Oregon Focus on Ratios, Rates & Percents Lesson 1 Answers

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1 Lesson 1 Answers or or , 2 : 3, 2 to 3, 1 : 2, 1 to 2, 4 : 1, 4 to , 2 : 3, 2 to a. 7 8 or 1; 1 : 1; 1 to 1 b. 7 1 c a. 1 4 b. 1 3 or ; : 1; to 1 1. a. 1 2 b a. 4 b a b a. The team won 3 games for every 4 games it lost. b. 3 : a. For every students wearing shorts, 1 person was wearing pants. b. 1 : a. : 8 b. 0 c. Comedy 1 4 or 1 : 4 Drama 1 or 1 : Action 2 or 2 : Adventure 1 or 1 : Cartoon 1 20 or 1 : a. Shannon: 9 b. Answers may vary. 1

2 Lesson 2 Answers 1. ratio: ; terms: 62, 3,12 2. ratio: ; terms:,000, 0, ratio: 1 2 ; terms: 0, 2 4. ratio: 1 3 ; terms: 1 27, ratio: 1 2 ; terms: 3 16, ratio: 3; terms: 324, a. 128, 64, 32, 16, 8, 4, 2, 1 b. 1 2 c. No, the numbers become small fractions that get close to 0, but never equal 0 (you cannot have a fraction of a person). 8. 1, 3, 9, 27, 81, 9.,000, 1,000, 0,, 1,. 1, 4, 16, 64, 26, not geometric 12. geometric ratio: geometric ratio: geometric ratio: not geometric 17. a. 1 b. 2 c. 4 d. 8, 16, 32, 64, 128, (fold it 7 times) e. Yes, the number of rectangles always doubles which means the sequence has a ratio of a. $3,000 b. 0.01, 0.02, 0.04, 0.08, 0.16, c. $,368, d. The second option 19. Answers may vary. 20. Answers may vary. Example: 1, 2, 3, 4,, (not multiplying to get the next term) a. 4 : 9 b. 4 : 1 2. a. : 7 b. : 12 c. 7 : a. 2 : 3 b. 2 : 1 1. geometric ratio: 1 2

3 Lesson 3 Answers 1. 4 inches 2. pounds 3. 1 minutes 4. 0 yards. 8 ounces inches 7. 8 quarts 8. 4 feet tons. 3 days feet quarts feet 14. 8,000 pounds minutes 16. a. 23,92 inches b or 0.4 miles 17. 6,2 inches 18. a. Shawna b. minutes c. 1 minute = 60 seconds 2 hours = = 7,200 seconds , 1 : 2, 1 to , 1 : 3, 1 to , 3 : 4, 3 to ratio: 4 terms: 1,280,, ratio: 1 2 terms: 1 2, ratio: 1 terms: 8, 8 (1.6) 2. ratio: 6 terms: 216, 1,296 3

4 Lesson 4 Answers centimeters 2. 3 grams 3. 1 meter centimeters. 1 milliliter kilometers centimeters 8. 2,000 milliliters 9. kilometers.,000 grams 11. 3,000 milliliters 13. 7,000 meters liters kilograms ,000 centimeters cm mm, 400 cm, km, 19. Answers may vary inches 21. 6,000 pounds cups 23. ratio: ; term: 0, ratio: 1 4 ; term: centimeters 4

5 Lesson Answers 1. a. 32 ft b. 384 in 2. a. 70 cm b. 700 mm 3. a yd b ft 4. a. 16 m b. 1,600 cm. a. 64 square feet b. 9,216 square inches 6. a. 2 square centimeters b. 21,000 square millimeters 7. a. 3 8 b square yards square feet 8. a. 12 square meters b. 120,000 square centimeters 9.,000 square centimeters. 9 square feet 11. a. 180 square feet b. 20 square yards c. $ a. 14 cm b. 8.2 square centimeters 13. a. 174 ft b. $2, a. 4 in b. 8 in c. 16 in d. 32 in e. 64 in f. 4, 8, 16, 32, 64, Yes, ratio = 2 1. a. small: 24 m ; large: 36 m b. 2 : 3 c. small: 24 square meters and large: 4 square meters d. 4 : a. 41 ft b. square feet 17. ratio: 1 2 terms: ratio: 1 7 terms: ratio: 2 terms: , 1, 1, 1, 1, every term equals 1

