. 1. Complete the table. Exponential Base Exponent Repeated FactorsStandard Notation Notation 93 93 9  9  9 729 45 7  7  7  7 1 0  10  10  10  10  10 262,144 Describe the mistake. Then find the correct solution. 2. 636 3 9 Mistake: Correct solution: 3. 299 9 18 Mistake: Correct solution: 4. 474  7 28 Mistake: Correct solution: 5. 351.82 n366.52 6. 100 r99.52 7. 4 7u 1 79 nru Practice 6

Copyright © Wright Group/McGraw-Hill LESSON 71 Name Date Time Exploring Exponents The number sentences below contain exponents.Find the pattern, and complete the number sentences. 1. 3  3 3 2 3  3  3 3 3 3  3  3  3 3 4 2. 5  5 5 2 5  5  5 5 3 5  5  5  5 5 4 3. 18  18 18 2 18  18  18 18 3 18  18  18  18 18 4 4. 7  7 7 3 7  7  7  7  5. 4  4  4  4  4  4  4  6. 26 7. If you were going to explain to someone how to use exponents to write a number, what would you say? Try This Write the repeated-factor expression or the exponential notation. 8. 28 6 9. 309  309  309  309 309  10. 23 2 3 188

189 Copyright © Wright Group/McGraw-Hill LESSON 71 Name Date Time Patterns with Fibonacci Numbers 1. The sequence of numbers 1, 1, 2, 3, 5, 8, 13, … is called the Fibonacci sequence.In the Fibonacci sequence, every number, starting with the third number, is equal to the sum of the two numbers that come before it. Examples: Third number: 1 1 2 Fourth number: 1 2 3 Fill in the next three Fibonacci numbers. 1, 1, 2, 3, 5, 8, 13, , , 2. Study the following pattern: 1 21 21 2 1 21 22 22 3 1 21 22 23 23 5 1 21 22 23 25 25 8 a. Write the next two number sentences in the pattern. b. Describe the pattern in words. 3.a. Solve the following problems: 2 2(1 3)  3 2(2 5)  5 2(3 8) 8 2(5 13)  b. Write the next two number sentences in the pattern. c. Describe the pattern in words.

Copyright © Wright Group/McGraw-Hill 190 190 LESSON 71 Name Date Time Counting Computer Passwords The computer at a local library provides a different computer password for every library card. The passwords can include letters, numbers, or a combination of letters and numbers. Both lower-case and upper-case letters can be used. This results in 62 choices for each character in the password. 62 choices for each character 1. List three possible 4-character passwords. a. b. c. 2. The total number of possible passwords can be found by using 62 as a factor 4 times. 62 62 62 62, or 62 4 Use your calculator to find the number of different possible 4-character computer passwords. AaB bCcD dEeF f GgH h I i J j Kk L l MmN n O o P p Q q R r SsT t UuV vWwX x YyZ z0 12 34567 89

191 Copyright © Wright Group/McGraw-Hill STUDY LINK 72 Guides for Powers of 10 4–6 376 Name Date Time There are prefixes that name powers of 10. You know some of them from the metric system. For example, kilo- in kilometer (1,000 meters). It’s helpful to memorize the prefixes for every third power of 10 through one trillion. Memorize the table below. Have a friend quiz you. Then cover the table, and try to complete the statements below. 1. More than 10 9, or one ,people live in China. 2. One thousand, or 10 , feet is a little less than 1 5of a mile. 3. Astronomers estimate that there are more than 10 12, or one , stars in the universe. 4. More than one million, or 10 , copies of The New York Timesare sold every day. 5. A kiloton equals one , or 10 , metric tons. 6. A megaton equals one , or 10 , metric tons. Standard Number-and-Word Exponential Prefix Notation Notation Notation 1,000 1 thousand 10 3 kilo- 1,000,000 1 million 10 6 mega- 1,000,000,000 1 billion 10 9 giga- 1,000,000,000,000 1 trillion 10 12 tera- Practice Find the prime factorization of each number, and write it using exponents. 7. 48  8. 60  Write each number in expanded notation. 9. 3,264  10. 675,511 

192 Copyright © Wright Group/McGraw-Hill LESSON 72 Name Date Time Powers of 10 Find the patterns and complete the table below. Do not use your Student Reference Book. 1,000,000 100,000 10,000 1,000 100 10 1 hundreds ones 10[100,000s] 10[100s] 10[tenths] 10 10 10 10 10 10 10 5 10 1 10 0 Describe at least three patterns that you see in the table. 1. 2. 3.

