Chapter 2: Ratio, Rate, and Percent

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1 Chapter : Ratio, Rate, and Percent Getting Started, p. 9 4 and since 4 and 0 since 0 and since and since a) number of red beads:number of blue beads 8:7 number of green beads:number of red beads 6:8 c) number of yellow beads:number of white beads : d) total number of beads number of green beads:total number of beads 6:4 e) total number of beads: total number of green beads 4:6. 6:0 4:; : 4:; :40 4: Therefore, parts a, b, and f are equivalent to 4:. 4. a) There are shaded squares and squares in total. number of shaded squares total number of squares There are shaded areas and 4 areas in total. number of shaded areas total number of areas 4 c) There is shaded square and 4 squares in total. number of shaded squares total number of squares 4 d) There are 4 shaded areas and 4 areas in total. number of shaded areas total number of areas % d) e) f) (all the same) % 0% 6. % or 4 0% a) c) % 0% % % % % 0 % Therefore, %,, and are equivalent a) i. There are 7 shaded squares and unshaded squares. number of shaded squares:number of unshaded squares 7: ii. There are shaded squares and 47 unshaded squares. number of shaded squares:number of unshaded squares :47 i. area of shaded squares 7 7 area of whole shape area of shaded squares area of whole shape 7 ii. area of shaded squares area of whole shape area of shaded squares area of whole shape c) i or 70% ii. 0. % 8. For each multiplication, count how many digits are to the right of the decimal point in the number on the right. In the number on the left, place a decimal point so that there are as many digits to its right as there are in the number on the right; this new number is the solution. a) c) 8.76 d) a) c) 08 d) 8 Make a guess; if that guess is too high then choose lower number for the next guesses, if it is too low then choose higher numbers for the next guesses. a) 4 c) 0 0 d) 6 60 e) f) 0 a) c) 0.0 d) e) f) Any number divided by itself is equal to one. a) c) d).. Solving Ratio Problems, p. 44. For example, a) i. :4 : ii. 8: : iii. 4: :9 iv. : : i. :4 is equivalent to : So : :. The scale factor is since. ii. 8: is equivalent to 4: So 4: :. The scale factor is since. iii. The scale factor is since 9. iv. : is equivalent to :. So : :. The scale factor is since. c) i. ii. 4 0 iii. 4 iv a) :8 :6 The scale factor is The missing term is 6. :4 0: :4 is equivalent to 4:. 4: 0: The scale factor is. The missing term is. 7. a) 4: 8:0 :4 4:8 Nelson Mathematics 7 Solutions -

