Rates Ratios and Proportions Review

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1 Rates Ratios and Proportions Review 1. small software company has a ratio of 9 computers to 28 employees. pproximately what fraction of the company's employees have a computer? a. b. c. d. opy and complete the statement. 2. In basketball, the field goal percentage is the ratio of the number of field goals made to the number of field goals attempted. Who has a better field goal percentage? class is attended by 18 girls and 24 boys. Write the ratio of girls to boys in the class as a fraction in lowest terms. etermine if the rates are equivalent ratios plums for $2, 12 plums for $8 6. n apartment complex has one- and two-bedroom apartments. Four out of every 15 apartments is a one-bedroom apartment. pproximately what fraction of the apartments have only one bedroom? 7. The sixth grade is taking a field trip. There are 150 students and 15 chaperones. a. What is the ratio of chaperones to students in simplest form? b. If the seventh grade also goes on the field trip with 140 students, how many chaperones will be needed to maintain the same chaperone to student ratio in part (a)? c. If only 286 students and 26 chaperones show up on the day of the field trip, what will the ratio of chaperone to student be? 8. Which rates are not equivalent? a. b. c. d. opy and complete the statement.

2 9. Write the rate and unit rate kilometers in 7 hours 11. EXTENE RESPONSE Write your answer on a separate piece of paper. company makes dog houses in three different sizes, small, medium, and large. ll of the dog houses have a similar shape and the largest sized dog house has a rectangular roof that is 60 inches wide by 75 inches long. It takes Michelle 27 minutes to put a coat of roofing compound on the roof of the large dog house. Part The small dog house has a roof that is 20 inches wide by 25 inches long. How does the area of the roof of the small dog house compare to the area of the roof of the large dog house? Part ssuming Michelle works at the same rate on all three roofs, how long does it take her to put the compound on the roof of the small dog house? Part The medium dog house has a roof that his 40 inches wide by 50 inches long. How long does it take Michelle to put the compound on the roof of the medium dog house? Explain your answer oz. bag of chocolate chips costs $ oz. bag of chocolate chips costs $4.40. a. Which size is the better buy? b. How much does each bag cost per ounce? c. If a 14 oz bag of chocolate chips that usually sold for $4.73 went on sale for $3.78, then which bag would be the best buy? 13. jar of olives has a circular lid with a circumference of about 6.6 inches. If the radius of the lid is doubled, what will the new circumference be?

3 a inches c inches b. 3.3 inches d. 6.6 inches 14. photography store sells scaled down prints of a painting. The prints have dimensions that are half those of the original painting. If the area of one of the prints is 21 square inches, what is the area of the original painting? 3 in. 7 in. a. 84 square inches c square inches b. 42 square inches d. 21 square inches 15. Typically, 60% of the customers who purchase a lift ticket at a local ski resort also rent skis. oes the number of ski rentals shown in the table agree with this statement for the given number of lift tickets sold? If not, state how many more or fewer ski rentals there should have been for a typical day. Northwest Slopes Lift Tickets Sold Ski Rentals a. No, 20 more customers rented skis than would have on a typical day. b. No, 17 more customers rented skis than would have on a typical day. c. Yes, 60% of the customers who bought a lift ticket also rented skis. d. No, 23 fewer customers rented skis than would have on a typical day. 16. student exercises for 33 minutes per day. fter exercising for five days, approximately how many seconds has the student exercised? a. 9,900 c. 990 b. 165 d Erica is opening a savings account that pays simple interest at a rate of 10% annually. How much interest will she earn after 4 years if the principal deposit is $1,000? Recall that the simple interest formula is I = prt, where I is the amount of interest, p is the principal, r is the interest rate, and t is the length of time in years. a. $375 c. $100 b. $400 d. $1,400

4 18. Mei is out to eat with her friends and the bill is $22.19 without sales tax. The sales tax where they live is 5%. What is the price of the meal (without tip)? Round the price to the nearest whole cent. a. $1.11 c. $23.52 b. $23.30 d. $ Mr. Zapata is putting wallpaper on a wall that is 10 feet tall and 10 feet wide. He has covered 40% of the wall. Which diagram shows Mr. Zapata s completed work? a. c. b. d. 20. If an employee correctly answers 38 out of 50 questions on a safety certification test, between which two percents does the employee s score lie? a. between 60% and 70% c. between 80% and 90% b. between 70% and 80% d. between 50% and 60% 21. If a 1.5-meter length of air hose is cut into 20 equal sections, how many centimeters long will each section of hose be? 22. How many ounces are there in a 5.3-pound bag of potatoes? 23. Mrs. Zapata s science class is studying how you can make fertilizer. The recipe for garden fertilizer is: 1 kilogram of potash 2 kilograms of phosphate 2 kilograms of nitrate If Mrs. Zapata makes 25 kilograms of garden fertilizer, how many kilograms of potash does she need?

