Ratios and Rates Review PDF

Date: ising Two-Term Ratios Compare two quantities using ratios. ) 1. Write a part-to-part ratio to compare the following items: *8 peaches...

Date: ising Two-Term Ratios Compare two quantities using ratios. ) 1. Write a part-to-part ratio to compare the following items: *8 peaches °3 apples 6 oranges ° 4 pears ° Use ratios when yous want te a) peaches to pears b) apples to oranges compare quantities with the : same units, for example, the c) oranges to peaches d) pears to apples amount of time spent doing , activities in a day or the areas 2. Calculate each missing term.. of two rectangles. a) 3:2=9:___ b) 36:27=4:____ e You can use equivalent , fractions or set up a proportion 3 4 16 to figure out an appropriate c) 418 = d) 12 a 9 - equivalent ratio. rr re For example, you spent $5 on CDs 3. Write three equivalent ratios for each ratio. for every $2 you spent on clothes. { You spent $16 on clothes. How a) 6 to 36 b) 11:33 c) 5 much did you spend on CDs? 8 Multiply $2 by 8 to get the amount spent on CDs;. multiply $5 by 8 to 4. Allison spends 2 h each school day on homework and getthe amountspent on clothes, 30 min practising music. x8 a) Write a ratio to compare Allison’s time on homework o™~ 4 : t 40 with the total number of hours in a day. Canes a. CDs 2 =. 16 Ns x8 b) , ; ; Write a ratio to compare Allison's time practising ; _. Ye L OU Spniiyso t $40 onin clouies clothes. J music with the total number of hours in a day. c) Calculate the number of hours Allison spends practising music in 30 school days. 5. Determine each ratio for the letters of the alphabet (A to Z). | a) the number of consonants to the total number of letters __ b) the total number of vowels to the total number of consonants Copyright © 2009 by Nelson Education Ltd. Chapter 3: Ratios and Rates 23  Date: ng Ratio Tables bo Use ratio tables to solve problems. 1. Complete each ratio table. | At-Home | Hel a) | You can use a ratio table and Girls | 3 30 60 a given ratio to create an — equivalent ratio. Boys | 4 20 60 ‘ ef ; ~ ‘ e Multiply or divide both terms in : _ one column by the same b) | Number of ~ ~ 4 9 21 amount. Goes : e Add or subtract numbers in two ‘alue ge o - 125 100 200 or more columns to get one Coins (cents) number in the equivalent ratio c) - you need, and read the table to 24 48 get the other number. For example, solve: 23 92 161 8:18=.:81 81 is not a multiple of 18, but it is 2. Solve using a ratio table. Show your steps. | a multiple of 9, which is also a factor of 18. Try to get a 9 as the a) 4:6 = 20: second term. +2 x9 SN 2 ™ 8 4 36 18 9 81 NF SS b) 50: = 75:30. +2 x9 ‘So, the ratio is 8: 18 = 36:81. 7 3. In asurvey, Grade 8 students were 3 : 1 in favour of going on a class trip. In all, 56 students were surveyed. How many Grade 8 students were in favour? 4. A bag of mixed chocolate has 60 g of dark chocolate for every 40 g of white chocolate. In 400 g of this mixture, how many grams are dark chocolate? 5. Marisa made 6 L of fruit punch from concentrate. She used 2 parts of water for 1 part of concentrate. How much concentrate did she use? 24 Chapter 3: Ratios and Rates Copyright © 2009 by Nelson Education Ltd.  Name: Total: /17 MATH 8 — RATES AND RATIOS 1) Write an equivalent ratio for each of the following. a) 12:28 b) 39:13 fz 2) Solve each proportion. a) 6:11 = 36:__ b) __ :30 = 6:1 /2 3) Punch can be made with grape juice and ginger ale in the ratio of 5:2. If 20 Litres of grape juice is used, how much ginger ale would you need? Work Answer With Correct Units j2 4) Calculate the area for each of the rectangles below. What is the ratio of the larger area to the smaller area in lowest terms? 9 cm 6 cm 5 cm 5¢ Answer With Correct Units ~ = = O /2 5) Blue and red paint are mixed together to make purple paint. What ratio would make the darkest shade of purple? a) 9 parts blue to 8 parts red b) 12 parts blue to 9 parts red /1 c) 16 parts blue to 14 parts red d) 96 parts blue to 100 parts red /9  6) To make lawn fertilizer, a manufacturer blends nitrogen, phosphoric acid and potash in the ratio of 3:7:10 respectively. a) If 36 kg of nitrogen are used in the mixture, find the amount of potash used. Work Answer With Correct Units {2 b) How much phosphoric acid is there in 780.5 kg of fertilizer? Work Answer With Correct Units jz 7) Write as a unit rate. 6 doughnuts for $7.29 /1 