193 Copyright © Wright Group/McGraw-Hill LESSON 72 Name Date Time Negative Powers of 10 Our base-ten place-value system works for decimals as well as for whole numbers. Negative powers of 10 can be used to name decimal places. Example:10 2  11 0 2  101 10   11 011 00.1 0.1 0.01 Very small decimals can be hard to read in standard notation, so people often use number-and-word notation, exponential notation, or prefixes instead. Tens Ones . Tenths Hundredths Thousandths 10s 1s. 0.1s 0.01s 0.001s Use the table above to complete the following statements. 1. A fly can beat its wings once every 10 3 seconds, or once every one thousandth of a second. This is one second. 2. Earth travels around the sun at a speed of about one inch per microsecond. This is 10 second, or a of a second. 3. Electricity can travel one foot in a nanosecond, or one of a second. This is 10 second. 4. In 10 second, or one picosecond, an air molecule can spin once. This is one of a second. Guides for Small Numbers Number-and-Word Exponential NotationStandard Prefix Notation Notation 1 tenth 10 1  11 0 0.1 deci- 1 hundredth 10 2  101 10  0.01 centi- 1 thousandth 10 3  1011 010  0.001 milli- 1 millionth 10 6  0.000001 micro- 1 billionth 10 9  0.000000001 nano- 1 trillionth 10 12 0.000000000001pico- 1 101010101010101010101010 1 10 10 10 10 10 10 10 10 10 1 10 10 10 10 10 10

194 Copyright © Wright Group/McGraw-Hill STUDY LINK 73 Interpreting Scientific Notation 8 Name Date Time Scientific notationis a short way to represent large and small numbers. In scientific notation, a number is written as the product of two factors. One factor is a whole number or a decimal. The other factor is a power of 10. Scientific notation:4 10 4 Meaning:Multiply 10 4(10,000) by 4. 4 º 10 44 º 10,000 40,000 Number-and-word notation:40 thousand Scientific notation:6 º 10 6 Meaning:Multiply 10 6(1,000,000) by 6. 6 º 10 66 º 1,000,000 6,000,000 Number-and-word notation:6 million Complete the following statements. 1. The area of Alaska is about 6 º 10 5, or thousand, square miles. The area of the lower 48 states is about 3 º 10 6, or million, square miles. 2. There are about 6 º 10 9, or billion, people in the world. 3. It is estimated that about 5 º 10 8, or , people speak English as their first or second language. 4. In Bengal, India, and Bangladesh there are about 2.6 º 10 8, or , people who speak Bengali. 5. At least 1 person in each of 1 10 7households, or , watches the most popular TV shows. Source: The World Almanac and Book of Facts, 2000 Guides for Powers of 10 10 3 one thousand 10 6 one million 10 9 one billion 10 12 one trillion Practice 6. 5 (3 24 2)  7. 3 (9 16)  8. 2 (9 h) 20 9. g(7 22 2)

195 Copyright © Wright Group/McGraw-Hill LESSON 73 Name Date Time Using Place Value to Rename Numbers Billions Millions Thousands Ones 100 10 1 100 10 1 100 10 1 100 10 1 1. 13 00 2. 3. 4. Example: 1. 2.3. Write the numbers from the name-collection box tag in the place-value chart. Then follow the pattern in Problem 1 to complete each name-collection box. 1,300 1,000 + 300 1 thousand 3 hundred 13 hundred 1 13 00 00 0  th ou sa n d s 1 13 0 th ou sa n d s 1.3 thou sa nd s 1,600,000 1,400,000 1,800

196 Copyright © Wright Group/McGraw-Hill LESSON 73 Name Date Time Writing in Expanded Notation A Standard Notation: 325 B Expanded Notation as an addition expression: 300 20 5 C Expanded Notation as the sum of multiplication expressions: (3 º 100) (2 º 10) (5 º 1) D Expanded Notation as the sum of multiplication expressions using powers of 10: (3 º 10 2) (2 º 10 1) (5 º 10 0) Write each number below in the other three possible ways, as shown above. 1.a. 5,314 b. c. d. 2.a. b. 2,000 700 50 6 c. d. 3.a. b. c. (9 º 100) (8 º 10) (3 º 1) d. 4.a. b. c. d. (7 º 10 3) (4 º 10 2) (5 º 10 1) (2 º 10 0)

