Lesson 1.1 Skills Practice Name_________________________________________________________ Date__________________________
Show Someone You Care- Send Flowers! Introduction to Ratios and Rates
Vocabulary Write the term or phrase from the box that best completes each statement. ratio rate unit rate proportion scaling up scaling down equivalent ratios Scaling up
1.
means to multiply the numerator and the denominator of a ratio
by the same factor. 2. A
rate Scaling down
3.
is a ratio that compares two quantities that are measured in different units. means to divide the numerator and the denominator of a ratio by the
same factor. 4. A
ratio
5. A
proportion
6. A
unit rate
is a comparison using division. is an equation that states that two ratios are equal. is a comparison of two measurements in which the denominator has a
value of one unit. 7.
Equivalent ratios
are ratios that represent the same part-to-part relationship or the same
part-to-whole relationship.
© 2011 Carnegie Learning
Problem Set Write each statement as a ratio using colons and in fractional form. 1. There are 5 boys for every 3 girls. 5 boys 5 boys : 3 girls, _______ 3 girls 2. There are 2 basketballs for every soccer ball. 2 basketballs : 1 soccer ball, _____________ 2 basketballs 1 soccer ball 3. There are 4 bananas in each fruit basket. 4 bananas : 1 fruit basket, _____________ 4 bananas 1 fruit basket
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4. There are 50 gallons of water used after 4 showers. 50 gallons of water 50 gallons of water : 4 showers, __________________ 4 showers 5. There are 3 blueberry muffins in each variety pack of 6 muffins. 3 blueberry muffins 3 blueberry muffins : 6 total muffins, __________________ 6 total muffins 6. You purchase a dozen roses for $42. 12 roses 12 roses : $42, ________ $42 7. There are 4 grape juice boxes in each variety pack of 10 juice boxes. 4 grape juice boxes 4 grape juice boxes : 10 total juice boxes, ___________________ 10 total juice boxes 8. Each bagel costs $0.45. 1 bagel 1 bagel : $0.45, _______ $0.45 Complete the model to answer each question. 9. For every 3 boys at soccer camp, there are 2 girls. If there are 20 children at soccer camp, how
© 2011 Carnegie Learning
many are girls?
There are 8 girls at soccer camp.
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Name_________________________________________________________ Date__________________________ 10. In a Friendship Bouquet, 2 out of every 5 roses are pink. If there are 6 pink roses, how many total roses are in the bouquet?
There are 15 total roses in the bouquet. 11. In an apartment building, there are 4 tenants who own cats for every 1 tenant who owns fish. If
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there are 5 tenants who own fish, how many tenants own cats?
There are 20 tenants who own cats.
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12. Each three pack of tennis balls costs $5.75. How many tennis balls can you buy for $23?
$ 5.75
$ 5.75
$ 5.75
$ 5.75
You can buy 12 tennis balls for $23. 13. Four light bulbs cost $3.20. How much does it cost to buy 14 light bulbs?
$ 3.20
$ 3.20
$ 3.20
$ 1.60
It costs $11.20 to buy 14 light bulbs.
$ 1.80
You can buy 10 pens for $6.
338 • Chapter 1 Skills Practice
$ 1.80
$ 1.80
$ 0.60
© 2011 Carnegie Learning
14. Three pens cost $1.80. How many pens can you buy for $6?
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Name_________________________________________________________ Date__________________________ Scale up the ratio to complete each proportion. ? 5 _______ 15. ________ 24 hours 3 days 1 day 33 ____
› ___ 72 24 ____ ___ 5 ›
1
3 33
72 hours
4 oranges _________ ? 5 17. __________ 15 apples 3 apples › 20 4 ____ 5 ___ __ ____ 3 35 › 15 20 oranges 35
48 eggs 12 eggs _________ 5 19. ________ ? $3.25 34 ____
› ___ _____ 5 48 12 ____
3.25
› 13 34
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$13
8 artichokes 5 ______ ? 21. ____________ $9.00 $4.50 › 16 8 ____ 5 ___ _____ ____ 4.50 32 › 9 16 artichokes 32
36 bagels 12 bagels _________ 5 16. _________ 1 dozen ? 33 ____
› 36 ___ 5 › ___ 12 ____
1
3 33
3 dozen
5 fiction books ? 18. __________________ 5 __________________ 2 non-fiction books 6 non-fiction books › 15 5 ____ 5 ___ __ ____ 2 33 › 6 15 fiction books 33
6 scones 5 __________ 18 scones 20. _________ ? $6.30 › 18 6 ____ 5 ______ _____ ____ 6.30 33 › 18.90 $18.90 33
1 pack of gum ______ 22. _____________ 5 ? $2.25 $0.75 › 3 1 ____ 5 _____ _____ ____ 0.75 33 › 2.25 3 packs of gum 33
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Scale down the ratio to complete each proportion. 72 oz red paint 3 oz red paint 23. _______________ 5 _____________ ? 48 oz blue paint
5 red tulips 15 red tulips 5 ___________ 24. _____________ 9 yellow tulips ?