6 Block 1 Review Answers , 1 : 2, 1 to 2, 3 : 8, 3 to 8, 2 : 1, 2 to 1, 1 :, 1 to, : 3, to 3, 1 : 4, 1 to 4 7. a. 7 : 9 b. 7 : 16 c. 9 : a. 2 : 1 b. 2 : 3 c. 1 : 3 9. a. 8 : 1 b. 2 : 3. ratio: 1 terms: 1, ratio: 1 3 terms: 1 81, ratio: 20 terms: , , 6, 12, 24, 48, , 0, 0, 2, , 1., 30, 90, 270, 8, 16. yes, the ratio is not geometric 18. yes, the ratio is feet ton cups inches 23.. pints ,000 pounds 2.,60 feet 26. days yards 28. grams centimeters liter centimeters millimeters kilometers meters 3. 2,000 liters kilograms 37. 0,000 centimeters 38. a. 20 cm b. 200 mm a. 2 3 yd b. 7 ft 40. a. 6 ft b. 72 in 41. a. 2 square yards b. 18 square feet 42. a. 8 3 square feet b. 4 square inches 43. a. 60 square meters b. 600,000 sq. centimeters 44. a. perimeter: 480 mm area: 14,400 mm² b. perimeter: 48 cm area: 144 cm² 6

7 Lesson 6 Answers a. 7.2 in b in 11. Natalia ~ 8 = 8. Tricia divided the denominator by the numerator ; 0.62 > ; < ; 0.8 < = = = a. Decimal Fraction b. Explanation and answers may vary. c. 7.8 cm 28. ratio: 3 terms: 243, ratio: terms: 200, ratio = 1 terms: 0.01, feet feet kilometers 34. 1,400 centimeters 3. 2,00 meters

8 Lesson 7 Answers a = 1 b = 1 c. Yes, both sums equal a = 1 b = 0.9 c. Yes, the answers look different but are the same. 1 = a b. repeat c a. Marcia b. No, both round to seconds ; 0. 3 > ; 0. 6 < ; 0.4 < 0. 8

9 Lesson 8 Answers miles 1 hour (30 miles per hour) 24 words 1 minute (24 words per minute) 20 miles 1 gallon 4. 6 days 1 job (20 miles per gallon) (6 days per job). $1. 1 pen ($1. per pen) miles per hour 1. a. $0.0 per song b. Music Hooray 16. Yes, Luke = 2 miles 0.0 miles Sally 20 minutes = 1 minute 40 minutes 20 minutes 2 miles 1 mile Luke and Sally switched the units in the numerator and denominator of the rates ounces 1 serving (16 ounces per serving) pounds 1 inch (4 pounds per inch) 8. feet 1 second ( feet per second) 9. 3 kilometers 1 hour (3 kilometers per hour). a. Jaden divided the numerator and denominator by 30 to get a denominator of 1. He found the unit rate. b. Jaxen converted the fraction to a decimal by finding c. 30 d. Yes, 6 miles per hour is the same as 0.1 mile per minute. The units changed. 11. $9 per ticket 12. $0. per cookie miles per gallon

10 Lesson 9 Answers 1. $ miles words 4. 9 kilometers. 8 gallons days miles calories 9. $ feet 1 minute 11. $ pencil miles 1 gallon 0.2 meters 1 second 2. words 1 minute (4 feet per minute) ($0.40 per pencil) (23.33 miles per gallon) (0.2 meters per second) (2. words per minute) 1. $0.67 ($0.67 per book) 1 book miles per gallon; 8 miles 17. $0.22 per pound; $ gallons miles 20. $ a. $18.2 b. $1.7 c. No, they cost $2.00 and she has $1.7 left ,000 meters centimeters feet 2. 1 feet 26. $3. per cake miles per hour

11 Lesson Answers 1. $6.7 3 sandwiches miles 4 hours 162 miles 6 gallons 16 jobs 4 days. Christine; 60 > 6. Marta; 7 < 8 7. package of 6 pens; $1.2 < $ pound bag $0.70 per pound < $0.7 per pound 9. a. Mark: 0 miles per hour Jamal: miles per hour b. Jamal c. Mark: 300 miles Jamal: 330 miles. $ $ $ a. 3 packages b. $60.00 c. 4 packages d. $40.00 e. 4 packages of 1 f. 20 pkg $1.00 per notebook 1 pkg $0.67 per notebook 14. a. 16 miles per hour b. 3 hours c. 12 miles per hour d. 4 hours e. -speed bike 1. a. balloons for $4.00 pkg $0.80 per balloon 4 pkg $0.90 per balloon b. $ a. 1 : 3 b. 1 : 4 c. 3 : a. 2 : 3 b. 2 : 1 11