2 8. a) For example, :6 is equivalent to :8. :8 6: The scale factor is The missing term is 8 6. :6 4: The scale factor is The missing term is 6 Therefore, :6 is equivalent to :8, 6:6, and 4: For example, 6:4 is equivalent to :9. :9 : The scale factor is. The missing term is :4 8: The scale factor is. The missing term is 4 6 Therefore, 6:4 is equivalent to :9, :7, and 8:6 c) For example, 48:6 is equivalent to 4:. 4: 6: The scale factor is 4. The missing term is 4 48:6 96: The scale factor is The missing term is 6 7 Therefore, 48:6 is equivalent to 4:, 6:, and 96:7 d) For example, : is equivalent to :. : : The scale factor is 6. The missing term is 6 : 66: The scale factor is. The missing term is 6. Therefore, : is equivalent to :, :0, and 66:6. 9. The ratio in the first diagram is :, the ratio in the second diagram is :, and the ratio in the third diagram is 60:. Since : and 60: are both equivalent to :, they all represent the same ratio for the number of orange sections to the total number of sections. a) 7:4 : 7:4 is equivalent to :. : : The scale factor is The missing term is. :6 : The scale factor is. The missing term is 6 9. a) The length is 6 cm. :0 6: The scale factor is 6. The missing term is Therefore, the alligator is 80 cm long. The height is cm. : : The scale factor is. The missing term is 0 Therefore, the elephant is 00 cm, or m, tall. c) The length is 4 cm. : 4: The scale factor is The missing term is Therefore, the snail is cm long. For example, I will convert the height to centimetres since I will draw in centimetres. 0 m 000 cm : 000 : 000 The scale factor is. The missing term is. Therefore, the CN Tower is cm high in the scale drawing. a) For example, 400 g: kg 400 g:0 g 400:0 For example, 6 cm:7 mm 60 mm:7 mm 60:7 c) 00 s : min 00 s:80 s 00:80 4. a) Katherine spends 7 h in school each day, so she spends 7 60 min 40 min. lunch break:total time in school 0:40 Katherine spends 0 min 0 min for lunch each week. She spends 40 min min each week in school. lunch breaks for a week:total time in school in one week 0: c) month 4 weeks lunch break for month 4 lunch break in week min There are 60 min in h. Therefore, she spent 600 min 60 min/h h for lunch each month.. a) There are numbers between and ; half of them are even and half of them are odd, that is, there are 0 even numbers and 0 odd numbers. Between and, is no longer included, so there are only 49 odd numbers between and. There are 0 even numbers and 49 odd numbers. number of even numbers:number of odd numbers 0:49 multiples of 6: 6,, 8, 4, 0, 6, 4, 48, 4, 60, 66, 7, 78, 84, 90, 96 multiples of 8: 8, 6, 4,, 40, 48, 6, 64, 7, 80, 88, 96 There are 6 multiples of 6 and multiples of 8. number of multiples of 6:number of multiples of 8 6: c) prime numbers:,,, 7,,, 7, 9,, 9,, 7, 4, 4, 47,, 9, 6, 67, 7, 7, 79, 8, 89, 97 The other numbers are all composite. There are prime numbers and composite numbers. number of prime numbers:number of composite numbers :74 6. : : The scale factor is 4. The missing term is 4 So there are 0 girls in Todd s class. total number of students boys + girls + 0 Todd is incorrect. There are students in his class. 7. :4 9: The scale factor is 4. The missing term is Therefore, Luca s adult height will be 7 cm 8. a) :: :: The scale factor is, since. The first missing term is 9. The second missing term is 6 The total number of ice cream cones sold is I will list all the ratios equivalent to :: until I find the one where the total number of ice cream cones is 8 Equivalent Ratio Total Cones :: 9::6 96:60: :6:66 0 :70:68 40 :7:70 0 8:80:7 60 :8: :90:76 80 Therefore, 4 vanilla, 90 chocolate, and 76 strawberry cones were sold. - Chapter : Ratio, Rate, and Percent

3 Exercises, page 48 mm. a) days c) $ week 6. a) For example, 4 chocolate bars $. 0 cm d) 4 months goals goals games games The scale factor that relates the two rates is since The missing term is goals goals games games The scale factor is The missing term is goals Therefore, games is equivalent to goal games and goals 0 games. For example, km km 60 min 6 min The scale factor that relates the two rates is since The missing term is km km 60 min min The scale factor that relates the two rates is since. The missing term is 60 Therefore, km 60 min is equivalent to km 6 min and km 0 min. c) For example, 6 pizzas pizzas 0 min min The scale factor that relates the two rates is since 0. The missing term is 6. 6 pizzas pizzas 0 min min The scale factor is The missing term is 0 6 Therefore, 6 pizzas 0 min is equivalent to pizzas min and pizzas 60 min. d) For example, 0 penalties penalties games 0 games The scale factor is The missing term is penalties penalties games games The scale factor that relates the two rates is since The missing term is. Therefore, 0 penalties is equivalent to 0 penalties and games 0 games penalties games. 7. a) To find the average rate, find the rate for h. 8 km km 7 h h The scale factor that relates the two rates is 7 since 7 7. The missing term is km 4 km 7 h h The average rate is 4 km/h. 8 km km 8 h h 8 km. km 8 h h The scale factor that relates the two rates is 8 since 7 8. The missing term is The average rate would be. km/h. 8. a) h h trucks 6 trucks 400 km km 4 wheels wheels h h trucks 6 trucks 4 wheels 400 km 80 km 8 wheels Therefore, in h you can Therefore, six trucks have drive 80 km. 8 wheels. c) h 8 h d) 6 boxes box $ $ 7 donuts donuts h 8 8 h $ 8 6 boxes 6 box $ 80 7 donuts 6 donuts Therefore, in 8 h you can Therefore, one box contains earn $8 donuts. e) 4 min min f) 6 pencils pencils 8 words words $. 07 $ 4 min min 8 words 6 pencils pencils 64 words $7 $. 06 Therefore, in min, you can Therefore the missing term is type 64 words B does not model this situation since the first rate shows the number of pizzas in the numerator and the second rate shows the number of players in the numerator. 4 km km 4 h h is equivalent to. km km h h km 4 60 km h 4 4 h Therefore, he will bike 60 km in 4 h. Nelson Mathematics 7 Solutions -

