Answers for Chapter 2 Masters

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1 Answers for Chapter 2 Masters Scaffolding Answers Scaffolding for Getting Started Activity # of white squares 2 A. i) = ii).2 Total # of squares B. 2% # of shaded squares 58 C. i) = ii).58 Total # of squares D. 58% E. Start Finish F. i) For example, 1 1 ii) For example, Fraction: ; Decimal:.1; Percent: 1%; Ratio: 1 white squares: total squares or 1: G.. For example, because a fraction with a denominator or can be changed easily to a percent and a decimal. For a percent, the numerator is the percent. For a decimal, the numerator is also the decimal in tenths or one hundredths. Scaffolding for Do You Remember? Questions 2,, 5, 6, & 2. a) Number of red squares:number of blue trapezoids = 8:7 b) Number of green triangles:number of red squares = 6:8 c) Number of yellow rhombi:number of white ovals = 2:1 d) Total number of shapes = = 2 number of green triangles:total number of shapes = 6:2 e) total number of shapes: total number of green triangles = 2:6. ii) For example, you can divide both numbers in 12:15 by to get :5. So they are equivalent iii) For example, 2: = :6, so it is not equivalent to :5 iv) For example, 9: = 9: and :5 = 8:, so 9: is not equivalent to :5 v) For example, I found out in iv) that 9: is not equivalent to :5 vi) For example, if I divide both numbers in 2: by 8, I get :5. So they are equivalent. 5. % d) e) f) (all the same) 1 2 b) a) c) % 2% % % 5% 6% 7% 8% 9% % a).5 is between. and.5 c).82 rounded to the nearest tenth is.8 e).25 is between.2 and. b) 5% is between % and % d) 25% is between 2% and % f) 1 = % =.25 = 1

2 . For example a) 2 = c) 2 = e) 7 =.7 = 2 In part b) I found out that I know that 7 1 = =. I know that 7.1 = 7. Guess: I think that Guess: = Test: 7.1 =.7 Test: Use a calculator test = b) 2 = d) = 16 f) 111 = 1.11 I know that 2 1 = 2 I know that 1 = I know that = 111 I know that 2 2 = I know that 2 = 2 I know that = 11.1 Guess: I think that = Guess: 1.6 Guess:.1 Test: Use a calculator to test. Test: 1.6 = 16 Test: = = Scaffolding for Lesson 2., Questions 5 5. For example, Step 1: Sam earns 25 cents per flyers. He wants to earn $5.. Step 2:.25: = 5.: Step : 1) I know that there are quarters in one dollar, so there are 5 = 18 quarters in $5.. 2) I could also use my calculator to divide $5. by $.25. This is 18. The scale factor is 18. Step : To solve the proportion I multiply both terms by 18. $ = $ Sam needs to deliver 18 flyers to earn $5.. Step 5: To check my work: 18 total flyers flyers per group = 18 groups of flyers. 18 groups of flyers.25 per flyer group = $5.. My answer is reasonable. Scaffolding for Lesson 2.6, Question 8 8. a) 5% of = 15 b) 25% of 88 = 22; 25% is equal to 22. So 5% is equal to and % is equal to 88. To check: 25% is the same as 1. 1 = 22 and = 22 = 88 c) % of 7 = 7; = ; 7 = 7. d) % of 16 = 12; = = e) 15% of 16 = 2 15 = is equivalent to. 2 = = f) % of 25 = 1 % is 1. So 1% is 1 = 2.5. % = 2.5 = 25. Chapter Test Master 6 1. a) For example, 1:, 6:2 b) For example,, c) For example, 218:18, 6: a) For example, 2 days = days 15 cm 5 cm b) For example, = 2 days 7days cm cm. a) = 6 b) = 1 c) = 5 d) = 6 76 Chapter 2: Ratio, Rate, and Percent

3 . 1:9 means that for every 1 cm in the drawing the actual wingspan is 9 cm So 2.8 = The actual wingspan is 252 cm or 2.52 m 2 kg 7 kg 5..5 = $ $ kg will cost $ Ratio Fraction Decimal Percent 5 5:2 or % 2 1: % : or :25 or.16 16% No, he is not correct. The ratio :1 means that for every people who are coffee drinkers and there is 1 person who is a tea drinker. That is a total of 5 people. So the ratio of tea drinkers to total people is 1:5. 1:5 = :. The scale factor is 8, so 1:5 = 8:. If people are surveyed, 8 would probably be tea drinkers. 8. a) Cross-country skiing 5 Downhill skiing Snowboarding Skating 55 Snowshoeing 2 Winter Camping b) For example, Cross-country skiing, downhill skiing and snowboarding are all forms of skiing = 165 students take part in these sports = 25 So 66% of the students prefer some form of skiing. 9. a) 9 b) 5 c) 16. cards For example, you save $. when you buy Bran Crunch. = This is a 25% saving. You save $1. when you but Fruit and Oat Cereal. 2 = This is a 2% saving. 5 Bran Crunch is giving you a better percentage saving. 12. a).6.2 =.12 b) =.9 1. a) 1.56 b).785 c) 5 d).6 77