› __ 72 ____ 5 › 3 ___ 48 ____ 2 424
› 5 ___ 5 › __ 15 ____
2 oz blue paint
3 yellow tulips
424
138 students ? 5 __________ 25. ____________ 1 teacher 6 teachers
43 ____
9
3 43
112 energy bars _____________ ? 5 26. _______________ 1 value pack 14 value packs
____› 23 138 ____ 5 ___ ____ 6 46 › 1
› 8 112 ____ 5 __ ____ › 1 14 ____ 414
23 students
8 energy bars
46
1 egg 12 eggs ______ 5 27. ________ ? $3.60 412 ____
› ___ _____ 5 1 12 ____ › 0.3 412
$0.30
1 yogurt cup 8 pack of yogurt cups ____________ 5 28. ____________________ ? $2.56 › 1 8 ____ 5 _____ _____ ____ 2.56 48 › 0.32 48
$0.32
12 pencils ______ 5 ? 29. __________ $0.22 $1.32
4 lb bananas ? 5 ______ 30. ____________ $1.18 $2.36
› 2 12 ____ 5 _____ _____ ____ 1.32 46 › 0.22
› 2 4 ____ 5 _____ _____ ____ 2.36 42 › 1.18
2 pencils
2 lb bananas
46
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42
© 2011 Carnegie Learning
3.60
414
Lesson 1.1 Skills Practice
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Name_________________________________________________________ Date__________________________ Scale down the rate to determine each unit rate. 31. ________ 75 miles 3 hours
130 miles 32. _________ 2 hours
____› 25 75 5 ___ ___ ____ 3 43 › 1
› 65 ____ 5 ___ 130
25 miles per hour
65 miles per hour
43
$48 33. _________ 4 pounds
2
$4 34. _________ 8 pounds
____› 12 5 ___ ___ 48 ____ 4 44 › 1
› 0.5 __ 4 5 ___
$12 per pound
$0.50 per pound
44
45 students 35. ___________ 3 teachers 43 ____
8
48 ____ ____› 48
1
153 miles 36. _________ 9 gallons 49 ____
› ___ ___ 5 15 45 ____ ›
› 17 ____ 5 ___ 153
15 students per teacher
17 miles per gallon
3
© 2011 Carnegie Learning
42 ____
____› 1 42
1
43
24 bracelets 37. ____________ 6 hours
9
____› 1 49
$28 38. _________ 8 gallons
____› 4 24 5 __ ___ ____ 6 46 › 1
› 5 ___ 3.5 ___ 28 ____›
4 bracelets per hour
$3.50 per gallon
46
48 ____
8
1 48
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342 • Chapter 1 Skills Practice
Lesson 1.2 Skills Practice Name_________________________________________________________ Date__________________________
Making Punch Ratios, Rates, and Mixture Problems
Problem Set Use ratios to answer each question. 1. Gerain and Deon are each making trail mix. Gerain’s recipe calls for 3 parts raisins to 2 parts almonds. Deon’s recipe calls for 4 parts raisins to 3 parts almonds. Which recipe has a higher concentration of almonds? 2 parts almonds ___ 5 14 Gerain’s recipe: ________________ 5 total parts 35 3 parts almonds ___ Deon’s recipe: ________________ 5 15 7 total parts 35 14 15 . ___ Because ___ , Deon’s recipe has a higher concentration of almonds. 35 35
2. Taisha and Shakina are each making punch. Taisha’s recipe calls for 5 parts pineapple juice to 3 parts orange sherbet. Shakina’s recipe calls for 8 parts pineapple juice to 6 parts orange sherbet. Which recipe will have a stronger orange flavor? 3 parts orange sherbet ___ 5 21 Taisha’s recipe: ______________________ 8 total parts 56
© 2011 Carnegie Learning
6 parts orange sherbet ___ Shakina’s recipe: ______________________ 5 24 14 total parts 56 24 . ___ Because ___ 21 , Shakina’s recipe has a stronger orange flavor. 56 56
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3. Jin and Nami are each making Hawaiian snack mix. Jin’s recipe calls for 5 parts dried pineapple to 2 parts macadamia nuts. Nami’s recipe calls for 3 parts dried pineapple to 1 part macadamia nuts. Which recipe has a higher concentration of macadamia nuts? 2 parts macadamia nuts ___ 8 5 Jin’s recipe: _______________________ 7 total parts 28 1 part macadamia nuts ___ 5 7 Nami’s recipe: ______________________ 4 total parts 28 8 . ___ Because ___ 7 , Jin’s recipe has a higher concentration of macadamia nuts. 28 28
4. Juanita and Lydia are each making lemonade. Juanita’s recipe calls for 4 parts lemon juice to 2 parts sugar syrup. Lydia’s recipe calls for 5 parts lemon juice to 3 parts sugar syrup. Which recipe has a stronger lemon flavor? 4 parts lemon juice ___ 5 16 Juanita’s recipe: __________________ 6 total parts 24 5 parts lemon juice ___ Lydia’s recipe: __________________ 5 15 8 total parts 24 16 . ___ Because ___ 15 , Juanita’s recipe has a stronger lemon flavor. 24 24
5. Leon and Cisco are each making snack mix. Leon’s recipe calls for 8 parts pretzels to 3 parts peanuts. Cisco’s recipe calls for 6 parts pretzels to 2 parts peanuts. Which recipe has a higher 3 parts peanuts ___ 5 24 Leon’s recipe: ________________ 11 total parts 88 2 parts peanuts ___ 5 22 Cisco’s recipe: _______________ 8 total parts 88 24 . ___ Because ___ 22 , Leon’s recipe has a higher concentration of peanuts. 88 88
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concentration of peanuts?