4 $ 6 $ 4 4 CDs CDs 6 4 is equivalent to 4. $ 4 $ 4 CD CDs $ 4 $ 4 CD CDs Therefore, he can buy CDs with $4 cars/0 min / min cars /0 min cars/ min Therefore, he can serve cars in min. $ 7 $ 6 h 4 h $ 7 $ 48 6 h 4 h Therefore, she will earn $48 in 4 h. 4. km 8 km h h km 8 km h. h Therefore, it will take him h to jog 8 km.. 6 kg kg $ $ 0 6 is equivalent to. kg kg $ $ 0 kg 4 8 kg $ 4 $ 0 Therefore, you can buy 8 kg of oranges for $ 6. a) 8 shots stopped shots stopped shots taken shots taken 8 shots stopped shots stopped shots taken. shots taken Therefore, the goalie can expect to stop shots per game. If there are shots in one game, then in games, there will be 7 shots c) If 8 out of shots are stopped, then shots are not stopped, so there are goals per shots taken. goals goals shots taken 7 shots taken goals 7. goals shots taken 7. 7 shots taken Therefore, they can expect goals in games 7. For example, a ratio is a comparison of two quantities that are measured in the same units. A rate is a comparison of two quantities that are measured in different units. A ratio would be used to compare the length of two boats, measured in metres. A rate would be used to compare how much money a student makes working for a certain number of hours. 8. km 60 km h h km 6 60 km h 6 6 h 6 h 60 min/h 6 min It would take h 6 min to complete the trip at km/h. 90 km 60 km h h 90 km km h h min/h 47 min to the nearest minute It would take h 47 min to complete the trip at 90 km/h. Since h 47 min h 6 min min, it would have taken min longer. 9. First, calculate how many minutes are in day (4 h). 60 min : h min : 4 h The scale factor is 4. The missing term is There are 440 min in day. 4 times times min 440 min 4 times times min min Therefore, a grey whale s heart beats 0 times in a day. The percentage of battery power used in h is % 68% %. % 68% h h % 68% h. h So, his battery will provide power for another h. a) Chevrolet Corvette: Honda Civic:.00 L 80 km L 6 L km 7 km L km.00 L 8 80 km 8 89 L 6 L L km 7 km 7. km The Chevrolet Corvette uses The Honda Civic uses 8. L 89 L of fuel in km of fuel in km. Honda Accord: Ferrari F40: 4 L 6 km L 466 L km 09 km L km 4 L 6 6 km L 466 L L km 09 km 09. km The Honda Accord uses The Ferrari F40 uses 6 L 9.09 L of fuel in km. Ford Escort:.6 L 94 km L km.6 L L 94 km 94. km The Ford Escort uses 8.69 L of fuel in km. of fuel in km. Ford Taurus: 7.74 L 8 km L km 7.74 L 8 8 km.8 7 L km The Ford Taurus uses 7 L of fuel in km. -4 Chapter : Ratio, Rate, and Percent

5 Porsche 9 Turbo: 46. L km L km 46. L. 89 L km. km The Porsche 9 Turbo uses 89 L of fuel in km. Therefore, the Honda Civic uses the least fuel since it uses the least litres of fuel per km. The Chevrolet Corvette and the Porsche 9 Turbo tie for using the most fuel because they use the most litres of fuel per km. 4 Communicate about Ratio and Rate Problems, p.. 6 I rewrote 4 0 as to make solving the 6 proportion easier. Since I know that I can 4 6 rewrite 4 as, and 4 0 as, this answer makes sense me. Therefore, Marlene can run 6 km in 4 min. 4. Chris s reasoning is correct. For example, litres of punch number of people I know that L of punch serves people. I must determine how many litres of punch Chris needs to serve 90 people. I can use a proportion to write the information I know. 6 Since I know that I can rewrite as, this answer makes sense to me. litres of punch Therefore, L of punch are needed.. 0. money earned number of flyers I know that Sam earns $ for every flyers he delivers. I need to determine how many flyers he has to deliver to earn $4.0 I can use a proportion to write the information I know I rewrote 0. as to make solving the proportion easier Since I know that I can rewrite as , this answer makes sense to me. 40 number of flyers 800 Therefore, Sam needs to deliver 800 flyers to earn $ No, his reasoning is not correct. For example, a ratio compares two quantities using the same units. Akeem s comparison uses two different units, so it is a rate, not a ratio. Akeem needs to convert L to ml before he can compare the capacities. 70:0 is the correct ratio. 7. Rosa is incorrect. For example, number of copies minutes I know that the photocopier can make 800 copies in h (60 min). I need to determine how many copies can be made in min. I can use a proportion to write the information I know. 0 number of copies I rewrote as to make solving the proportion easier. Since I know that I can rewrite as 0, this answer makes sense to me. number of copies 0 Therefore, the photocopier can make 0 copies in min. 8.. m above water 9 m above water m below surface m below surface. m above water 6 9 m above water m below surface 6 7 m below surface No, since 9 m + 7 m 8 m, the iceberg is 8 m from top to bottom g 400 g g g 76 $76, which is less than $0, so you would buy the peanuts at the bulk-food store. a) For golden raisins: For dark raisins: $. 066 $ $. 0 $ g 00 g g 00 g $. 066 $.0 g $. 0 $7 00 g g 00 g 00 g of golden raisins cost 00 g of dark raisins cost $. $7. $.0 $7 $ You would save $ by buying the cheaper raisins. For golden raisins: For dark raisins: $. 066 $. 6 $. 0 $. 6 g g g g $ $.6 $ $.6 g. 0 g g g 0 g of golden raisins can 660 g of dark raisins can be bought for $.6. be bought for $.6. Nelson Mathematics 7 Solutions -