Make each sentence true by inserting parentheses. 1. 2 = 32 4 / 1 2. 3 = 4 3 1 / 2 3. 4 3 1 4 / 2 4. Write seven names for 8. Use only numbers less than 10, and use at least three different operations in each name. Use parentheses. Follow the directions in Problem 7 to fill in the last two rows. 197 Copyright © Wright Group/McGraw-Hill STUDY LINK 74 Using Parentheses Name Date Time Reminder:When you have a pair of parentheses inside another pair, the parentheses are called nested parentheses. Example:8 ((5 6) 2) / 4 Make each sentence true by inserting parentheses. 5. 1 4 1 3/ 2 6. 7 4 3/ 21 7. Add two names to your name-collection box in Problem 4. Use nested parentheses. Find the number that each variable represents. 8. 215 2(1 11 2a) 9. (1 1 2p) 2 212 10. 65 8d7 1 85 11. 6.4 y6 2 5 Practice 8 222 223

198 Copyright © Wright Group/McGraw-Hill LESSON 74 Name Date Time Reviewing Parentheses 1. Read the following sentence. Mary Grace the lizard ate three crickets. This sentence could have multiple meanings. 1. The speaker is telling someone named Mary Grace that the lizard ate three crickets. 2. The lizard, named Mary Grace, ate three crickets. 3. The speaker is telling someone named Mary that the lizard, named Grace, ate three crickets. Without commas, it’s hard to tell which meaning was intended. Write the number of the meaning next to each sentence below. a. Mary Grace, the lizard, ate three crickets. b. Mary Grace, the lizard ate three crickets. c. Mary, Grace the lizard, ate three crickets. By adding commas, the meaning of a sentence becomes clear. In number sentences, parentheses are used to indicate what to calculate first. 2. Insert parentheses in each sentence to make the sentence true. a. 3 4 7 33 b. 6 9 5 51 c. 27 / 4 5 6 9 3. Insert parentheses in the expressions below, and find their solutions. a. 7 5 4  b. 6 9 3 

199 Copyright © Wright Group/McGraw-Hill LESSON 74 Name Date Time Describing Dot Patterns The total dots in this dot array can be found by using patterns. Here is one way to find the total: Use shape outlines or colors to identify a pattern on this dot array. Write a number model for your pattern. Then write a number story that matches your number model. Number model: Number story: ((3 3) (4 3) 4)

Copyright © Wright Group/McGraw-Hill 200 STUDY LINK 75 Order of Operations 223 Name Date Time Rules for Order of Operations 1 Do operations inside parentheses. 2 Calculate all expressions with exponents. 3Multiply and dividein order, from left to right. 4Addand Subtractin order, from left to right. Solve. 1. 4 5 º 6  2. (2 3) 2 3. 12 º 2 8 2  4. 115 10 23 º 5  5. 6 º (3 2 2) 2  6. 7 9 º 7 3  Write true or false for each number sentence. Follow the rules for order of operations. 7. 3 4 º 5 35 8. (3 4) º 5 35 9. 0 3 º 4 12 10. 0 (3 º 4) 12 11. 36 12 3 º 4 12. 36 (12 3) º 4 13. 8 2 6 1 14. 8 (2 6) 1 Practice Find the number that each variable represents. 15. 354 º 26 z 16. 907 º 86 r 17. 3.000 1.75 s 18. 0.006 3.2 0.75 4 h

201 Copyright © Wright Group/McGraw-Hill LESSON 75 Name Date Time Evaluating Expressions Janet and Alisha are using their calculators to evaluate expressions. Janet has a four-function calculator, and Alisha has a scientific calculator. They both enter the same key sequence, but their calculator displays are different. 1. Study the key sequence and calculator displays below. 2. Decide the order that each calculator used to perform the operations. Use parentheses to write a number sentence that models each order. a. Number model for Janet’s calculator: b. Number model for Alisha’s calculator: 3. Use your number models in Problem 2 to evaluate the following key sequence. Then complete the table for each calculator. Key Sequence Janet’s Display Alisha’s Display 16 13 2 5 + 3 4. Write number models that show what each calculator did in Problem 3. a. Number model for Janet’s calculator: b. Number model for Alisha’s calculator: Key Sequence Janet’s Display Alisha’s Display 2 ÷ 8 – 7 + 3 5 Try This