Lesson 1.2 Skills Practice
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Name_________________________________________________________ Date__________________________ 6. Belinda and Cristina are each making a wildflower seed mix to plant in their gardens. Belinda’s mix calls for 8 parts poppy seeds to 5 parts daisy seeds. Cristina’s mix calls for 10 parts poppy seeds to 8 parts daisy seeds. Which mix will produce a higher concentration of poppy flowers? 8 parts poppy seeds ____ 5 144 Belinda’s mix: ____________________ 13 total parts 234 10 parts poppy seeds ____ Cristina’s mix: _____________________ 5 130 18 total parts 234
© 2011 Carnegie Learning
144 Because ____ . ____ 130 , Belinda’s mix will produce a higher concentration of poppy flowers. 234 234
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Use ratios to answer each question. 7. Carmen is making a strawberry drink. The recipe calls for 5 parts strawberry juice to 3 parts water. Carmen would like to make 64 fluid ounces of the strawberry drink. How many fluid ounces of strawberry juice and water does Carmen need? Number of fluid ounces in one part of the recipe: 8 fluid ounces _______________ 5 ______________ 64 fluid ounces 1 part
8 parts
Number of fluid ounces of strawberry juice: 8 fluid ounces 5 ________ x ______________ 1 part 5 parts
(1)(x) 5 (8)(5)
x 5 40
Number of fluid ounces of water: 8 fluid ounces 5 ________ x ______________ 1 part 3 parts
(1)(x) 5 (8)(3)
x 5 24
Carmen will need 40 fluid ounces of strawberry juice and 24 fluid ounces of water to make
© 2011 Carnegie Learning
64 fluid ounces of strawberry drink.
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Name_________________________________________________________ Date__________________________ 8. Elena is making a grape drink. The recipe calls for 2 parts grape juice concentrate to 6 parts water. Elena would like to make 80 fluid ounces of the grape drink. How many fluid ounces of grape juice concentrate and water does Elena need? Number of fluid ounces in one part of the recipe: 10 fluid ounces _______________ 5 _______________ 80 fluid ounces 1 part
8 parts
Number of fluid ounces of grape juice concentrate: 10 fluid ounces 5 ________ x _______________ 1 part 2 parts
(1)(x) 5 (10)(2)
x 5 20
Number of fluid ounces of water: 10 fluid ounces 5 ________ x _______________ 1 part 6 parts
(1)(x) 5 (10)(6)
x 5 60
Elena will need 20 fluid ounces of grape juice concentrate and 60 fluid ounces of water to make
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80 fluid ounces of grape drink.
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9. Jose is making a trail mix. The recipe calls for 3 parts golden raisins to 2 parts cashews. Jose would like to make 30 cups of trail mix. How many cups of golden raisins and cashews does Jose need? Number of cups in one part of the recipe: 30 cups _______ 6 cups ________ 5 5 parts
1 part
Number of cups of golden raisins: 6 cups _______ 5 x _______ 1 part 3 parts (1)(x) 5 (6)(3)
x 5 18
Number of cups of cashews: 6 cups _______ 5 x _______ 1 part 2 parts (1)(x) 5 (2)(6)
x 5 12
© 2011 Carnegie Learning
Jose will need 18 cups of golden raisins and 12 cups of cashews to make 30 cups of trail mix.