8) Circle which is the best deal at the bowling alley in Sherwood Park. 4 games for $11 7 games for $17.50 10 games for $22.50 /1 9) An airplane can travel 9000 km in 12 hours. How far can it travel in 4.5 hours? Work Answer With Correct Units /2 /8  RATES MAD MINUTES 1) Write the following as a unit rate. a) $560 pay for 7 hours work b) 0.5 kg of steak for $7.50 c) a plant grows 4.8 cm over 48 days 2) Sheila travels 1800 km in 20 hours. How far would she travel in 61/2 hours? Solve Using Unit Rate Solve Using Proportions 3) Which is the better buy? Costco advertising bananas: $12.48 / 10 kg Or Safeway advertising bananas: $0.96 / 750g Solve Using Unit Rate Solve Using Proportions 4) It takes 7.6 hours to travel from Fort Sask. to Regina at an average speed of 102 km/h. How far is it to Regina? 5) It is 536 km to Calgary from Fort Saskatchewan. If it takes Fouad 5.1 hours to get there, what is the average speed while travelling? 6) Bubba travels from Fort Sask. to West Edmonton Mall at 112 km/h (not very law-abiding). On the return trip during rush hour traffic he averages 87 km/h. What is the difference in time between trips? The distance from Fort Saskatchewan to West Edmonton Mall is 50 km.  WORLD RECORD RATES 1) Howard Berg of Edmonton is the world’s fastest reader. On average, he can read 90 pages/min. a) How many pages could he read in 12 minutes? b) How long would it take him to read 1350 pages? 2) Joey Chesnut of the U.S. holds the record for the most hotdogs eaten over a 12 minute period. Joey ate 66 hotdogs in 12 minutes. a) Express this as a unit rate. b) How many hotdogs could he eat in 30 minutes?  3) Usain Bolt of Jamaica is the world’s fastest man in the 100 metre dash. He ran the distance in 9.58 sec. a) What is this as a unit rate? b) How long would it take him to run 500 m at this rate? 4) Raisins are $6.32 for 800 grams at Co-op and $2.63 for 350 grams at No-Frills. Which store has the better deal? A —- Solve Using Unit Rates B - Solve Using Another Rate  WHY DIP THE PABRY FIG CAT 20 MUCH? Find the unit price of each item described. Round each price to the nearest cent. Write the letter of each exercise above its answer. (S) 5 lb of potatoes for $2.19 (A) 60 oz of honey for $4.89 $__sper Ib per oz (A) 200 ft of foil for $6.24 (M) 1 dozen roses for $29.75 $ per ft $ per rose © 36 0z of peanut butter for $4.39 (H) 25 greeting cards for $7.95 $ per oz $ sper card (N) 18 issues of a magazine for $28.90 © 147 oz of detergent for $9.27 $ per issue $ per oz @) 1 dozen doughnuts for $4.50 Ww) 7 tennis lessons for $99 $ per doughnut $ per lesson Cd) 22 oz of cereal for $3.67 (K) 3.5 lb of cheese for $8.94 $ per oz $ per Ib Copyright © Wright 0.38 | 0.44 2.67 Ketchup Fried chicken (©) 140z for $0.99 $ per oz Math with Pizzazz! ) 5 pieces for $4.79 §$ per piece (F) 64 oz for $3.10 $ per,oz ©) 21 pieces for $18.77 $ per piece Chocolate candy bar Aspirin Cd) 1.65 oz for $0.50 $ per oz () 30 tablets for $2.59 $ per tablet ©) 8ozfor$1.95 §$ per oz @) 165 tablets for $7.28 $ per tablet this page for classroom use with Solve. A monthly magazine charges $17.40 for a S) A sports store pays $380 for a case of 144 one-year subscription (12 issues). The baseballs. The store sells the baseballs for same magazine sells on the newsstand for $4.75 each. How much less is their cost $2.00 a copy. How much do you save on than their selling price for each ball? each issue by buying a subscription? $ A season ticket to the Olde Theater costs For film and processing, a 36-exposure roll $76 and admits you to 6 plays. Single of film costs $19.20. A 24-exposure roll tickets to each play cost $15. How much do costs $16.40. How much can you save per you save on each play by puying & season picture by choosing the better buy? ticket? $ Permission f 0.02 2.33 | 0.89 | 0.15 | 2.16 | 0.07 | 0.96 | 0.46 | 0.04 | 0.30 | 0.09 | 2.11 | 0.24 | 0.55 rs MIDDLE SCHOOL MATH WITH PIZZAZZ! BOOK B B-71 TOPIC 6-c: Using a Calculator: Unit Prices  When Does a Farmer Go to a Drug Store? Round each solution to the nearest tenth and find it in the answer boxes. Write the letter of the answer in each space containing the number of the problem.. Alain Prost won the British Grand Prix by 7. Herman van Springel won the PbS driving for 1.41 hours at an average Bordeaux-to-Paris, France, bicycle race speed of 139.2 miles per hour. How by riding