8-1 Ratios and Rates Use the table to write each ratio. 1. alligators to penguins 2. eels to sea turtles 3. sharks to alligators 4. penguins to eels 5. sea turtles to sharks Animals at the Aquarium Sharks 17 Eels 7 Sea Turtles 11 Penguins 6 Alligators 3 6. Write three equivalent ratios to compare the number of diamonds with the number of spades in the box. Use the table to write each ratio as a fraction. 7. Hawks wins to Hawks losses Soccer Team Stats Kings Hawks Wins 18 13 8. Kings losses to Kings wins Losses 10 15 9. Kings losses to Hawks losses 10. Hawks wins to Kings loses 11. A 5-lb sack of potatoes costs $4.32. An 8-lb sack of potatoes costs $6.78. Which is the better deal? 12. Jessie charges Jim $45.00 for 3 hours of tutoring. Mike charges Jim $90.00 for 5 hours of tutoring. Who offers Jim the better hourly rate of pay? 65 Holt Middle School Math Course 1
8-2 Proportions Find the missing value in each proportion. 1. 1 8 33 n 2 1 2. 1 2 3 6 n 3. n 5 8 1 0 4. 1 6 n 5 2 5. 3 0 2 9 n 6. 4 n 24 1 8 7. 1 6 n 9 1 8. 1 5 4 5 4 1 8 3 n 9. 8 4 n Write a proportion for each model. 10. 11. 12. Jonathan decided to pledge $1.45 for every dollar donated in the charity auction. If the charity auction takes in a total of 75 dollars, how much money will Jonathan donate? 13. Gerald scored 15 points for his basketball team for every 25 minutes he played in the season. If he played 200 minutes in the season, how many points did he score? 66 Holt Middle School Math Course 1
8-3 Proportions and Customary Measurement Find each missing value. 1. 5 yards inches 3. cups 16 fluid ounces 5. 12 pounds ounces 7. seconds 7 minutes 9. pints 4 cups 11. months 3 years 2. inches 19 feet 4. 2 weeks days 6. hours 7 days 8. cups 6 gallons 10. 108 inches yards 12. 63 feet yards Compare. Write,, or. 13. 2 quarts 4 cups 15. 180 seconds 3 minutes 17. 56 ounces 4 pounds 19. 2 miles 2,700 yards 14. 6 feet 100 inches 16. 4 cups 20 fluid ounces 18. 36 hours 1 1 2 days 20. 3 1 2 pounds 55 ounces 21. 54 months 4.5 years 22. 13 yards 500 inches 23. Jacob, in a marathon, walked for 3 1 2 hours. How many seconds did he walk in the marathon? 24. Kristy was measuring sugar for a large pitcher of lemonade. She measured 3 pounds of sugar. How many ounces did she actually measure? 25. Marcia was on vacation for 2 full weeks. How many hours was she on vacation? 26. Todd drove from Baltimore, MD to New York City, a distance of 192 miles. How many feet did Todd drive? 67 Holt Middle School Math Course 1
8-4 Write the correct answer. 1. The two triangles are similar. Find the missing length x and the measure of A. 12 ft Similar Figures C 75 16 ft x F 75 20 ft A 24 ft 35 B D 70 30 ft 35 E 2. The two triangles are similar. Find the missing length x and the measure of J. x M 94 48 m 24 m H 94 24 m P 43 80 m 43 N K 43 40 m J 3. The two triangles are similar. Find the missing length x and the measure of N. 17.5 cm M 66 15 cm 35 cm H 66 x L 50 20 cm N G 50 40 cm 64 J 4. Lenny made a long rectangular pen to keep his dog in. What are the measures of all the angles in the pen? Explain how you know. 5. Lenny s dog had puppies and he decides to build a pen big enough for all the dogs. He saw a pen that is a triangular shape with the sides measuring 6 feet, 12 feet, and 9 feet. He wants his pen to be a similar triangle with the largest side measuring 20 feet. How long would the other two sides be? 68 Holt Middle School Math Course 1
8-5 Indirect Measurement Write the correct answer. 1. Use similar triangles to find the height of the building. 2. Use similar triangles to find the height of the tree. h h 6 ft 3 m 13 ft 39 ft 4 m 36 m 3. A lamppost casts a shadow that is 15 yards long. A 3-foot-tall mailbox casts a shadow that is 5 yards long. How tall is the lamppost? 4. An 8-foot-tall statue stands in the park and casts a shadow that is 16 feet long. A dog stands next to it and is 3 feet tall. How long is the dog's shadow? 5. A building casts a shadow that is 420 meters long. At the same time, a person who is 2 meters tall casts a shadow that is 24 meters long. How tall is the building? 6. On a sunny day around noon, a tree casts a shadow that is 12 feet long. At the same time, a person who is 6 feet tall standing beside the tree casts a shadow that is 2 feet long. How tall is the tree? 7. A pole casts a shadow that is 21 feet long. A 3-feet-tall child standing next to the pole casts a shadow that is 9 feet long. How tall is the pole? 8. Jeremy has two trophies next to each other sitting in the window of his room. His football trophy is 7 inches tall and his basketball trophy is 13 inches tall. As the light shines in, the basketball trophy s shadow measures 26 inches. How long is the football trophy s shadow? 69 Holt Middle School Math Course 1