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Lesson 1.2 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 10. Miguel is making a snack mix. The recipe calls for 6 parts of spicy tortilla chips to 3 parts of corn chips. Miguel would like to make 45 cups of snack mix. How many cups of spicy tortilla chips and corn chips does Miguel need? Number of cups in one part of the recipe: 45 cups _______ 5 cups ________ 5 9 parts
1 part
Number of cups of spicy tortilla chips: 5 cups ______ 5 x _______ 1 part 6 parts (1)(x) 5 (5)(6)
x 5 30
Number of cups of corn chips: 5 cups ______ 5 x _______ 1 part 3 parts (1)(x) 5 (5)(3)
x 5 15
Miguel will need 30 cups of spicy tortilla chips and 15 cups of corn chips to make 45 cups of
© 2011 Carnegie Learning
snack mix.
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11. Carla is making a bean salad. The recipe calls for 4 parts green beans to 3 parts yellow wax beans. Carla would like to make 56 ounces of bean salad. How many ounces of green beans and yellow wax beans does Carla need? Number of ounces in one part of the recipe: 8 ounces __________ 5 _________ 56 ounces 7 parts
1 part
Number of ounces of green beans: 8 ounces 5 _______ x _________ 1 part 4 parts (1)(x) 5 (8)(4)
x 5 32
Number of ounces of yellow wax beans: 8 ounces 5 _______ x _________ 1 part 3 parts (1)(x) 5 (8)(3)
x 5 24
Carla will need 32 ounces of green beans and 24 ounces of yellow wax beans to make
© 2011 Carnegie Learning
56 ounces of bean salad.
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Lesson 1.2 Skills Practice
page 9
Name_________________________________________________________ Date__________________________ 12. Shawna is making smoothies. The recipe calls for 2 parts yogurt to 3 parts blueberries. Shawna wants to make 10 cups of smoothie mix. How many cups of yogurt and blueberries does Shawna need? Number of cups in one part of the recipe: 10 cups _______ 2 cups ________ 5 5 parts
1 part
Number of cups of yogurt: 2 cups _______ 5 x _______ 1 part 2 parts (1)(x) 5 (2)(2)
x54
Number of cups of blueberries: 2 cups _______ 5 x _______ 1 part 3 parts (1)(x) 5 (2)(3)
x56
© 2011 Carnegie Learning
Shawna will need 4 cups of yogurt and 6 cups of blueberries to make 10 cups of smoothie.
Chapter 1 Skills Practice • 351
© 2011 Carnegie Learning
352 • Chapter 1 Skills Practice
Lesson 1.3 Skills Practice Name_________________________________________________________ Date__________________________
For the Birds Rates and Proportions
Vocabulary Define the term in your own words. 1. convert to change a measurement to an equivalent measurement in different units.
Problem Set Write the ratio described by each problem situation. Write the ratio as a decimal. Round to the nearest thousandth, if necessary. 1. An adult female elephant weighs about 8000 pounds. A newborn baby elephants weighs about 200 pounds. Write the ratio of the baby elephant’s weight to the adult female elephant’s weight. _______ 5 0.025 200 lb
8000 lb
2. An adult pygmy shrew weighs about 3.5 grams. A newborn pygmy shrew weighs just about 0.25 gram. Write the ratio of the newborn pygmy shrew’s weight to the adult pygmy shrew’s weight. 0.25 g ______ < 0.071 3.5 g
3. An adult tiger weighs about 650 pounds. A baby tiger weighs about 2 pounds at birth. Write the © 2011 Carnegie Learning
ratio of the newborn tiger’s weight to the adult tiger’s weight. ______ < 0.003 2 lb
650 lb
4. An adult blue whale weighs about 200 tons. A baby blue whale weighs about 3 tons at birth. Write the ratio of the newborn blue whale’s weight to the adult blue whale’s weight. 3 tons 5 0.015 _________ 200 tons
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5. An adult male giraffe weighs about 3000 pounds. A baby giraffe weighs about 110 pounds at birth. Write the ratio of the newborn giraffe’s weight to the adult male giraffe’s weight. _______ < 0.037 110 lb
3000 lb
6. An adult female polar bear weighs about 750 pounds. A baby polar bear cub weighs about 1.3 pounds at birth. Write the ratio of the newborn polar bear’s weight to the adult female polar bear’s weight. ______ < 0.002 1.3 lb
750 lb
Write the rate described by each problem situation.