5 24. If a certificate of deposit () pays annual simple interest at a rate of 5%, how much interest would be earned on a deposit of $3,400 after 2 years? Recall that the simple interest formula is I = prt, where I is the amount of interest, p is the principal, r is the interest rate, and t is the length of time in years. 25. Zachary is buying a computer on credit. The price of the computer is $650.00, plus 5% because he is buying on credit. He will make 10 equal payments, one a month for the next 10 months. How much is his monthly payment? Express your answer in dollars and cents.

6 Rates Ratios and Proportions Review nswer Section 1. NS: PTS: 1 IF: Level REF: MMT10052 NT: NT.SS.MTH RP.2 TOP: Lesson 8.1 Ratios KEY: approximate ratio fraction convert MS: omprehension NOT: NS: PTS: 1 IF: Level REF: ML10413 LO: NTM 6-8.NOP.3.d TOP: Lesson 8.1 Ratios KEY: equivalent ratio proportion 3. NS: Lena PTS: 1 IF: Level REF: ML10415 TOP: Lesson 8.1 Ratios KEY: compare decimal ratio word MS: omprehension NOT: NS: PTS: 1 IF: Level REF: MMT10579 NT: NT.SS.MTH RP.1 TOP: Lesson 8.1 Ratios KEY: ratio fraction word 5. NS: Yes PTS: 1 IF: Level REF: MMT10584 NT: NT.SS.MTH RP.1 TOP: Lesson 8.1 Ratios KEY: compare ratio 6. NS: PTS: 1 IF: Level REF: MMT10053 TOP: Lesson 8.1 Ratios KEY: ratio fraction simplify MS: omprehension NOT: NS: a. 1 to 10 b. 14 chaperones c. 1 to 11 PTS: 1 IF: Level REF: MSM MS.01 NT: NT.SS.MTH RP.1 LO: NTM 6-8.PRS.1 NTM 6-8.NOP.3.d NTM 6-8.ME.2.e NTM 6-8.ON.3 NTM 6-8.NOP.1.c NTM 6-8.NOP.1.d NTM 6-8.PRS.2 TOP: Lesson 8.1 Ratios

7 KEY: Multi-Step ratio MS: pplication NOT: NS: PTS: 1 IF: Level REF: ML10430 TOP: Lesson 8.2 Rates KEY: equivalent rate 9. NS: PTS: 1 IF: Level REF: ML10429 NT: NT.SS.MTH RP.1 LO: NTM 6-8.NOP.1.d NTM 6-8.NOP.3.d NTM 6-8.ME.2.e TOP: Lesson 8.2 Rates KEY: equivalent rate 10. NS: ; PTS: 1 IF: Level REF: ML10424 NT: NT.SS.MTH RP.2 TOP: Lesson 8.2 Rates KEY: ratio rate terms lowest unit rate unit 11. NS: Part The area of the roof of the small dog house is one-ninth the area of the roof of the large dog house. Part 3 minutes Part 12 minutes; The dimensions of the roof of the medium dog house are twice the dimensions of the roof of the small of dog house. This means the area of the roof of the medium dog house is four times the area of the roof of the small dog house. It will take four times as long to coat the roof of the medium dog house as it would to coat the roof of the small dog house. PTS: 1 IF: Level REF: MT60194 LO: NTM 6-8.NOP.3.d NTM 6-8.ON.3 NTM 6-8.ME.2.c NTM 6-8.ME.2.e NTM 6-8.PRS.2 NTM 6-8.PRS.4 NTM 6-8.PRS.3 NTM 6-8.NOP.1.c NTM 6-8.NOP.1.d NTM 6-8.PRS.1 TOP: Lesson 8.2 Rates KEY: proportion length dimension area width MS: pplication NOT: NS: a. the 20 oz bag b. the 12 oz. bag costs $0.30 an ounce, and the 20 oz. bag costs $0.22 an ounce. c. the 20 oz bag PTS: 1 IF: Level REF: MS MS.02 LO: NTM 6-8.ME.2.f NTM 6-8.PRS.2 NTM 6-8.NOP.3.d NTM 6-8.ON.3 NTM 6-8.PRS.1 NTM 6-8.NOP.1.c TOP: Lesson 8.2 Rates KEY: Multi-Step rate ounce MS: pplication NOT: NS: The circumference of a circle is given by the formula. If the radius of the circular lid is doubled then the diameter will also be doubled. The expression for the new circumference becomes, or twice the original circumference. So the circumference of the larger lid will be about 13.2 inches. How many dimensions are being scaled? Will the new lid be larger or smaller than the old lid?