8-6 Scale Drawings and Maps Use the map to answer the questions. 1. On the map, the distance between Key West and Key Largo is 1 inch. What is the actual distance in miles? 2. On the map, the distance between 3 Everglades and Cuba is 1 1 inch. 0 What is the actual distance? 3. Use a ruler to measure the distance between Big Cypress Swamp and Key Largo on the map. About how far is the actual distance? 4. Some people want to construct a connection from Cuba to mainland Florida. It is 250 miles long! If it were shown on this map, how many inches long would it be? N W E S Gulf of Mexico 1 in. 100 miles FLORIDA Key West Big Cypress Swamp CUBA Florida Everglades Keys ATLANTIC OCEAN Key Largo Use the scale drawing to answer each question. 5. This scale drawing is of the lighthouse on Key West, originally built in 1825. What is the actual height of the smaller building just outside of the lighthouse? 6. The original lighthouse was 66 feet tall. It was rebuilt at its present height after a hurricane destroyed it in 1846. How tall would half of the original lighthouse be in this scale drawing? 1 in. 40 feet 70 Holt Middle School Math Course 1
8-7 Percents Write each percent as a fraction in simplest form. 1. 28% 2. 63% 3. 14% 4. 75% 5. 30% 6. 98% 7. 5% 8. 90% 9. 16% Write each percent as a decimal. 10. 42% 11. 96% 12. 1% 13. 13% 14. 56% 15. 9% Order the percents from least to greatest. 16. 92%, 8%, 52%, 62% 17. 56%, 9%, 97%, 76% 18. Marlene correctly answered 76% of the questions on her science test. What fraction of the test questions did she answer correctly? Write your answer in simplest form. 19. Jeremy ran 2 5 of his total running goal for the day. What percent of his total running goal did Jeremy complete? 71 Holt Middle School Math Course 1
8-8 Percents, Decimals, and Fractions Write each decimal as a percent. 1. 0.17 2. 0.85 3. 0.64 4. 0.33 5. 0.19 6. 0.8 7. 0.23 8. 1.02 9. 0.25 Write each fraction as a percent. 10. 1 0 20 2 11. 2 12. 15 1 0 13. 3 5 14. 6 8 2 15. 2 0 Compare. Write,, or. 16. 32% 1 3 17. 0.8 6 7 1 18. 0.05 5% 19. 2 3 0.05 5 5 20. 1 40% 21. 3 2 0 20% 22. Michael completed 6 8 of his test. What percent of his test does he still need to complete? 23. After reading a book for social science class, 100 students were asked whether or not they enjoyed it. One fifth of the students did not like the book. How many students liked the book? 72 Holt Middle School Math Course 1
8-9 Percent Problems Find the precent of each number. 1. 7% of 65 2. 56% of 30 3. 95% of 275 4. 66% of 66 5. 14% of 89 6. 51% of 698 7. 65% of 102 8. 103% of 57 9. 3% of 200 10. 48% of 210 11. 87% of 78 12. 5.5% of 600 13. 23% of 326 14. 1% of 250 15. 80% of 5 16. 2% of 15 17. 29% of 410 18. 15% of 400 19. Fred ordered 15 pizzas for a party. Three-fifths of those pizzas were just cheese. How many pizzas were just cheese? 20. Jenny sold 380 boxes of cookies for her Girl Scout troop. Fiftyfive percent of the cookies she sold were oatmeal cinnamon boxes. How many boxes of oatmeal cinnamon cookies did she sell? 21. Keon jumps rope for 20 minutes. If he has completed 80% of his routine, how many minutes will Keon jump rope in all? 22. Michelle ran 460 miles this month preparing for a race. Thirtyfive percent of the miles she ran were during bad weather. How many miles did Michelle run in bad weather? 73 Holt Middle School Math Course 1
8-10 Uses of Percents Write the correct answer. 1. Michelle and Rhonda eat dinner at a fancy restaurant. Their bill came to $105.36. They gave their waiter a tip that was 22% of the bill. About how much money did they give the waiter for his tip? 2. Christine buys a necklace that costs $18.62 and a ring that costs $7.98. She uses a 35%-off coupon on the purchase. If Christine pays with a $20 dollar bill, about how much change should she get back? 3. The church s goal for the fundraiser was $18,000. They exceeded the goal by 8%. How much money did the church raise? 4. Kelly decided to get sandwiches for herself and some friends. The cashier said that if she spent over $10 she would get 15% off. The total bill was $13.27. How much was the total bill after the discount? 5. Lauren had a 26%-off coupon for the flower store. She bought a bouquet of roses that are regularly priced at $51.23. How much did Lauren spend on the bouquet of roses after using her coupon? 6. Joe bought two pizzas for $16.78. He wants to give the delivery person an 18% tip. How much money should Joe give the delivery person? 7. A television costs $258.98. The sales tax rate is 8.5%. How much will it cost to buy the television? 8. Milton bought a bike that costs $84.21. The sales tax rate is 6%. How much did Milton pay for the bike altogether? 9. Tana bought $74.12 worth of CDs at the music store. She gets a 19% discount since she is an employee at the store. What was the actual price of the CDs she bought before the discount? 10. Ronald saves $10.00 to buy a new book. The book s original price was $15, but it was on sale for 35% off with a 6% sales tax. Does he have enough money to buy the book? Explain. 74 Holt Middle School Math Course 1