for 13.59 hours at an average many miles was the race? speed of 26.65 miles per hour. How far EEE mi did he ride? Walter Poenisch swam from Havana, ee mi EEE EEE Cuba, to Duck Key, Florida, in 34.25 In 1934 Walter Nilsson rode a unicycle hours. His average speed was 3.76 miles 3,306 miles from New York to California. per hour. How far did he swim? If he averaged 28.5 miles a day, how mi many days did the trip take? EEE. Matt Biondi set a record by swimming i EERE ES 100 meters at an average speed of 2.052 Dave Dowdle set a record by running meters per second. How long did he take for 24 hours at an average speed of 7.1 to swim the 100 meters? miles per hour. How far did he run? Copyright © Wright iS mi EEEEEEEEEEEEEEEEEEEEEEEREE. Abaseball pitch has been clocked at a 10. A hockey puck has been clocked at a speed of 147.9 feet per second. At this speed of 166 feet per second. At this speed, how long does it take the baseball speed, how long would it take the to travel from the pitcher's mound to puck to travel the 200-foot length of Math with Pizzazz! (Binder home plate, a distance of 60.5 feet? a hockey rink? Ss. Teuvo Louhivouri set a record by riding a 11. Guiseppe Cantarella set a record by bicycle 515.8 miles in 24 hours. What roller skating 1,320 feet in 34.9 was his average speed? seconds. mph A. What was her average speed in feet PEER. The record for traveling across the per second? _____fps use with United States on a motorcycle is 74.6 hours. If the distance traveled was 2,945 What was her average speed in miles EERE miles, what was the average speed of per hour? (1 foot per second = 0.68 the motorcycle? mile per hour.) instructors to reproduce this page for mph mph EEE Answers 1 — 6: Answers 7 — 11: (B) 06 (1) 48.7 (A) 128.8 (R) 1.2 (L) 27.3 (W) 362.2 (N) 21.5 (G) 34.2 (M) 39.5 (Y) 164.4 (H) 170.4 (S) 25.7 (D) 196.3 (T) 0.4 (P) 126.9 (E) 37.8 (v) 1.4 (F) 116 Permission [ 9 M1Al5 19 [11A1 5 IANA] 1 [11B] 2 [8 [2 [iole6 | 2 fislisl 3 [ipl 4 ( TOPIC 6-e: Using a Calculator: MIDDLE SCHOOL MATH WITH PIZZAZZ! BOOK B B-73 Speed, Time, and Distance  Why Did Notso Bright Save Burned-Out Light Bulbs? Solve each problem. Find your answer and notice the two letters next to it. Write these letters in the two boxes above the exercise number at the bottom of the page. Suppose your heart beats an average of 72 times a minute. Each time your heart beats, it pumps about 0.02 gal of blood. At that rate, how much blood is pumped in an hour? gal (2) A new car costs $15,795. The car weighs 2,832 pounds. What is the cost for each pound of car? (Round to the nearest cent.) $F Answers (3) King Midas once said that his daughter was "worth her weight in LD 251 gold." Suppose gold was worth $420 an ounce and his daughter weighed 90 pounds. According to King Midas, how much was she NH 72.27 worth? (1 pound= 16 ounces). $e ST 13 (4) The speed of sound is 760 miles per hour. At that speed, how long would it take to travel around the world, a distance of about 25,000 RO 604,800 miles? (Round to the nearest hour.) h @ for 1 ssroom use with Middle Schoo! Math with Pizzazz! (Binder B). Copyright © IS 86.4 (5) WORLD RECORD: A famous diamond called the "Polar Star" was sold for a record price of $113,000 per carat. The diamond weighs OM 299 41.3 carats. How much was paid for it? $ PL 28 (6) The speed of light is 186,000 miles per second. At that speed, how RA 497 long would it take to travel from Earth to Mars, a distance of 9 48,000,000 miles? (Round to the nearest second.) Ss DA 4,666,900 (7) A famous professional basketball player was paid $1,000,000 last El 5.58 year. He played in 76 games for an average of 44 minutes per game. ° How much did he earn for each minute of playing time? (Round to TR 7547 the nearest dollar.) $ On the way back from a field trip, two buses stopped for gas. One od bus took 26.1 gallons and the other 32.7 gallons. If gas cost $1.229 US 258 ce this per gallon, how much did all of the gas cost? (Round to the nearest cent.) BI 619,480 Permission ‘s given to inst tors to repxd ©) WORLD RECORD: To raise money for charity, Jonathan Hook TO 33 kissed 4,106 women in 8 hours on March 10, 1983. To the nearest second, how many seconds did he average for each kiss? (1 hour= 3600 seconds) Ss ee ee 4 6 2 8 1 5 9 2 7 TOPIC 6-f: Using a Calculator: Mixed Applications B-74 MIDDLE SCHOOL MATH WITH PIZZAZZ! BOOK B