202 Copyright © Wright Group/McGraw-Hill LESSON 75 Name Date Time Discovering Exponent Patterns Try This Look for a pattern in the number sentences below. Then use the pattern to solve Problems 1–3. 7 27 37 5 12 712 312 10 34 634 634 12 1. 222 3 Explain how you can prove your answer to Problem 1 is correct. 2. 555 7 3. 94 894 2 Describe the pattern you are using to solve the problems. 4. Circle the problem below for which the pattern does notwork. 28 55 3 14 814 9 22 522 2 5. What do you think happens when two numbers with the same base are divided? 6. Solve this problem to check your prediction. 2 5/ 2 3

203 Copyright © Wright Group/McGraw-Hill STUDY LINK 76 Making Line Graphs Name Date Time Bar graphs, circle graphs, and line graphs display information in a way that makes it easy to show comparisons, but line graphs can also show trends. 1. Use the information in the line graph to write two true statements about movie ticket sales. 2. The table data lists the estimated percent of households with television sets from 1940 to 2000. Plot the data on the line graph below. Estimated Percent of Households with Television Sets, 1940–2000 Year1940 1950 1960 1970 1980 1990 2000 Percentage0% 12% 88% 96% 98% 98% 98% 3. Compare the information in the line graphs from Problems 1 and 2. What relationships do you see? 1920 1930 1940 1950 1960 1970 1980 1990 2000 100 80 60 40 20 0 Millions of Tickets Average Number of Movie Tickets Sold per Week (in Millions), 1922–2000 Total Population 1930 123 million 1960 151 million 2000 281 million 1940 1950 1960 1970 1980 1990 2000 Percent of Total Households Estimated Percent of Households with Television Sets, 1940–2000 100% 80% 60% 40% 20% 0% 124

204 Copyright © Wright Group/McGraw-Hill LESSON 76 Name Date Time Looking at Line Graphs Look closely at the graph you have. List each of the following features for your graph. If any of the features are missing from your graph, make up one that is appropriate. 1. Title of the graph: 2. Label for the horizontal axis: 3. Label for the vertical axis: 4. Range of the data: 5. Write three questions that can be answered by looking at your graph. 6. Line graphs are often used to show trends—how things change over time. If your graph shows a trend, describe what it shows. If not, explain what you think the graph tells you.

205 Copyright © Wright Group/McGraw-Hill LESSON 76 Name Date Time Graphing Sets of Data on a Line Graph The following table shows the average high and low temperatures (°F) of a city in the Midwest United States. Average Temperatures (°F) MonthJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec High33 36 46 59 72 80 85 82 75 62 49 38 Low20 22 29 39 51 60 65 64 56 45 36 25 Make a line graph for this data using the grid below. Use a different colored pencil to connect the points for each data set. 1. Choose and write a title for the graph. 2. Label each axis. 3. Plot all the points for the high temperatures. Connect the data points. Write the words High Temperatureabove the line formed. 4. Plot all the points for the low temperatures. Connect the data points. Write the words Low Temperatureunder the line formed. vertical axis label horizontal axis label title Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Copyright © Wright Group/McGraw-Hill 206 STUDY LINK 77 Greater Than or Less Than? Name Date Time 13. 92.47 f105 14. 32 15 25 8 s10 2 15. 413 2n5 16. 413 2r3 16 2 Name a number between each pair of numbers. 1. 2 and 3 2. 1.5 and 2 3. 5 and 6 4. 9.5 and 10 Order each set of numbers from leastto greatest. 5. 51 4, 3.8, 1.2, 1, 5 3 8 6. 6, 4 1 2, 0.5, 7, 0 True or false? Write T for true and F for false. 7. 6 5 8. 51 2 5 3 6 9. 2.5 3.5 10. 4 is less than 0 Write one true and one false number sentence. In each sentence, use at least one negative number and one of the , , or symbols. Label each sentence T or F. 11. 12. Practice Find the number that each variable represents. 32 66 67 91