6 Mid-Chapter Review, p. a) For example, :6 : The scale factor is The missing term is :6 : The scale factor is. The missing term is 6 8. :6 0: The scale factor is 4. The missing term is Therefore, to 6 is equivalent to to, to 8, and 0 to 4. For example, 8:4 is equivalent to :. : :9 The scale factor is. The missing term is 6. 8:4 :84 The scale factor is The missing term is 8 6. Therefore, 8:4 is equivalent to :, 6:9, and 6:84. c) For example, 6:4 is equivalent to 4:. 4: 0: The scale factor is. The missing term is. 6:4 : The scale factor is. The missing term is 6 8. Therefore, 6 4 is equivalent to 4, 0 8, and. a) 40 cm: m 40 cm:00 cm 40:00 min: h min:0 min :0 c) 0 g: kg 0 g:0 g 0:0. a) :4 :6 The scale factor is 4. The missing term is 4 : 60:0 The scale factor is. The missing term is 4 since 4 c) 0:48 0: The scale factor that relates the two rates is since 0 The missing term is 48 d) 4: : , so 7. 9 The missing term is 4 7. e) :0 :0 0 0, so 0 The missing term is. f) 8:4 6: 6 8., so The missing term is The boat in the diagram is cm long. :0 : The scale factor is. The missing term is 0 00 Therefore, the actual length of the boat is 000 cm, or 0 m.. 9 m high m high 6 m long m long The scale factor that relates the two rates is, since 6 The missing term in 9. Therefore, the fence post is m tall. 6. passes complete passes complete pass attempts pass attempts passes complete 0 passes complete pass attempts pass attempts Therefore, he can expect to complete 0 passes. 7. a) ratio; For example, it is a ratio since both heights are measured using the same units. rate; For example, it is a rate since pens and money are measured using different units. c) rate; For example, it is a rate since distance and time are measured using different units. 8. $ 400 $ weeks weeks $ $ 400 weeks 6 weeks Therefore, she will earn $400 over the summer holidays km 4 km h h 0 4 km h h Therefore, it will take him h to cycle 4 km. kg 0 kg $. 40 $ kg 0 kg $. 4 0 $ 0 Therefore, 0 kg of potatoes will cost $ :4 :76 :4 is equivalent to :8. :8 :76 The scale factor is 4.. The missing term is The camp can t hire 4. coaches, so they should hire 4 or coaches. Or maybe they can hire 4 full-time coaches and coach who can work half-time. For example, I interpreted the calculation as the ratio of the number of coaches to the number of players. Ratios and Percents, p. 8. a) The figure is divided into squares, 44 of which are shaded % The figure is divided into squares, 6 of which are shaded. 6 6% I know that 40, so 6 is the number I m or 90% 40 Therefore, she saved 90% of the shots. -6 Chapter : Ratio, Rate, and Percent

