Dwnload Full Using and Understanding Mathematics 6th Edition Bennett Solutions Manual PDF
Dwnload Full Using and Understanding Mathematics 6th Edition Bennett Solutions Manual PDF
Dwnload Full Using and Understanding Mathematics 6th Edition Bennett Solutions Manual PDF
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UNIT 2A
TIME OUT TO THINK QUICK QUIZ
Pg. 74. Answers will vary. This question should help 1. a. Think of the unit miles per hour; the unit of
the student think about the units associated with mile is divided by the unit of hour.
everyday numbers. Even if they pick a page 2. b. The area of a square is its length multiplied by
number from the newspaper or magazine, note that its width (these are, of course, equal for squares),
this has units of “pages.” This would be a good and thus a square of side length 2 mi has area of
topic for a discussion either during or outside of
class. 2 mi × 2 mi = 4 mi 2 .
3. c. When multiplying quantities that have units, the
60 s
Pg. 76. Using , the solution would be units are also multiplied, so ft 2 × ft = ft 3 .
1 min
60 s 4. b. 1 mi3 = (1760 yd)3 = 17603 yd 3 .
3000 s × = 18,000 s 2 / min . Since the
1 min
question asked for minutes, you would know there 5. c. 1 ft 2 = 12 in × 12 in = 144 in 2 .
was an error since the units of s2/min are incorrect. 6. a. Divide both sides of 1 L = 1.057 qt by 1 L.
Pg. 78. Answers will vary, but this question should 7. c. The metric prefix kilo means 1000, so a
help the student make the connection between kilometer is 1000 meters.
abstract ideas of measurement and the ancient 8. c. Water boils at 100˚C (at sea level), so 110˚C is
origin of units as body measures. This would be a boiling hot.
good topic for a discussion either during or outside
9. a. Apples are most likely to be sold by units of
of class.
weight (or more accurately, mass), and thus euros
Pg. 80. Literally, a megabuck is a million dollars. But per kilogram is the best answer.
it is used colloquially to mean “a lot of money.”
10. b. $1.32 per euro means 1 euro = $1.32, which is
Another example of the use of metric prefixes is
more than $1.
“nanotechnology” for very small machines. This
would be a good topic for a discussion either
during or outside of class. DOES IT MAKE SENSE?
Pg. 84(1st). Even without carrying out the 7. Does not make sense. 35 miles is a distance, not a
conversions, it should be obvious that this is a speed.
Fahrenheit temperature; 59°C is more than
halfway between the freezing and boiling points of 8. Does not make sense. Two ft 2 describes an area,
water, which means it is well over 100°F (a not a volume.
precise conversion shows it is 138.2°F). No 9. Makes sense. Liquids are measured in liters, and
populated place on Earth gets this hot, so the since one liter is about a quart, drinking two liters
forecast of 59° must refer to a Fahrenheit is a reasonable thing to do.
temperature.
10. Does not make sense. First of all, we use the unit
1 1 of kilogram to measure mass, not weight, though
Pg. 84(2nd). = 0.6158, = 0.9950,
1.624 1.005 mass and weight are often used interchangeably in
1 1 everyday conversation. Even so, a bicyclist with a
= 0.7576, = 83.33, and mass of 300 kg would weigh more than 650
1.320 0.0120
pounds (on the surface of the earth), which is an
1
= 12.73. The values in the two columns unheard of weight for a professional cyclist.
0.07855 11. Makes sense. 10,000 meters is 10 kilometers,
are reciprocals of one another (at least which is about 6.2 miles, a common length for
approximately). For example, the conversion foot races. Anyone who can run six back-to-back
factor used to convert from euros to U.S. dollars is 9-minute miles has no trouble running 10,000
$1.320 meters in less than an hour.
and the conversion factor to change from
1 euro 12. Does not make sense. The unit of meter measures
1 euro length, not volume.
U.S. dollars to euros is . These numbers
$1.320
are reciprocals.
BASIC SKILLS AND CONCEPTS 16. Answers may vary depending on whether fractions
are reduced.