207 Copyright © Wright Group/McGraw-Hill LESSON 77 Name Date Time Change in Price A local store is changing the price of some popular items. Listed below are the items with the new changes. Complete the table. 1. Which item has the largest price increase? 2. Which item has the largest price decrease? 3. Which item has a 20% change? 4. If you were to purchase a hat and belt after the price change, would you pay more or less than the original price? How much more or less? 5. If you purchased one each of the items before the price changes and one of each item after the price changes, what would be the total change in cost? State your answer as a positive or negative number. Explain your solution. Item Original PriceChange in Price Change in Price Price After (Fraction) (Dollars) Change Gloves$5.00 1 5 $1.00 $4.00 Hats$7.50 11 0 $6.75 Belts$10.00 1 4 Socks$1.50 1 2 Pants$12.00 21 0 Shirts$8.50 13 0

Copyright © Wright Group/McGraw-Hill 208 STUDY LINK 78 Positive and Negative Numbers 81 91–94 Name Date Time 200 225 Rule out in out  25  in Write or . 1. 7 6 2. 0.01 32 3. 8.5 10 3 4.  3 4 1.6 Find the account balance. $1 cash. $1 debt. 5. Balance $ 6. Balance $ Solve these addition problems. 7. 15 6  8. 17 (5)  9. 56 (32)  10. 90 (20)  11. 18 (15)  12. 987 987  13. Use the rule to complete the table.   in out 25 50 25 100 100 0 Find the number that each variable represents. 14. 32 3 3j 15. 79 3 a 3 16. 1 29 5º y y 5 77 5 17. 17 05 0  p p 1 25 0 Practice                 

209 Copyright © Wright Group/McGraw-Hill STUDY LINK 79 Addition and Subtraction Problems 92–94 Name Date Time Solve each problem. Be careful. Some problems involve addition, and some involve subtraction. 1. 25 (16)  2. 0 (43)  3. 4 (4)  4. 4 4  5. 29 (11)  6. 9 (11)  7. 100 15  8. 10 10.5  9. 41 2(2 1 2)  10. 10 20 11. For each temperature change in the table, two number models are shown in the Temperature after Change column. Only one of the number models is correct. Cross out the incorrect number model. Then complete the correct number model. Reminder: To subtract a number, you can add the opposite of that number. Temperature Temperature Temperature after Change before Change Change 40° up 7° 40 7  40 (7)  10° down 8° 10 (8)  10 8  15° up 10°15 10  15 10  (15° below zero) 20° down 10°20 10  20 (10)  (20° below zero) Find the number that each variable represents. 12. 684 º 96 u 13. 69 e23 14. 32.486 1.645 w 15. 9.45 m3.99 Practice

210 Copyright © Wright Group/McGraw-Hill LESSON 79 Name Date Time Comparing Elevations This number line shows the elevation of several places. Elevation measures how far above or below sea level a location is. For example, an elevation of 5,300 for Denver means that Denver is 5,300 feet above sea level. An elevation of 280 for Death Valley means that some point in Death Valley is 280 feet below sea level. Fill in the table below. Use the example as a guide. Example: If you start at Denver and travel to Atlanta, what is your change in elevation? Solution: Draw an arrow next to the number line. Start it at the elevation for Denver (5,300 feet). End it at the elevation for Atlanta (1,000 feet). Use the number line to find the length of the arrow (4,300 feet). Your final elevation is lower, so report the change in elevation as 4,300 feet down. Write a number model for the problem: 5,300 1,000 4,300. 5,300 Denver, CO 2,400 Tucson, AZ 1,000 Atlanta, GA 600 Chicago, IL 0 Sea Level 280 Death Valley, CA 1,300 Dead Sea (Israel/Jordan) 4,300 Start at Travel to Change in Elevation Number Model Denver Atlanta 4,300 feet down 5,300 1,000 4,300 Chicago Tucson feet Death ValleyDead Sea feet Dead SeaDeath Valleyfeet TucsonDeath Valleyfeet Dead Sea Atlanta feet

211 Copyright © Wright Group/McGraw-Hill LESSON 710 Slide Rule 21012345678 Fraction slider Integer slider Fraction holder345678 2 1 0 –1 –2 Integer holder 0 –1 –2 –3 –4 –5 –6 –7 –8 –9 –10 –11 –12 –13 –14 –15 –16 –17 –18 –19 – 201 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19 2011 15 17 18 19 20 16 14 13 12 11 10 9 8 7 6 5 34 2 1123 910 45 768 11 1312 1716 15 14 18 19 20 0