4 Chapter 2 Task (Master) C. F. For example, Ball A Ball B Ball C Type of ball Basketball Golf ball Tennis ball Drop height 2 m or 2 cm 1 m or cm 1 m or cm Bounce height 16 cm 7 cm 52 cm Ratio of bounce height: 16:2 or 7: 52: drop height 82: Bounce height as percent 82% 7% 52% of drop height Ranking of greatest Most bounce Second most Least bounce bounce in the balls bounce G. For example, some types of balls bounce better than others. The size of a ball does not tell how well it will bounce. Of the balls we tested, the basketball bounced best, the golf ball next best, and the tennis ball the worst. Chapter Project: Building a Cottage Answers (continued from p. 9) After Lesson a) Area of master bedroom is..5 = m 2 area of bedroom 2 is m 2. m = 11 m 2 area of bedroom is. m 2. m =.125 m 2 total area of all the bedrooms: = 7.9 m 2 b) The area of the back part of the house (bedrooms, hall, and bath) is a rectangle that is 7 mm by 5 mm. This is 8. m m = m 2 in the real cottage. The area of the front part of the house (entry, kitchen, living area, dining area) is a rectangle that is 7 mm by 5 mm. This is 8. m 6.25 m = 5.68 m 2 in the real cottage. The total area of the cottage is = 5.68 =.9625m 2. This can be rounded to m 2. c) The area of the bedrooms from part a) is 7.9m 2. This can be rounded to 8 m 2. The ratio of the area of the bedrooms to the area of the whole cottage is approximately 8:. This could be rounded to 1:. After Section 2.5 If you used the rounded ratio, the percentage of the total area that the bedrooms cover is 1: =. =. %. 8 If you used 8:, the percentage of the total area that the bedrooms covers is 1. = This can be rounded to 6.5%. Lesson 5 Reflecting Answers (continued from p. ). For example, find the scale factor that changes the denominator of the fraction you know to. Multiply (or divide) the numerator of this fraction to get a fraction out of. This is the percent.. For example, you would write the decimal as an equivalent fraction with a denominator of. The number in the numerator is the percent. 78 Chapter 2: Ratio, Rate, and Percent

5 Lesson 6 Reflecting Answers (continued from p. 8) 2. For example, I used a scale factor of 5 and then a scale factor of. For example, I used a scale factor of.8 because.8 = 8. For example, to use the proportion statement you need to use a decimal scale factor. This is more difficult to work with than using the strategy insteps A to D. The first strategy is a mental math strategy and might be better to use if you are in a restaurant.. For example, A 15% tip can be broken down into % + 5%. Both of these numbers are easy to work with because 5% is half of %. A 1% tip can be broken down into % and %. Three percent is not as easy to work with. Lesson 6 Checking Answers (continued from p. 9) d) For example, =.5 5 Therefore, 12% of 5 = 5. Lesson 8 Reflecting Answers (continued from p. 6). a) For example, Fawn chose because the dividend was tenths. To change tenths to a whole number (moving it one column to the left) you have to make it ten times larger. b) For example, when you multiply both the numerator and the denominator by the same number it is the same as multiplying by 1. This is because 1 1 = 1. For example, the fraction is like a ratio. When you multiply both the numerator and the denominator by the same number, the ratio stays the same. It is balanced.. For example, her estimate helped her know that the answer should be a two-digit number close to. Lesson 8 Key Assessment Answers (continued from p. 7) b) 11. m 1. m = = = Nathan will have 8 pieces with some rope left over. c) You can use the answer from b) to help solve this. Each 1. m piece from part b) could be cut in half to make a.7 m piece. Then there would be twice as many.7 m pieces as there were 1. m pieces, that is, 8 2 = 16 pieces. There would be some rope left over from cutting the 1. 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 16 pieces. d) If you have 11 m of rope, you could cut 22 half metre pieces, because there are 2 half metres in each metre and 2 11 = 22. You can t get another half metre from the. that is left over. So Nathan could make 22 pieces. 79

Extra Practice 1. Name Date. Lesson 1: Numbers in the Media. 1. Rewrite each number in standard form. a) 3.6 million

Extra Practice 1. Name Date. Lesson 1: Numbers in the Media. 1. Rewrite each number in standard form. a) 3.6 million Master 4.27 Extra Practice 1 Lesson 1: Numbers in the Media 1. Rewrite each number in standard form. a) 3.6 million 3 b) 6 billion 4 c) 1 million 2 1 d) 2 billion 10 e) 4.25 million f) 1.4 billion 2. Use