7 7. Fraction Ratio Decimal Percent a) : 0% : 4 40% c) : % d) : 0% e) 4 :4 % 8. a) 6 of the squares are not shaded. 6 6%; 64 of the squares are not shaded % % or 06., 64% or a) 0 0 I know that 0, so 7 is the number I m I know that 0, so is the number I m or % 46 0 or % c) 9 d) 4 I know that 4, so I know that 0, so 9 4 is the number I m 4 0 is the number I m or % or 80% 0 e) I know that 4, 4 so is the number I m 4 7 or 7% 4 a) % 48 0 I know that 0, so 48 is the number I m or % c) 6 I know that 4, so 6 4 is the number I m or % d) 6 % I know that, so 6 is the number I m or 60% e) I know that 0, so 0 is the number I m or 40% 0 f) I know that 4, 4 so is the number I m 4 or % 4 I know that 4, so 4 is the number I m or % Therefore, 60% of the average rainfall has fallen. a) i. % or 0. ii. % or iii. 76% or 076. iv. 7% or v. 98% or 098. vi. 80% or 080. i. 76 ii. iii iv. v. vi. a) 74%, 66%, 4%, % I will convert each number into a percent. % % and 68 % 68% Therefore, the order from greatest to least is 68, 4%, 6%, and Nelson Mathematics 7 Solutions -7

8 c) I will convert each number into a percent or % or 7% % 8% and 06 % 6% Therefore, the order from greatest to least is 79%, 4, 8,, %, and d) I will convert each number into a percent. is equivalent to or % is equivalent to % % 0 8 % 8% and 46 % 46% Therefore, the order from greatest to least is 97%, 6%, 6 60, 46, 8, and sales tax 4. a), sales tax 8 or $08 $00 7 sales tax, sales tax 7 or $07 $00 6 sales tax c), sales tax 6 or $06 $00. I will change each student s mark into a percent. Andrew: I know that 4, so 4 is the number I m or % Mohammed: 8 40 I know that 40, so 8 is the number I m or 9% 40 Ian: is equivalent to I know that, so 9 is the number I m or 90% Tyrone: 4 0 I know that 0, so 4 is the number I m or % Therefore, their marks in order from greatest to least are 9%, 9%, 90%, and 68% (Mohammed, Andrew, Ian, Tyrone) I know that 0, so is the number I m 0 0 or % Therefore, the milk has a % fat content. 7. Lindsay lost % 8% % of her tennis matches. The ratio of losses to wins is :8. 8. a) I know that 80, so 48 is the number I m or 60% 80 Therefore, they won 60% of their games. percent tie games % percent won percent lost % 60% 0% % 9. The price increased by $7 $ $ I know that 0, so 0 is the number I m or 40% 0 Therefore, the price increased by 40%. -8 Chapter : Ratio, Rate, and Percent

9 a) 9: c) 67 67% a) For example, you could use the proportion to calculate as a percent. Since the scale factor is not a whole number and since the percent scale factor, the percent will not be a whole number. For example, 7. I could use the proportion to 7 calculate as a percent. Since the scale factor is not a whole 7 number and since the percent scale factor, the percent will not be a whole number. 6 Solving Percent Problems, p. 6. a) For example, I know that % of 60 is 6. Since % is half of %, I know that % of 60 is half of 6. So % of 60 is. I add 6 and to get c) % or 0., so % of or 9 6. a) For example, Therefore, % of 60 is. For example, % or, so % of or 4 c) For example, Therefore, 0% of 4. d) For example, Therefore, % of a) For example, I know that 0%, so 0% of 0 0 or For example, Therefore, 7% of 4 is 8. c) For example, Therefore, 0% of 4 is 9. d) For example, Therefore, % of 0 is 6. e) For example, Therefore, % of 00 is f) For example, Therefore, 44% of 0 is 8. a) 0 0 is equivalent to. 0 Therefore, 0% of 0 is. is equivalent to Therefore, % of 88 is c) 7 is equivalent to Therefore, % of 70 is 7. Nelson Mathematics 7 Solutions -9

10 d) 7 7 is equivalent to Therefore, 7% of 6 is e) 4 is equivalent to Therefore, % of 60 is 4. f) Therefore, 44% of 0 is or % Therefore, % of the computers failed to pass inspection. a) not blond hair % % 7% 7% % + % + % total students Therefore, there are 48 students in the class. total is equivalent to 4. total 4 total 4 48 Therefore, there are 48 students in the class. a) Therefore, the dealer wants to make $00 profit. sale price price of car + profit $ $00 $ For example, I calculate 0% of $ and get $ so I know that she left a 0% tip The new chocolate bar is 0 g + g 60 g. 4. g 8 g 7 g or 8. 9% 8. 6 Therefore, you have increased your fat intake by about 9%.. a) Therefore, the dress originally cost $0 sale price original price discount $00 $40 $60 6. No. For Jane s Jean Shop: sale price original price discount $80 $40 $40 Denim Discounters final sale price st sale price st sale price nd discount original cost st discount $6 $0 $80 $4 $44.80 $6 Therefore, the jeans would be cheaper at Jane s Jean Shop. - Chapter : Ratio, Rate, and Percent