Copyright © Wright Group/McGraw-Hill 212 Copyright © Wright Group/McGraw-Hill STUDY LINK 710 Positive and Negative Number Review 92–94 221 223 Name Date Time Write ,or . 1. 8 5 2. 3 10 3. 10 20 4. 12 15 5. 3 4 1 6. 32 6 Add or subtract. 7. 20 15  8. 14 (7)  9. 8 12  10. 3 (9)  11. 4 7  12. 10 16  13. 5 (11)  14. 8 12  Some of the following number sentences are true because they follow the rules for the order of operations. Some of the sentences are false. Make a check mark next to the true number sentences. Insert parentheses in the false number sentences to make them true. 15. 3 7 º 5 38 16. 5 20 5 1 17. 2 3º 4 4 18. 2 3 º 4 10 19. 3 5 º 2 (6)37 20. 42(3) (5) º 2 20 21. a. Julie arrived 20 minutes before the race began. She started right on time. It took her 24 minutes to finish the 6-kilometer race. She stayed 10 minutes after the race to cool off; then she left. If she arrived at the race at 9:10 A.M., what time was it when she left? b. Explain how you found your answer.

213 Copyright © Wright Group/McGraw-Hill LESSON 710 Name Date Time Using a Slide Rule for Mixed Numbers Use your slide rule to solve the problems below. 1. 13 1 23 3 4 2. 18 1 1 2 3. 11 5 8(6 3 4)  4. 16 1 23 3 8 5. 12 3 8(4 3 4)  6. 5 1 8(14 1 2)  Write an explanation for how to use a slide rule to solve problems with multidigit mixed numbers. LESSON 710 Name Date Time Using a Slide Rule for Mixed Numbers Use your slide rule to solve the problems below. 1. 13 1 23 3 4 2. 18 1 1 2 3. 11 5 8(6 3 4)  4. 16 1 23 3 8 5. 12 3 8(4 3 4)  6. 5 1 8(14 1 2)  Write an explanation for how to use a slide rule to solve problems with multidigit mixed numbers.

Copyright © Wright Group/McGraw-Hill 214 STUDY LINK 711 Unit 7 Review 5–9 Name Date Time 1. Circle the number sentences that are true. 25 (6) 32 4 22 4 15 º 15 º 15 15 3 21 º 21 21 3 5 (58) 53 25 5 2(2) Write each number as a power of 10. 2. 1,000,000 3. 10,000 4. 1 hundred-thousand 5. 1 billion Match the number written in number-and-word notation with its standard notation. Fill in the oval next to the correct answer. 6. 3 million 7. 20 thousand 300,000 200,000 30,000,000 20,000 3,000,000 2,000,000 30,000 20,000,000 8. 640 thousand 9. 2.6 million 6,400,000 26,000,000 64,000,000 2,060,000 640,000,000 20,600,000 640,000 2,600,000 Write the following numbers in expanded notation. 10. 8,759 11. 87.59

215 Copyright © Wright Group/McGraw-Hill STUDY LINK 711 Unit 7 Review continued Name Date Time Write each number in scientific notation. 12. 8 million 13. 7 billion 14. 3 thousand 15. 17 billion 16. Louise bought three 6-pack containers of yogurt. She ate 5 individual containers of yogurt in one week. How many containers did she have left? Number model: Answer: 17. The water in Leroy’s and Jerod’s fish tank had evaporated so it was about 5 8inch below the level it should be. They added water and the water level went up about 3 4inch. Did the water level end up above or below where it should be? How much above or below? Number model: Answer: Find the number that each variable represents. 18. 2.4 62.8 3.752 f 19. 86.54 b87 20. 33 1 3% p100% 21. 6,284 4 a 22. 8,463 8 v 23. 963 7 k 5–9

216 Copyright © Wright Group/McGraw-Hill LESSON 711 Name Date Time Broken CalculatorProblems Change the display in the calculator without using the broken key. You may only add and subtract negative numbers to reach the ending number.The first one is done for you. Starting Ending Broken Keystrokes Number Number Key Make up five problems of your own. When you have finished, trade papers with your partner, and solve each other’s problems. You may only add and subtract negative numbers to reach the ending number.Starting Ending Broken Keystrokes Number Number Key 38 48 0 38 5 5 24 70 6 200 89 1 351 251 0 1,447 1,750 3 (–) – (–) –