12 Lesson 11 Answers 1. Hours Total miles traveled miles miles minutes. 1. hours minutes miles 8. miles miles > 8 miles ; 9 miles 1 hour 1 hour 1 hour 16 centimeters 30 centimeters 1 minute < 1 minute ; 7 yards 6 yards 14 yards > ; 1 day 1 day 2 days kilometers < 6 kilometers ; 1 week 1 week 13. Hillary 14. Gabriella 1. Red crew 16. 1, centimeters 4 minutes 24 kilometers 4 weeks yds 9 ft 2 yards = 6 feet 21. B 22. A 23. B inches per minute 2. 36,960 feet per hour 26.,60 feet per hour 27. 9,000 meters per year feet per second meters per hour miles pounds in miles 12

13 Block 2 Review Answers ; 0.37 < ; 0.2 > ; 0.8 > miles 1 gallon days 1 job 2. miles 1 hour meters 1 minute 27. $0.0 1 picture (30 miles per gallon) (7 days per job) ( miles per hour) (4 meters per minute) ($0.0 per picture) oz 1 serving (12 ounces per serving) pounds $4.00 per notebook 30. $0.33 per marble miles per gallon 32. Jenna $ tickets miles 38. $ $3.33 per toy car 40. millimeters per second miles per gallon apples

14 Block 2 Review Answers 43. $ $16.00 toys miles 4 hours calories 30 ounces 47. Casey 48. Janelle 49. $ $ a. 4 packages b. $48.00 c. 3 packages d. $42.00 e. 3 packages of 8 pens f. 6 pkg $2.00 per pen 8 pkg $1.7 per pen 2. 4 miles miles 4. 3 hours. The second frog that hops 1 meter every 4 minutes would win B 60. A ,400 feet per hour inches per hour 63. 8,000 meters per minute 14

15 Lesson 12 Answers ; 40% ; 32% 3. 0 ; % 4. a. 0% b. 2% c. 0% d. 7% e. 0% a. b. c. 2 d. 200% % 2. 8% 26. a = 1 3 or 3 b = 3 c. It is three times larger than when she bought it. 27. a b c. 7 out of 1,000 stores have it in stock servings 29. Answers may vary. 30 squares bed 24 squares dresser 20 squares desk 26% left over 30. 1,840 feet 31. 8,000 pounds 32. weeks kilometers 1

16 Lesson 13 Answers 1. _ 1, 0.2, 2% 4 2. _ 1, 0., 0% _ 3, 0. _ 6, 66. _ 6 % 4. _ 4, 0.8, 80%. _ 3, 0.7, 7% 4 6. _ 2, 0.4, 40% 7. 4% 8. 60% 9. 6.%. % % % 13. 0% % _ 3 % or 66. _ 6 % % % % 19. a. (shade 3 squares) b. 2% c. 7% 20. a. (shade 4 squares) b. 66. _ 6 % c. 33. _ 3 % 21. a. (shade 1 section) b _ 3 % or 33. _ 3 % c _ 3 % or 66. _ 6 % 22. _ 1, 0.24, 2% %, 2 _ 3, , 1 _ 1, 130% 4 2. a. 4% b. % 26. a. _ 9 b. 0. _ c.. _ (about 6%) % 28. Fraction 1_ 1_ 4 1_ 3 2_ 1_ 2 3_ 2_ 3 3_ 4 4_ _ _ Decimal _ _ Percent 20% 2% 33 1_ 3 % 40% 0% 60% 66 2_ 3 % 7% 80% 0% 16

17 Lesson 14 Answers $ $ % m or 7 cm % 1. 6% 16. 6, 8 17., , % by 2% by 4 0% by 2 33 _ 1 % by line 3.2 cm 22. line 1.4 cm 23. line 7 cm 24. line 4. cm 2. line 0.9 cm % % % % 30. % 31. 2% 32. a. _ 3 4 b. _ 1 4 c. 1 d. 7% e. 2% f. 0% 18. 2, 40 17

18 Lesson 1 Answers 1. 3 pansies cards from his favorite team feet boys. a. $8.99 b. $ a. $12.00 b. $ $ a. $14.00 b. $16.00 c. $ $2.2. $ $ a. $3.60 b. $ a. $17.60 b. $ $ a. $1,440 b. $2, a. $0.7 b. $ No, 0% and 2% $7.0 7% $ _ 1 ; ; _ 1 ; ; ; ; ,000 meters per hour days per job pencils per package 27. Yan 18