2 miles per 30 minutes, or ___________ 2 miles 30 minutes
9. Marcus jogged 3 miles in 45 minutes. 3 miles per 45 minutes, or ___________ 3 miles 45 minutes
11. In 3 hours, Jacob mowed 4 lawns. 4 lawns per 3 hours, or ________ 4 lawns 3 hours
354 • Chapter 1 Skills Practice
8. Isabella drove 300 miles in 5 hours. 300 miles per 5 hours, or _________ 300 miles 5 hours
10. In 1 hour, Monique made 4 bead necklaces. 4 necklaces 4 necklaces per 1 hour, or ____________ 1 hour
12. In 25 minutes, Norton read 14 pages. 14 pages 14 pages per 25 minutes, or ___________ 25 minutes
© 2011 Carnegie Learning
7. Gina rode her bike 2 miles in 30 minutes.
Lesson 1.3 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ Convert each rate. 13. Convert the rate 5 feet per 3 seconds to yards per hour. 18,000 ft 3600 sec _________ ______ 3 _________ 5 5 ft 3 sec
1 hr
3 hr
6000 ft 5 _______ 1 hr
1 yd ________ 6000 yd ft _______ 6000 3 _____ 5 1 hr
3 ft
3 hr
2000 yd 5 ________ 1 hr
The rate 5 feet per 3 seconds is equivalent to 2000 yards per hour.
14. Convert the rate 1000 fluid ounces per 2 hours to cups per minute. 1000 fl oz 1 hr 1000 fl oz 3 _______ 5 _________ _________ 60 min 120 min 2 hr 25 fl oz 5 _______ 3 min
1c 25 c _______ 25 fl oz 3 ______ 5 _______ © 2011 Carnegie Learning
3 min
8 fl oz
24 min
1.04 c < ______ 1 min
The rate 1000 fluid ounces per 2 hours is equivalent to approximately 1.04 cups per minute.
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15. Convert the rate of 10 yards per 5 minutes to feet per hour. 10 yd _______ 600 yd ______ 3 60 min 5 _______ 5 min 1 hr 5 hr 120 yd 5 _______ 1 hr 120 yd _____ _______ 3 3 ft 5 ______ 360 ft 1 hr 1 yd 1 hr The rate 10 yards per 5 minutes is equivalent to 360 feet per hour.
16. Convert the rate of 48 feet per hour to inches per minute. 48 ft 3 _______ 1 hr 5 _______ 48 ft _____ 1 hr 60 min 60 min 4 ft 5 ______ 5 min 48 in. 4 ft ______ 3 ______ 12 in. 5 ______ 5 min 1 ft 5 min 9.6 in. 5 ______ 1 min The rate 48 feet per hour is equivalent to 9.6 inches per minute.
12 pt 720 pt _______ 3 _______ 60 min 5 ______ 15 min 1 hr 15 hr 48 pt 5 _____ 1 hr 48 pt ____ 1 qt _____ 48 qt _____ 3 5 1 hr 2 pt 2 hr 24 qt 5 _____ 1 hr The rate 12 pints per 15 minutes is equivalent to 24 quarts per hour.
356 • Chapter 1 Skills Practice
© 2011 Carnegie Learning
17. Convert the rate of 12 pints per 15 minutes to quarts per hour.
Lesson 1.3 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 18. Convert the rate of 48 ounces per 2 hours to pounds per day. 24 hr ______ 3 ______ 5 ________ 1152 oz 48 oz 2 hr
1 day
2 days
576 oz 5 _______ 1 day
1 lb _______ 576 oz 5 ______ 5 ________ 576 lb 1 day
16 oz
16 days
36 lb 5 ______ 1 day
The rate 48 ounces per 2 hours is equivalent to 36 pounds per day.
© 2011 Carnegie Learning
Scale each ratio up or down as needed to complete the proportion. 5 ____ ? 19. ______ 16 oz 3 lb 1 lb
c 32 20. ____ 4c 5 ____ 1qt ?
16 5 ___ 48 ___ 1 3
__ 32 4 5 ___
48 ounces
8 quarts
6000 lb 5 ___ ? 21. _______ 1t 3t
4 qt 20 qt ____ 5 22. _____ 5 gal ?
1
8
6000 5 _____ 2000 _____ 1 3
20 5 __ 4 ___ 5 1
2000 pounds
1 gallon
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Lesson 1.3 Skills Practice
in. 5 _______ 108 23. ______ 36 in. 1 yd ?
page 6
5 ____ ? 24. _______ 5280 ft 4 mi 1 mi
36 5 ____ 108 ___ 1 3
21,120 5280 5 _______ _____ 1 4
3 yards
21,120 feet
10,800 sec _________ sec 5 3600 25. __________ 3 hrs ?
? 5 ____ 26. _______ 216 in. 1 yd 6 yd
10,800 _____ 5 3600 _______ 1 3
216 5 ___ 36 ____ 1 6
1 hour
36 inches
Convert each measurement using a rate. 28. How many feet are in 15 yards?
1 pt 36 c 3 ____ 5 18 pt 2c
15 yd 3 _____ 3 ft 5 45 ft 1 yd
There are 18 pints in 36 cups.
There are 45 feet in 15 yards.
