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Name:_________________________________________________________Date:_____/_____/__________ Note: The pages in this packet are meant for additional practice. Students are NOT expected to complete every problem in the packet. Rather, students should use these pages as a resource-- in addition to studying the notes and past quizzes. It is suggested that students complete several problems from each of the following pages in order to be fully prepared for test. TOPICS COVERED ON “Proportions” TEST: Ratios Solving a Proportion Proportion Word Problems Scale Drawing Proportions Percent Proportions Consumer Applications (Tax, Tips, Discounts) Similar Figure Proportions NOTES SPACE/HELPFUL TIPS (to be filled out in class): 1. Define ratio. 2. What are the 3 ways to write a ratio? 3. What is the difference between a ratio and a rate? 4. What is a unit rate? 5. Define a proportion. 6. What is true about the cross-products of a proportion? 7. What is true about the corresponding angles and corresponding sides of similar figures? On the back of this cover page is the Unit 8 “Quick Guide” – for your reference. Work hard, study hard! Unit 8, “Proportions” Quick Guide RATIOS/ SOLVING A PROPORTION 3 inches PROPORTION WORD PROBLEMS SCENARIO 1. How much would you pay for 5 apples if 12 apples cost $.96? 2. A recipe calls for 1 ½ cups of sugar for a 3-pound cake. How many cups of sugar would be used for a 5-pound cake? 3. Two numbers are in the ratio 3:2. The smaller number is 36. What is the larger number? 4. There are 3 girls for every 7 boys at the park. If there are 28 boys at the park, how many girls are there? 5. There are 15 hershey kisses for every 3 chocolate bars in the Easter basket. If there are 20 hershey kisses, how many total kisses and bars are there? 6. The ratio of teachers to students on the D.C. field trip is 1 : 5. If there are 23 teachers on the trip, approximately how many students are on the trip? 7. If eight jars of peanut butter is $26.99, what is the unit rate for peanut butter? 8. If Sheila can type 300 words in 5 minutes, how fast can she type in 1 minute? (SHOW WORK HERE) SCALE DRAWINGS Scale: 2 in = 7 ft. 1. Living Room 4 in. 2. Dining Room 3. Kitchen 10 ft. 1.5 in. 4. Basement 5. Bedroom 25 ft. 3 in. Scale: 0.25 in = 5 ft. 6. Living Room 1 in. 7. Dining Room ¾ in. 8. Kitchen 9. Basement 10. Bedroom 20 ft. 1 ½ in. 12 ft % 100 1. 2. 3. 4. 5. 6. = 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 PERCENT PROPORTIONS % 100 = 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 CONSUMER APPLICATIONS You may use either the percent proportion OR the multiplication method to solve these: 1. You purchase $49.67 worth of groceries. There is a 5% sales tax. What is the total, including tax? 2. You purchase an $85 pair of shoes. You also have a coupon for 15% off. What is the sale price? 3. You purchase some essentials at Five Below for $14.99 before tax. The tax is 7%. How much will you pay in tax only? 4. You purchase a $200 leather jacket online and use a 25% discount code. What is the discount amount? 5. The bill at a restaurant is $48.40. Your family wants to tip 18%. How much is the total, including the tip? 6. Martin went to the mall with his friends. He wanted to buy his mom a birthday present. He went into the jewelry store and found a diamond necklace on sale for 60% off. The original price of the necklace is $450. How much does he pay? 7. The bill at Outback Steakhouse is $35.50. How much would a 15% tip be? 8. Devon wants to buy the new Jordan’s at Footlocker. They are $150 originally, but there is a sale going on for 30% off of all shoes. How much does Devon need to purchase the Jordan’s? SIMILAR FIGURES 1) Lance the alien is 5 feet tall. His shadow is 8 feet long. 5 ft 32 ft 8 ft At the same time of day, a tree’s shadow is 32 feet long. What is the height of the tree? a) 20 feet b) 24 feet c) 29 feet d) 51 feet 2) Pentagon JKLMN is similar to pentagon VWXYZ. What is the measurement of angle X? L a) 30 b) 60 c) 150 d) 120 K 150 J 3) W Y N V Z 60 M L Z 18 feet 24 feet 8 feet Y N 12 feet X M What is the length of YX ? a) 2 feet b) 3 feet c) 4 feet d) 6 feet SIMILAR FIGURES 4) Triangle PQR is similar to triangle DEF as shown. E Q 6 cm 4 cm P 6 cm R D 9 cm F Which describes the relationship between the corresponding sides of the two triangles? a) 5) PQ 4 DE 6 PQ 6 DE 4 b) c) PQ 4 EF 9 d) PR 6 DE 6 The shadow cast by a one-foot ruler is 8 inches long. At the same time, the shadow cast by a pine tree is 24 feet long. a) 3 feet b) 16 feet c) 36 feet d) 192 feet 1 foot What is the height, in feet, of the pine tree? 8 inches 24 feet 6) 9. If triangles ADE and ABC shown in the figure to the right are similar, what is the value of x? 12 C B 4 a) 4 b) 5 c) 6 d) 8 e) 10 x E D 2 3 A MULTIPLE CHOICE If there are 4 oranges, 5 apples, and 6 pears, what is the ratio of apples to total amount of fruit? A 5:4 C 5 : 15 B 5:9 D 15 : 5 If there are 6 teachers and 21 students on the trip, what is the ratio of students to teachers? A 6 : 21 C 21 : 6 B 6 : 27 D 27 : 6 MULTIPLE CHOICE