19 Lesson 16 Answers 1. certain 2. impossible 3. equally likely 4. likely. equally likely 6. equally likely 7. likely 8. unlikely 9. certain. impossible 11. _ 1 ; Answers may vary. Describe something that will never happen. 13. Answers may vary. Describe something that is certain to happen. 14. Answers may vary. Describe something that is unlikely to happen. 1. a. 7 ; 0.7 b. It has mostly red jelly beans %, a. 90%; 9 b. Yes, 90% is very likely to occur , 40% 19. a. 0. _ 6 ; 66 2 _ 3 % b. No, although the chance is high, it is not certain. 20. a. hamburger _ 1 4 taco 3 20 Spaghetti 1 sandwich _ 2 stir fry 1 b. hamburger 0.2 taco 0.1 spaghetti 0.1 sandwich 0.4 stir fry 0.1 c. hamburger 2% taco 1% spaghetti % sandwich 40% stir fry % d. sandwiches e. spaghetti and stir fry 21. chocolate, strawberry, vanilla 22. a. 1 _ 2 b. 0. c. 3 _ 8 d e. 1 _ 8 f %, _ 1, _ 3, 0.4, 4% , 7%, 4 _ $ $

20 Lesson 17 Answers 1. {heads, tails} 2. {1, 2, 3, 4,, 6} 3. {blue, blue, red} 4. {1, 2, 3, 4,, 6, 7, 8, 9}. {blue, green, green, green, green, red, red} 6. {Bob, Tim, Joe} 7. _ 2 or 0.4 or 40% 8. 7 or 0.7 or 70% 9. 1 _ 3 or 0. _ 3 or 33. _ 3 %. _ 1 or 0.2 or 20% or 0.3 or 30% 12. a. Answers may vary. Find number of heads b. Answers may vary. number of heads Find 20 c. Answers may vary. number of heads Find a. truck 2 1 van 4 1 SUV 1 _ car 2 _ b. car 14. a. _ 1, 0.2, 20% b. 11, 0., % a. 40 b. _ 1, 0.2, 20% c. _ 3, 0.37, 37.% 8 d. 7, 0.17, 17.% 40 e. _ 1, 0.2, 2% 4 f. hearts 16. _ 2, 4%, , 2, 23% ,, 0% 19. $ $ d. 1; Answers may vary. 20

21 Lesson 18 Answers , 0.2, 2% 17. 1, 0., 0% , 0., 0% , 0.87, 87.% 20. 0, 0, 0% 21. Answers may vary. (e.g., P(yellow) = P(green) = 1 8 ) a. 1 9 b a b c d. 1 2 e. 0 f. 1 g. No, they must be defective. She should have rolled 2 or 3 sevens. 27. (coloring varies) a. green 6 sectors b. blue 2 sectors c. red 1 sector d. yellow 3 sectors 28. a. 1 b a. 1 4 b unlikely

22 Lesson 19 Answers 1. perimeter = 22 in area = 28 square inches 2. perimeter = 16 in area = 12 square inches 3. perimeter = 24 m area = 24 square meters 4. perimeter = 30 cm area = 30 square centimeters. perimeter = 40 yd area = 0 square yards 6. perimeter = 0 ft area = 0 square feet 7. 1 _ 3 8. a. 8.6 cm b cm c. 38.6% 9. 1 _ 2. 1 _ #9 1 _ _ _ 8 # 1 _ 2 # # #14 3 _ 4 #1 7 _ miles 18. $7 19. $

23 Block 3 Review Answers ; 70% ; 16% ; 20% % , 0.7, 7% , 0.3, % 13. 3, 0.6, 60% 14. % 1. 80% 16. % 17. 2% % % , 2, 4% 22. 2%, 0.2, $ $ m or 7 cm 32. line is 1.6 cm 33. line is 8.8 cm 34. $ $ $ $ $ $ unlikely 41. equally likely 42. certain %, 1 3,

24 Block 3 Review Answers 43. impossible 44. likely 4. a. 3 4 ; 0.7 b. Mostly pink jelly beans 46. a. 1 ; 20% b. No, 0.2 is an unlikely probability 47. a. football b. football 22 people baseball 6 people basketball 12 people 48. {tails, heads} 49. {1, 2, 3, 4,, 6} 0. {red, red, blue, blue, blue, white} a. 2 or 0.4 or 40% b. 6 2 or 0.24 or 24% c. 9 2 or 0.36 or 36% d or 0.64 or 64% a. 1 2 b. 1 c perimeter = 80 in area = 400 square inches 66. perimeter = 98 in area = 420 square inches 67. perimeter = 36 cm area = 4 square centimeters # # #