29. How many feet are in 96 inches?
30. How many seconds are in 4 hours?
5 8 ft 96 in. 3 ______ 1 ft 12 in.
s 5 14,400 s 4 hr 3 _______ 3600 1 hr
There are 8 feet in 96 inches.
There are 14,400 seconds in 4 hours.
31. How many ounces are in 7 pounds?
32. How many tons are in 18,000 pounds?
16 oz 5 112 oz 7 lb 3 ______ 1 lb
59t 18,000 lb 3 _______ 1 t 2000 lb
There are 112 ounces in 7 pounds.
There are 9 tons in 18,000 pounds.
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27. How many pints are in 36 cups?
Lesson 1.4 Skills Practice Name_________________________________________________________ Date__________________________
Tutor Time! Using Tables to Solve Problems
Problem Set Complete each table. 1. The ratio of boys to girls participating in intramural basketball is 7 boys to 4 girls. Boys
7
21
42
84
Girls
4
12
24
48
2. Perry is delivering newspapers. In 2 hours he delivers 60 newspapers. Newspapers
30
60
90
105
Hours
1
2
3
3.5
© 2011 Carnegie Learning
3. Joelle’s new printer can print 10 photos in 5 minutes. Photos
2
10
25
50
Minutes
1
5
12.5
25
4. Denisa is mixing blue paint and white paint to create a shade of light blue paint. She creates the shade she likes by mixing 12 ounces of blue paint with 8 ounces of white paint. Blue paint (oz)
1.5
12
18
27
White paint (oz)
1
8
12
18
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5. Belinda is making fruit salad. The recipe calls for 3 cups of sliced peaches to 2 cups of halved grapes. Peaches (c)
1.5
3
4.5
6
Grapes (c)
1
2
3
4
6. Mattie is stuffing envelopes. She stuffs 100 envelopes in 1 hour. Envelopes
25
50
100
200
Hours
0.25
0.5
1
2
Determine the unit rate to answer each question. 7. Luis mowed 8 lawns this week and earned $56. How much would Luis have earned if he had mowed 10 lawns? $7 $56 ________ 5 _______ 8 lawns
1 lawn
The unit rate is $7 per lawn. $7 10 lawns 3 _______ 5 $70 1 lawn
© 2011 Carnegie Learning
If Luis had mowed 10 lawns, he would have earned $70.
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Lesson 1.4 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 8. Eva babysat for two families this weekend. She babysat 4 hours for the Rodgers family and 5 hours for the Mitchell family. She made a total of $58.50 for the weekend. Both families pay her the same amount per hour. How much did she earn from the Rodgers family? $6.50 $58.50 ________ 5 ______ 9 hours
1 hour
The unit rate is $6.50 per hour. $6.50 4 hours 3 ______ 5 $26 1 hour Eva earned $26 from the Rodgers family.
9. Rita made 12 pairs of earrings in 2 hours. How many pairs of earrings could she make in 3 hours? 12 pairs _______ 6 pairs ________ 5 2 hours 1 hour The unit rate is 6 pairs per hour. 6 pairs 3 hours 3 _______ 5 18 pairs 1 hour
© 2011 Carnegie Learning
In 3 hours, Rita could make 18 pairs of earrings.
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Lesson 1.4 Skills Practice
page 4
10. Pedro planted 12 plants in his garden in 45 minutes. How long did it take him to plant 5 plants? 3.75 minutes ___________ 45 minutes 5 ____________ 12 plants
1 plant
The unit rate is 3.75 minutes per plant. 3.75 minutes 5 plants 3 ____________ 5 18.75 minutes 1 plant It took Pedro 18.75 minutes to plant 5 plants in his garden.
11. Raul walked 2.5 miles in 1 hour and 15 minutes. How long did it take Raul to walk 0.5 mile? 1 hour and 15 minutes 5 75 minutes 75 minutes 5 ___________ 30 minutes ___________ 2.5 miles 1 mile The unit rate is 30 minutes per mile. 5 15 minutes 0.5 mile 3 ___________ 30 minutes 1 mile
12. Perry earned $96 shoveling snow from 8 driveways. How much would Perry have earned if he had shoveled 10 driveways? $12 $96 5 ___________ ____________ 8 driveways 1 driveway The unit rate is $12 per driveway. $12 10 driveways 3 ___________ 5 $120 1 driveway If Perry had shoveled 10 driveways, he would have earned $120.
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It took Raul 15 minutes to walk 0.5 mile.
Lesson 1.5 Skills Practice Name_________________________________________________________ Date__________________________
Looks Can Be Deceiving! Using Proportions to Solve Problems
Vocabulary Describe a situation in which you would use each of the following. 1. variable Use a variable to represent an unknown number in an equation.
2. means and extremes method Use the means and extremes method when you need to solve a proportion with a missing quantity by setting the product of the means equal to the product of the extremes. 3. solve a proportion Solve a proportion to determine all the values of the variables that make a proportion true.