11 7. sleep: % is about ; 4 h 8 h school: % is equivalent to 4 ; 4 4 h 6 h job: % ; 4 h 4 h or h 4 min homework: 7% 07; 07 4 h 7 h meals: 8% is just a little more than 7%, so estimate h entertainment: For example, I can see that Matthew sends half the day sleeping and entertaining. There are h in half a day and I already estimated that he spends 8 h sleeping. He spends h 8 h 4 h on entertainment. Matthew spends 8 h sleeping, 6 h at school, two and a half hours at his job, nearly two hours on homework, just under two hours on meals, and about 4 hours on entertainment Therefore, Jasleen has grown 0 cm Therefore, they produced 0 units per day before the new process was introduced new tax rate previous tax rate + increase $ $ $0 cm by cm photo: area cm cm 80 cm 4 cm by 0 cm photo: area 4 cm 0 cm 70 cm The area increased by 70 cm 80 cm 40 cm or 00% 80 8 Therefore, the area of the photo was enlarged by 00%. 7 Decimal Multiplication, p. 66. a) 4 squares are in the overlap of rows and 8 columns, so squares are in the overlap of rows and 7 columns, so a) For example, 9.7 is about, and 6 is about a half, so is about half of, or. For example,.7 is about 4 and.86 is about 6, so.7.86 is about 4 6 or a) For example, multiply and divide by Therefore, For example, multiply and divide by Therefore, a) squares are in the overlap of rows and 6 columns, so 6 6 squares are in the overlap of 7 rows and 8 columns, so a) For example, to estimate, 8 is close to 0 and is close to 0, so 8 would be close to 0 0 To calculate, Multiply one term by Multiply Divide product by so 8 04 For example, to estimate, is close to 0 and is close to, so would be close to 0. To calculate, 0 Multiply one term by 0. Multiply.. Divide product by so Nelson Mathematics 7 Solutions -

12 c) For example, to estimate, is close to 0 and 0 is close to 0, so 0 would be close to 0 0 To calculate, 0.0 Multiply one term by Multiply Divide product by. so d) For example, to estimate, 6 is close to and 0 is close to 0, so 6 0 would be close to 0. To calculate, 0 0 Multiply one term by Multiply Divide product by. so e) For example, to estimate, 0 is close to 0, so 0 would be close to 0 To calculate, 0 0 Multiply one term by..0 Multiply..0 0 Divide product by. so 0 0 f) For example, to estimate, is close to and is close to, so would be close to. To calculate,.0 Multiply one term by.. Multiply... Divide product by. so. It is easier to multiply 64 mentally because is the same as, which is a convenient fraction because multiplying by is like dividing by : 64 It is harder to multiply 7 64 because 7 is 7, which is not a convenient fraction Try all the possibilities: from from from from from from This is the closest to. Distance speed time 9 km/h. h 7 km Cost price per kg number of kg $/kg.4 kg $ guitar picks cost $.04, so half as many would cost half as much: 6 would cost $ 8 picks would cost $.04 + $ $7.6.. Distance speed time 7. km/h. h 87 km 6. Cost price per L number of L 8 /L 8. L 486. or $ Area length width. m. m 6. m 8. Area of ceiling length width 4. m.9 m 6.8 m The area of the ceiling is larger than the area that can be covered with one can of paint. So one can is not enough to paint the ceiling with two coats. 9. Total income $0 + 9% of sales $ $47.8 $0 + $4 $9 Adult height of Miguel height at 9 m 9 78 m Adult height of Romona height at 07 m m About 9 97 births took place. Number of city dwellers 79% of (to the nearest person) First reduction 0% of $9000 $9000 $800 Price after first reduction $9000 $800 $700 Second reduction 0% of $700 $700 $440 Price after second reduction $700 $440 $760 The final sale price is $76 4. Meagan is wrong: 69; Chapter : Ratio, Rate, and Percent