8 Will the lid have the same circumference after its dimensions are doubled? OJ: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. NT: 6: 6.RP.1 ST: 6: 6.RP.1 KEY: circle dimensions scale circumference MS: M NS: The dimensions of the actual painting are twice those of the print. So the painting has dimensions of 14 inches by 6 inches and an area of square inches. How many dimensions are scaled to create each print? Which is larger, the print or the original painting? Will the painting have the same area as the print that has half its dimensions? REF: The rts OJ: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. NT: 6: 6.RP.1 ST: 6: 6.RP.1 KEY: area rectangle scale dimensions MS: M NS: Multiply the theoretical probability that a customer will rent skis by the total number of customers. Then compare this result with the number of customers who rented skis according to the table. In order for 60% of the customers who bought a lift ticket to have also rented skis, 20 fewer customers would have had to have rented skis. What is the experimental probability that a customer rented skis? What percent of the customers who bought a lift ticket rented skis? How many of the customers who bought a lift ticket rented skis? PTS: 1 IF: loom s Level: nalysis Webb s Level: Level 2 REF: Health/Physical Education OJ: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the KEY: experimental probability predict problem solving MS: M NS: Multiply the daily minutes of exercise by 5 and then multiply by 60 to convert minutes to seconds.

9 What units should your answer be in? How do you convert minutes to seconds? Should the answer be less than a minute? REF: Health/Physical Education OJ: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. NT: 6: 6.RP.3.d ST: 6: 6.RP.3.d KEY: minutes second (time) conversion MS: M NS: Use the simple interest formula I = prt, where p is $1,000, r is 0.1, and t is 4 years. Substitute the appropriate values into the interest formula and solve for I. For how many years is the account earning interest? This is the total value of the account after the period. What is the amount of interest earned? OJ: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the KEY: percent simple interest problem solving decimals MS: M NS: The bill is $22.19 without sales tax. The sales tax on this bill is (rounded to the nearest cent). The price of the meal (without tip) is:. This is just the sales tax. You must add it to the price of the meal. id you multiply the percentage correctly? You need to add the tax to the price, not subtract it. REF: Mathematics OJ: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the

10 KEY: problem solving percent tax MS: M NS: Each column represents 10% of the wall. Since Mr. Zapata has already wallpapered 40% of the wall, you would look for the picture that has 4 columns covered. 4 columns This is more than the percentage covered. Remember, in a 10-by-10 grid, each column equals 10%. ount the columns carefully to determine the correct percent. This is less than the percentage covered. PTS: 1 IF: loom s Level: omprehension Webb s Level: Level 1 REF: Mathematics OJ: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the KEY: percent area number sense MS: M NS: ivide the number of correct answers by the total number of questions to write the result as a decimal. Then multiply by 100 to write the result as a percent and compare. The employee s score lies between 70% and 80% What fractional portion of the questions were answered correctly? How can you compare the fraction of correct answers to the percents listed? Write the fractional portion of correct answers as a decimal. How does it compare to the percents listed? PTS: 1 IF: loom s Level: pplication Webb s Level: Level 2

11 OJ: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the KEY: comparing fractions percent MS: M NS: 7.5 OJ: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. NT: 6: 6.RP.3.d ST: 6: 6.RP.3.d KEY: conversion units meters centimeters metric conversion MS: M NS: 84.8 OJ: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. NT: 6: 6.RP.3.d ST: 6: 6.RP.3.d MS: M NS: 5 KEY: conversion units pounds ounces REF: Science OJ: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. NT: 6: 6.RP.1 ST: 6: 6.RP.1 KEY: ratio equivalent forms proportion problem solving MS: M NS: 340 OJ: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the KEY: percent problem solving decimals MS: M NS: REF: Mathematics OJ: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the KEY: problem solving finance payments MS: M