4. inverse operations Use inverse operations to isolate the variable in an equation.
Problem Set © 2011 Carnegie Learning
Tell which method (scaling, unit rate, or means and extremes) you would use to solve for each variable and explain why. 20 1. __ 2 5 ___ x 3
100 2. ___ 16 5 ____ x 4
Use the scaling method because it is easy
Use the unit rate method because the
to see that the numerator is multiplied by
denominator is a multiple of the numerator,
10, so the denominator must also be
so a unit rate is easy to find.
multiplied by 10.
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Lesson 1.5 Skills Practice
page 2
x 4. ___ 49 5 __ 7 5
50 3. ___ 23 5 ___ x 48 Use the means and extremes method
Use the unit rate method because the
because there are no clear relationships
denominator is a multiple of the numerator,
among the numbers.
so a unit rate is easy to find.
x 6. ___ 63 5 __ 36 4
x 5. ___ 37 5 __ 15 8 Use the means and extremes method
Use the scaling method because it is easy
because there are no clear relationships
to see that the denominator is divided by 9,
among the numbers.
so the numerator must also be divided by 9.
Solve for each variable using the means and extremes method. Round to the nearest hundredth, if necessary. x 7. ___ 4 5 ___ 28 35
8. 12 : 6 5 60 : x
28x 5 ____ 140 ____ 28
28
x 5 5
9. 560 : 80 5 x : 300 (80)(x) 5 (560)(300) 168,000 80x 5 ________ ____ 80 80 x 5 2100
364 • Chapter 1 Skills Practice
(6)(60) 5 (12)(x) 360 5 ____ 12x ____ 12 12 30 5 x
7 10. ____ 41 5 __ 282 x (282)(7) 5 (41)(x) 41x ____ 1974 5 _____ 41 41 48.15 < x
© 2011 Carnegie Learning
(28)(x) 5 (4)(35)
Lesson 1.5 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ x 11. ___ 39 5 __ 2 9
12. 74 : 31 5 2 : x
(9)(x) 5 (39)(2)
(31)(2) 5 (74)(x)
9x 5 ___ 78 ___ 9 9
x < 8.67
0.84 < x
1351 13. __ x 5 _____ 7 3 (3)(1351) 5 (x)(7)
___ 62 5 ____ 74x
74
74
14. 26 : x 5 117 : 9 (x)(117) 5 (26)(9)
4053 5 ___ 7x _____ 7 7
117x 5 ____ 234 _____ 117 117
579 5 x
x 5 2
Use the given information to answer each question. 15. In the first quarter (3 months), a store sold 32 limited-edition action figures. If this quarter’s sales represent a typical sales pattern, how many action figures should they expect to sell in a year?
___ f 32 5 ___ 3 12 © 2011 Carnegie Learning
f 5 128 The store should expect to sell 128 action figures in a year.
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Lesson 1.5 Skills Practice
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1 cups of flour and __ 16. A recipe calls for 3 __ 3 cup of sugar. If you want to make the recipe with 6 cups 2 4 of flour, about how much sugar will you need?
__ __ 3 4
3 1
2 5 __ 6 ___ s
2 s 5 1 __ 7 2 cups of sugar. You will need 1 __ 7
17. Marlene is planning a trip. She knows that her car gets 38 miles to the gallon on the highway. If her trip is going to be 274 miles and one gallon of gas is $2.30, about how much should she expect to pay for gas? 38 5 ____ 274 ______ d $2.30 d 5 $16.58 Marlene should expect to pay about $16.58 for gas.
18. It takes Roger about 8 minutes to type a 500-word document. How long will it take him to type 8 5 _____ t ____ 500 3300 t 5 52.8 It will take Roger 52.8 minutes to type the essay.
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© 2011 Carnegie Learning
a 12-page essay with 275 words per page?
Lesson 1.6 Skills Practice Name_________________________________________________________ Date__________________________
The Price Is . . . Close Using Unit Rates in Real World Applications
Problem Set Calculate the unit rates for each item. 1. A bottle of fruit juice contains 63 ounces and costs $2.25. Calculate the unit rate showing ounces per dollar and the unit rate showing dollars per ounce. ______ 5 ______ 28 oz 63 oz
$2.25
$1
$2.25 ______ $0.04 ______ < 63 oz
1 oz
The unit rate is 28 ounces per dollar or about $0.04 per ounce.
2. A dozen scones cost $5.95. Calculate the unit rate showing scones per dollar and the unit rate showing dollars per scone. 2 scones __________ < _________ 12 scones $5.95
$1
$5.95 $0.50 __________ < ________
© 2011 Carnegie Learning
12 scones
1 scone
The unit rate is about 2 scones per dollar or about $0.50 per scone.