217 Copyright © Wright Group/McGraw-Hill 217 STUDY LINK 712 Unit 8: Family Letter Name Date Time Fractions and Ratios In Unit 4, your child reviewed equivalent fractions. In this unit, we will apply this knowledge to compute with fractions and mixed numbers. Students will learn that the key to fraction computation with unlike denominators is to find common denominators. Unit 8 also introduces fraction multiplication. Students will use folded paper to represent fractions of a whole. Then the class will study fraction multiplication using area models, which are diagrams that show a wholedivided into parts. This concept building will lead to a rule for multiplying fractions: b aº dc ba ºº dc Example: 2 5º 3 4 2 5º º3 4   26 0, or 13 0 For mixed-number multiplication, students will rename the mixed numbers as fractions, then use the rule to multiply. Finally they rename the product as a mixed number. Example: 21 2º1 2 3 5 2º 5 3 5 2º º5 3   2 654 1 6 Your child might want to use partial products to solve this problem: 2 1 2º1 2 3can be thought of as (2  1 2)º(1 2 3). There are 4 partial products, as indicated by arrows: 2º12 2º 2 3 4 3  1 2º1 1 2  1 2º 2 3 2 6 Add the partial products: 2  4 3 1 2 2 62 8 6 3 6 2 62 1 634 1 6 Your child will play several games such as, Build-ItandFraction Action, Fraction Friction,to practice sorting fractions and adding fractions with unlike denominators. Finally, as part of the American Tour, students will explore data related to population distribution and household sizes. Please keep this Family Letter for reference as your child works through Unit 8.(2 1 2)º (1 2 3)

Copyright © Wright Group/McGraw-Hill 218 Unit 8: Family Letter cont. STUDY LINK 712 area model A model for multiplication problems in which the length and width of a rectangle represent the factors and the area represents the product. discount The amount by which a price of an item is reduced in a sale, usually given as a fraction or percent of the original price, or as a “percent off.” For example, a $4 item on sale for $3 is discounted to 75% or 3 4of its original price. A $10.00 item at 10% off costs $9.00, or 11 0less than the usual price. majority A number or amount that is more than half of a total number or amount. quick common denominator The product of the denominators of two or more fractions. For example, the quick common denominator of 3 4and 5 6is 4 624. In general, the quick common denominator of baand dcis b d. unit fraction A fraction whose numerator is 1. For example, 1 2,1 3,1 8, and 21 0are unit fractions. Unit fractions are especially useful in converting between measurement systems. For example, because 1 foot 12 inches you can multiply a number of inches by 11 2to convert to feet. unit percent One percent (1%). Vocabulary Important terms in Unit 8: In Unit 8, your child will practice skills with fractions and other numbers by playing the following games. For detailed instructions of most games, see the Student Reference Book. Build-ItSeeStudent Reference Book,p. 300. This game for partners requires a deck of 16 Build-Itfraction cards. This game provides practice in comparing and ordering fractions. Factor CaptorSeeStudent Reference Book,p. 306. Partners play this game with a calculator and paper and pencil. This game provides practice finding factors of a number. Mixed-Number SpinSeeStudent Reference Book,p. 322. Partners use a spinner to randomly select fractions and mixed numbers, used to complete number sentences. This game provides practice in adding and subtracting fractions and mixed numbers. Frac-Tac-ToeSeeStudent Reference Book,p. 274–276. This game for partners requires a deck of number cards 0–10 and a gameboard similar to a bingo card. The game provides practice converting between fractions, decimals, and percents. Fraction Action, Fraction FrictionSeeStudent Reference Book,p. 312. This game for partners requires a set of 16 Fraction Action, Fraction Frictioncards. The game provides practice adding fractions with unlike denominators. Name That NumberSeeStudent Reference Book,p. 325. Partners play a card game. This game provides practice in using order of operations to write number sentences. Building Skills through Games