25 Lesson 20 Answers 1. diameter 2. chord 3. none 4. none. radius 6. central angle 7. chord 8. diameter 9. central angle. See student work. 1 in ft 16. mm cm m yd in 21. cm yd mm in ft yd _ See student work. 12. See student work. 4 cm See student work See student work. 180 This angle creates a diameter of the circle

26 Lesson 21 Answers cm cm ft in. 4.7 m 6. 1,26 mi in mm ft. a ft _ 7 ft ( ft) π ft b. smallest 3.14 largest 22 7 c. When the diameter is small, the answers are close to each other. If the diameter is large, the answers vary more. Both approximations are accurate to the nearest tenth. 11. Donna, because she used the diameter of in. 12. Answers may vary. 2 ft 13. The circumference is more than 3 times the diameter and 6 3 = 18, so the circumference is larger than 18 ft. 14. The circumference is more than 3 times the diameter and 3 = 30, so the circumference is larger than 30 cm ft 16. 1,26 ft mi 18. a. 0 m b. 1 in 19. No 3.14 is an approximation for π so 31.4 ft is an approximation for the circumference. 20. See student work. 2 in 21. See student work. 6 cm 22. See student work _ _ 2. 2 _ 9 26

27 Lesson 22 Answers 1. 6 mm 2. ft 3. in in. 19 cm m in ft mm km yd m ft m 1. Kim ~ she used the diameter, but Maria doubled the diameter to find the circumference. 16. $ $ in _ _ 3 27

28 Lesson 23 Answers 1. neither 2. similar 3. congruent 4. congruent. neither 6. similar 7. Yes, they are always the exact same shape, but can be different sizes. 8. Yes, they are always the exact same shape, but can be different sizes. 16. a. RO corresponds to PI OS corresponds to IN SE corresponds to NK RE corresponds to PK b. ÐR corresponds to ÐP ÐO corresponds to ÐI ÐS corresponds to ÐN ÐE corresponds to ÐK c. 1 = _ 9 3 = _ 3 1 or 3 : = = = _ 1 1 or 1 : a. 13 in b. 13 in c. equal 19. Each side is half its corresponding side in IME Y 1 cm 1. cm 9. No These are two rectangles that are not the exact same shape.. No These are two triangles that are not the exact same shape. 11. See student work. 12. See student work. U O 2 cm 20. Answers may vary. Example: 1 in 2 in 3 in 6 in in in m 13. See student work See student work. 1. a. CA corresponds to SU AR corresponds to UV CR corresponds to SV b. ÐC corresponds to ÐS ÐA corresponds to ÐU ÐR corresponds to ÐV c. = 8 16 = 6 12 = _ 1 2 or 1 : m

29 Lesson 24 Answers 1. 1 : : 3. 1 : : 3. 1 : : : : 2 9. : in ft 12. m cm m 1. 4 in 16. The second rectangle is 4 times as large as the first. 17. The second triangle is three times as large as the first. 18. See student work. a. 4 cm b. 1 : : in 21. Answers may vary. Sides should be in a ratio of 2 : 3. Example: 2 in 4 in 3 in 6 in : 1. They are the exact same size and shape so they have equal perimeters. 23. a. LA corresponds to TR AK corresponds to RE LK corresponds to TE b. ÐL corresponds to ÐT ÐA corresponds to ÐR ÐK corresponds to ÐE c. _ 3 9 = 4 12 = 6 18 = _ 1 3 or 1 : in cm m 29

30 Block 4 Review Answers 1. diameter 2. central angle 3. none 4. chord. a. 24 cm b. 9 in c. 4 1 _ 2 m 6. a. 4 ft b. 2. mm c. 3 1 _ 4 km _ _ _ cm ft in cm mm ft 19. 1,884 ft in in m cm mm 2. 8 ft 26. congruent 27. similar 28. neither 29. See student work. 30. a. always b. sometimes c. sometimes 31. a. RO corresponds to WE OA corresponds to ES AM corresponds to ST MR corresponds to TW b. ÐR corresponds to ÐW ÐO corresponds to ÐE ÐA corresponds to ÐS ÐM corresponds to ÐT c. _ 8 2 = _ 4 1 or 4 : a. TI corresponds to JO IM corresponds to ON MT corresponds to NJ b. ÐT corresponds to ÐJ ÐI corresponds to ÐO ÐM corresponds to ÐN c = = = _ 1 1 or 1 : : : : : 37. : ft m cm m in

Name Period Date. are equivalent because they both simplify to 43. Two fractions are equivalent when they simplify to the same value.

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