13 8 Decimal Division, p. 70. a) c) c) a) For example,.6 is close to 4 and 9 is close to, so.6 9 is close to 4 4. For example, 78 is close to and is close to, so 78 is close to 7. a) Convert to a fraction then multiply numerator and denominator by so Convert to a fraction then multiply numerator and denominator by So, a) c) Convert to a fraction then multiply numerator and denominator by So, a) So, So, c) So, 6.8. d) So, e) So, 4.4 f) So, 04 0 Nelson Mathematics 7 Solutions -

14 a) A dime is worth $ $ 0 $ 0 $ $. 0 $ 0 $ $. 0 $ $ $ Therefore, I would have dimes. A nickel is worth $0. $ 0 $ 0 $ 0 $. 00 $ 0 $ 0 $. 0 0 $ $ 0 $ 0 Therefore, I would have 0 nickels. c) A quarter is worth $. $ 0 $ 0 $ $. 0 $ 0 $ 0 $. 0 $ $ 0 $ 46 Therefore, I would have 46 quarters. d) A penny is worth $0 $ 0 $ 0 $ 0 $. 00 $ 0 $ 0 $. 0 0 $ $ 0 $ 0 Therefore, I would have 0 pennies. To divide 0 I converted it to a fraction (. ) 00. and then multiplied by to make the denominator a whole number. The result is, or. So, in the end, to divide 0, I multiplied by. After converting to a fraction and multiplying by I will have 9. Since 9 ends in, it is divisible by ; the remainder will be Similarly, I get 9 0 9, but the ones digit in 9 is not even, so it is not divisible by ; I will get a remainder of a) 80 cm 8 m 4 4 m 8 m Therefore, there will be 4 pieces, plus some rope left over. 4 m 4 m Therefore, there will be 8 pieces, plus some rope left over. c) 7 m is half of 4 m, each 4 m piece from part could be cut in half. Then there would be twice as many 7 m pieces as there were 4 m pieces, that is, 8 6 pieces each 7 m long. There would be some rope left over from cutting the 4 m pieces, but it would not be as long as 7 m, so Nathan could not make another 7 m piece from this extra rope. Nathan could make 6 pieces each 7 m long. d) half a metre m 4 m m Therefore, there will be pieces. 4. time distance speed a) km 4. km / h km. km / h It will take about h to walk It will take about h to walk km at 4. km/h. km at. km/h.. Divide L L glasses can be filled, with some cola left in the bottle. 6. $0 000 Divide /L To the nearest litre, I can buy almost L of gasoline. 7. Divide $9 $8.0/h Susan worked h. -4 Chapter : Ratio, Rate, and Percent

15 8. Divide km 4.7 h The train s average speed was about km/h. 9. a) Divide 8 m The adult male was about m tall. Divide 8 m The adult female was about 7 m tall. Divide 80 L L/min It will take exactly 8 min. a) 9 cm cm cm cm 9 cm cm cm cm 9 cm 08 cm cm cm Therefore, 08 cm of ice will result. 9 cm cm The scale factor that relates these two cm cm ratios is 09, since The missing term is Therefore, about 97 cm of water must be frozen to produce cm of ice. 40 km m Divide m 0 m/s It would take about s. There are 60 s/min 60 min/h 4 h/day seconds in a day s s/day Therefore, it would take about 400 days. time distance speed Distance Speed Time Bullet Train 7 km 7.km/h 8 h Airplane 9 km 68 km/h 7... h Car 04 m 90 km/h 6... h The times required are, from least to greatest, 7 h, 8 h, and 6 h, for the airplane, bullet train, and auto, respectively. Chapter Self-Test, p. 7 a) white squares:green squares 4: white squares total squares 4 6 c) green squares total squares or 7% 6 6. Therefore, 7% of the squares are green. For example, :9 : The scale factor is. The missing term is 9 7. :9 0: The scale factor is The missing term is 9 9 :9 :8 The scale factor is The missing term is Therefore, :9 is equivalent to :7, 0:90, and :8.. a) The scale factor is. The missing term is 6 4 The scale factor that relates the two ratios is since 6. The missing term is 4 4. Nelson Mathematics 7 Solutions -