219 Copyright © Wright Group/McGraw-Hill Do-Anytime Activities To work with your child on the key concepts, try these rewarding activities. 1.Ask your child to measure the lengths of two objects using a ruler. Then ask him or her to calculate the sum and difference of their lengths. 2.Ask your child to explain how to use the fraction operation keys on his or her calculator. For example, ask your child to show you how to enter fractions and mixed numbers, simplify fractions, and convert between fractions and decimals. 3.Help your child identify advertisements in signs, newspapers, and magazines that use percents. Help your child find the sale price of an item that is discounted by a certain percent. For example, a $40 shirt reduced by 25% costs $30. As You Help Your Child with Homework As your child brings assignments home, you might want to go over the instructions together,clarifying them as necessary. The answers listed below will guide you through this unit’s Study Links. Unit 8: Family Letter cont. STUDY LINK 712 Study Link 8 1 1. 3 6 2. 2 3 3. 5 6 4. 1 29 0 5. 19 7 6. 4 7 7.Sample answer: The quick common denominator is 21 º17, or 357. 1 21 1 1 21 1º º1 17 7   1 38 57 7, and 19 7 10 79 ºº2 21 1   1 38 59 7. So 19 7is greater. 8.0.759.0.6  10.0.625 11.0.712.0.5513.0.84 14.Sample answer: 1 8is half of 1 4(0. 225 0.125 ). 5 8 4 8 1 80.50.125, or 0.625. 15.16.17. 18.19.20. 21.Sample answer: 6 7 1 71. 1 8is less than 1 7, so 6 7 1 8is less than 1. Study Link 8 2 2. 2 3.10 2 3 5.5 1 2 7.69.1411.5 1 4 13.9 3 8 15.8 1 4 Study Link 8 3 1.113.106.6 5 3 7.2 1 2 9.2 1 5 11.5 4 9 13.2 1 4 15. 1 2 Study Link 8 4 1. 4 5;1 25 05 0 2. 1 2 3. 1 2 4. 1 2 5. 1 2 6. Study Link 8 5 1. 13 2, or 1 4 2. 16 5, or 2 5 5.Nina: 1 2; Phillip: 1 6; Ezra: 1 6; Benjamin: 1 6  4 61 6 5 6 6 6 15

Copyright © Wright Group/McGraw-Hill 220 Study Link 8 6 1. 1 3º 2 5 12 5 3. 7 8º 1 3 27 4 5. 1 10 8, or 5 9 7. 1 22 5 9. 65 3 11.9; 3 Study Link 8 7 7. 8. 5.Rules and tables vary. Study Link 8 8 1. a. 4 26 4, or 1 1 11 2 b. 1 40 0, or 1 4 c. 8 25 4, or 3 1 23 4 d. 1 27 45, or 7 27 4 e. 2 69 06, or 4 1 14 5 f. 3 46 04, or 9 11 0 2. a.8 5 9 b.5 1 2 c.2 11 2 3. a.5b.5 5 8 Study Link 8 9 1. 14 05 0; 0.45; 45% 13 0; 0.3; 30% 12 0; 0.2; 20% 11 05 0; 0.15; 15% 2.Calculated discounts: $100.00; $1,600.00; $7.84; $0.75; $8.70; $5.28; $810.00; $385.00 Study Link 8 10 1.4;203.1,200 miles 5.16 min.6.yes Study Link 8 11 Sample answers for Problems 1– 4: 1. 1 14 6,2 38 2,3 45 0 2. 6 8,19 2,1 12 6 3. 1 2,2 4,3 6 4. 4 6,6 9,18 2 5. 3 8 6. 5 9 7. 7 9 8. 17 2 9.Sample answer: I changed 14 0and 17 2to fractions with a common denominator. 14 0 2 64 0and 17 2 3 65 0. Because 1 2 3 60 0,17 2 is65 0away from 1 2, and 14 0is66 0away from 1 2. So, 17 2is closer to 1 2. 11. 1 11 8 13. 1 27 4 14. 13 0 15.3 1 3 Study Link 8 12 1.52.22 3.3 4 5 5.1 5 9 7.8 15 2 9.11 1 4 11.4 1 2 13. 1 25, or 7 1 2 Unit 8: Family Letter cont. STUDY LINK 712 Rule º 4 in()out() 2 3 8 3, or 2 2 3 4 5 1 56, or 3 1 5 8 9 3 92, or 3 5 9 5 4 2 40, or 5 7 3 2 38, or 9 1 3 Rule º 1 4 in()out() 2 1 2 3 3 4 5 6 25 4 2 3 1 6