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Lesson 1.6 Skills Practice
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3. A 2.5 pound bag of apples costs $2.99. Calculate the unit rate showing pounds of apples per dollar and the unit rate showing dollars per pound of apples. 0.84 pound 2.5 pounds ___________ ___________ < $2.99
$1
$2.99 $1.20 ___________ < ________ 2.5 pounds
1 pound
The unit rate is about 0.84 pound of apples per dollar or about $1.20 per pound of apples.
4. An 8 pound bag of oranges costs $4.95. Calculate the unit rate showing pounds of oranges per dollar and the unit rate showing dollars per pound of oranges. 1.62 pounds 8 pounds ____________ < _________ $4.95 $1 $4.95 $0.62 _________ < ________ 8 pounds 1 pound
5. A box of 40 envelopes costs $2.50. Calculate the unit rate showing number of envelopes per dollar and the unit rate showing dollars per envelope. 40 envelopes _____________ 16 envelopes _____________ 5 $2.50 $1 $2.50 $0.06 _____________ < ___________ 40 envelopes
1 envelope
The unit rate is 16 envelopes per dollar or about $0.06 per envelope.
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© 2011 Carnegie Learning
The unit rate is about 1.62 pounds of oranges per dollar or about $0.62 per pound of oranges.
Lesson 1.6 Skills Practice
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Name_________________________________________________________ Date__________________________ 6. A package of 200 cotton balls costs $1.99. Calculate the unit rate showing cotton balls per dollar and the unit rate showing dollars per cotton ball. balls balls _______________ < _______________ 100 cotton 200 cotton $1.99
$1
$1.99 $0.01 _______________ < ____________ 200 cotton balls 1 cotton ball The unit rate is about 100 cotton balls per dollar or about $0.01 per cotton ball.
Estimate the unit rates of each item to determine which is the better buy. 7. A 4 liter bottle of laundry detergent costs $7.99. A 6.5 liter bottle of laundry detergent costs $16.99. Which is the better buy? $7.99 ___ $8 ______ < 4L 4 L
$2 5 ___ 1 L
$16.99 _____ $17 _______ < 6.5 L 6.5 L
© 2011 Carnegie Learning
$2.60 < ______ 1 L
Because $2 , $2.60, the 4 liter bottle is the better buy.
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Lesson 1.6 Skills Practice
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8. A 64 ounce bottle of apple juice costs $1.99. A 140 ounce bottle of apple juice costs $2.80. Which is the better buy? $1.99 ______ $2 ______ < 64 oz 60 oz $0.03 < ______ 1 oz $2.80 $3 _______ < _______ 140 oz
140 oz
$0.02 < ______ 1 oz Because $0.02 , $0.03, the 140 ounce bottle is the better buy.
9. A sleeve of 4 golf balls costs $6.99. A 20 pack of golf balls costs $24.95. Which is the better buy? $6.99 $7 ___________ < ___________ 4 golf balls 4 golf balls $1.75 5 __________ 1 golf ball
$1.25 5 __________ 1 golf ball Because $1.25 , $1.75, the 20 pack is the better buy.
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© 2011 Carnegie Learning
$24.95 $25 ____________ < ____________ 20 golf balls 20 golf balls
Lesson 1.6 Skills Practice
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Name_________________________________________________________ Date__________________________ 10. A 2.2 pound package of chicken costs $5.99. A 5.1 pound package of chicken costs $9.95. Which one is the better buy? $5.99 $6 ___________ < _________ 2.2 pounds
2 pounds
$3 5 ________ 1 pound $9.95 $10 ___________ < _________ 5.1 pounds 5 pounds $2 5 ________ 1 pound Because $2 , $3, the 5.1 pound package is the better buy.
11. A 4 pack of dinner rolls costs $2.20. A 12 pack of dinner rolls costs $5.40. Which is the better buy? $2.20 $2 ______ < ______ 4 rolls 4 rolls $0.50 5 ______ 1 roll $5.40 $5.00 _______ < _______ © 2011 Carnegie Learning
12 rolls
12 rolls
$0.42 < ______ 1 roll Because $0.42 , $0.50, the 12 pack is the better buy.
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Lesson 1.6 Skills Practice
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12. An 18 ounce jar of peanut butter costs $1.29. A 64 ounce jar of peanut butter costs $3.80. Which is the better buy? $1.29 $1 __________ < __________ 18 ounces
20 ounces
$0.05 5 ________ 1 ounce $3.80 $4.00 __________ < __________ 64 ounces
60 ounces
$0.07 < ________ 1 ounce
© 2011 Carnegie Learning
Because $0.05 , $0.07, the 18 ounce jar is the better buy.
372 • Chapter 1 Skills Practice