16 c) is equivalent to The scale factor that relates the two ratios is since 9. The missing term is since 4. d) is equivalent to. The scale factor is. The missing term is 4. For example, I would set up and solve the following proportion. :600 9:. The scale factor is 9, and the missing term is The actual height of the building is 400 cm, or 4 m.. coffees 9 coffees $. 400 $ The scale factor is 4.. The missing term is $ $8. Therefore, Marianne will need $8 to buy 9 large coffees. 6. $7 $ 7 9 h h 9 is equivalent to 8. $8 $ h h The scale factor is The missing term is $8.00 $96. Therefore, she would earn $96 in h or 0% 0 percent of other gases % percent of oxygen % 0% 80% Therefore, 80% of the air is made up of other gases. 8. Fraction Ratio Decimal Percent a) :60 % : 8 8% c) 8 8: 8 8% 9. a) So, 40% of is is equivalent to or 70% Therefore, out of 0 is 70%. c) Therefore, 8% of 0 is Therefore, 70 fans are at the game. 8 $. 0 $ 8 0. $. 0 $. 00 Therefore, the CD cost $.0 40 $ $ $. 0 8 $ 8 Therefore, Akeem sold it for $8.00 $.0 $8 a) total people number of children + number of adults or % 40 Therefore, % of the crowd are children. percent of adults % percent of children % % 4% 4. For example, the decimal equivalent of % is and the decimal equivalent of 7% is 7. You can multiply an amount by in your head but that s not easy to do with 7.. For example, the decimal equivalent of % is 0 and the decimal equivalent of % is It is easy to multiply an amount by both 0 and in your head. -6 Chapter : Ratio, Rate, and Percent

17 6. For example, to calculate 0% of you might take half of (divide it by ). To calculate 4% of you would probably set up and solve the proportion 4: : 7. a) For example, 4 is about, and. is a little more than. 4., and my answer should be a little more than that, which is about. 7 is more than half but less than, so is a bit less than halfway between 7.4 and half of This is about. c) For example, 6. is about 60 and 9 is about 60, so the answer is about. d) is about, and dividing by is the same as multiplying by 46 is about, and so (7.9 4.) (7.9 4.) Chapter Review, p. 7 a) For example, 9:0 8: The scale factor is The missing term is 0 4 9:0 :60 The scale factor is. The missing term is 9 7. Therefore, two equivalent ratios for 9:0 are 8:40 and 7:6 For example, 4: 6: The scale factor is 4. The missing term is 4 4: :0 The scale factor is 6. The missing term is Therefore, two equivalent ratios for 4 c) For example, : 4: The scale factor is The missing term is 6 : :9 The scale factor is. The missing term is 6. Therefore, two equivalent ratios for to are 4 to 6 and 6 to 9. are 6 0 and 4 0. a) 8 8 $ For example, an equivalent ratio is 8 The scale 0 4 factor that relates the two ratios is, since kg g 80 g 80 g For example, an equivalent ratio is. The scale 80 factor that relates the two ratios is 80 since a) :7 : The scale factor is. The missing term is 6. 6:9 7: The scale factor is The missing term is 9 8. c) 4: 8:4 The scale factor is The missing term is 7 since 7 4. d) : :48 The scale factor is 4. The missing term is : : The scale factor is 8.. The missing term is Therefore, the ostrich will be 8. cm tall in the drawing. For example, Every centimetre in my diagram represents 0 cm in real life. I divided by 0 to find the scale factor and then multiplied cm by the scale factor to determine how tall I should draw the ostrich. 80 km km 80 km. is equivalent to 60. h h h 60 km km h h 60 km 00 km h h Therefore, the car will travel 00 km in h. 6. Fraction Ratio Decimal Percent a) 4 4: % 0 6 6: 6 6% c) 86 86: 86 86% d) : 0 % e) : 0 % 7. No she is not correct. For example, the total number of cars is The ratio of red cars to total cars is 6:4. She would have to calculate the percent for 6 4. Nelson Mathematics 7 Solutions -7

18 8. Ingredient a) Fraction (by weight) Decimal (by weight) sausage 8 08 cheese crust 0 0 tomato sauce mushrooms 0 c) No the graph would look exactly the same. This is because fractions decimals and percents can all be written as equivalent values. 9. a) Therefore, % of 84 is Therefore, 4% of 00 is 48. c) 0 Therefore, % of 0 is Therefore, 0 tickets are sold. Raj: saved amount earned amount spent $8 $4 $ % Raj saved about 8% of his earnings. Michael saved $ % Michael saved 4% of his earnings. Therefore, Raj saved a greater percent of his earnings. a) 8 squares are in the overlap of rows and 9 columns, so 9 8. There are 8 groups of 40 squares, and each group of 40 represents 4. Therefore a) 4 4 Multiply one term by Multiply Divide product by So, Multiply one term by Multiply Divide product by So, c) So, 6.. d) So, Chapter : Ratio, Rate, and Percent