3 1 3 ⋅1 3
13. a. × = = 275 11 45 9
4 2 4⋅2 8 a. 2.75 = = b. 0.45 = =
100 4 100 20
2 3 2⋅3 2
b. × = = 5 1 116 29
3 5 3⋅5 5 c. 0.005 = = d. 1.16 = =
1000 200 100 25
1 3 1+ 3 4
c. + = = =2 65 13 4123
2 2 2 2 e. 6.5 = = f. 4.123 =
10 2 1000
2 1 4 1 4 +1 5
d. + = + = = 3 34 17
3 6 6 6 6 6 g. 0.0003 = h. 0.034 = =
10, 000 1000 500
2 1 2 ⋅1 2 1
e. × = = = 1 3
3 4 3 ⋅ 4 12 6 17. a. = 0.25 . b. = 0.375
1 3 2 3 2+3 5 4 8
f. + = + = = 2 3
4 8 8 8 8 8 c. ≈ 0.667 d. = 0.6
5 1 5 2 5− 2 3 3 5
g. − = − = = 13 23
8 4 8 8 8 8 e. = 6.5 f. ≈ 3.833
3 2 3⋅ 2 2 6
h. × = =1 103 42
2 3 3⋅ 2 g. = 2.06 h. ≈ 1.615
1 1 5 3 8 50 26
14. a. + = + = 1 4
3 5 15 15 15 18. a. = 0.2 b. ≈ 0.444
10 3 10 ⋅ 3 10 3 5 9
b. × = = =1 4 12
3 7 3⋅ 7 7 7 c. ≈ 0.364 d. ≈ 1.714
3 1 6 1 5 11 7
c. − = − = 28 56
4 8 8 8 8 e. ≈ 3.111 f. ≈ 5.091
1 2 3 6 8 9 23 11 9 11
d. + + = + + = =1 102 15
2 3 4 12 12 12 12 12 g. ≈ 2.082 h. = 3.75
6 4 18 4 22 7 49 4
e. + = + = =1
5 15 15 15 15 15 19. a. 104 × 107 = 104 + 7 = 1011
3 2 3⋅ 2 6
f. × = = b. 105 × 10−3 = 105−3 = 102
5 7 5 ⋅ 7 35
c. 106 ÷ 102 = 106 − 2 = 104
1 13 2 13 15 5 1
g. + = + = = =2 108
3 6 6 6 6 2 2 d. = 108− ( −4) = 1012
3 10 3 3 ⋅10 ⋅ 3 3 10−4
h. × × = = =3
5 3 2 5⋅3⋅ 2 1 1012
e. −4
= 1012 − ( −4) = 1016
15. Answers may vary depending on whether fractions 10
are reduced.
f. 1023 × 10−23 = 1023− 23 = 100 = 1
35 7 3
a. 3.5 = = b. 0.3 = g. 104 + 102 = 10, 000 + 100 = 10,100
10 2 10
5 1 41 h. 1015 ÷ 10−5 = 1015− ( −5) = 1020
c. 0.05 = = d. 4.1 =
100 20 10 20. a. 10−2 × 10−6 = 10−2+ ( −6) = 10−8
215 43 35 7
e. 2.15 = = f. 0.35 = = 10−6
100 20 100 20 b. −8
= 10−6− ( −8) = 102
10
98 49 401
g. 0.98 = = h. 4.01 = c. 1012 × 1023 = 1012 + 23 = 1035
100 50 100
10−4
d. = 10−4− 5 = 10−9
105
1025
e. = 1025−15 = 1010
1015
20. (continued) 33. The daily consumption has units of gallons per
person, or gal/person.
f. 10 + 10 = 10 + 1 = 11
1 0
34. The density of rock has units of grams per cubic
g. 102 + 10−1 = 100 + 0.1 = 100.1
centimeter, or g/ cm3 .
h. 102 − 101 = 100 − 10 = 90
12 in
$0.90 35. 24 ft × = 288 in
21. 3.5 lb × = $3.15 1 ft
1 lb
1 yd
5.25 oz 36. 24 ft × = 8 yd
22. 23 baseballs × = 120.75 oz 3 ft
1 baseball
60 s
$3200 37. 25 min × = 1500 s
23. 6 months × = $19, 200 1 min
1 month
365 day
1 building 38. 32 year × = 11, 680 days
24. 3000 people × = 20 buildings 1 year
150 people
60 min 60 s
25. a. The area of the arena’s floor is 200 ft × 150 ft 39. 2.5 hr × × = 9000 s
1 hr 1 min
= 30,000 ft 2 , and the volume of the arena is 200 ft
mi 1 hr 1 min mi
× 150 ft × 35 ft = 1,050,000 ft 3 . 40. 17,200 × × ≈ 4.78
hr 60 min 60 s s
b. The surface area of the pool is 30 yd × 10 yd =
365 day 24 hr
300 yd 2 , and the volume of water it holds is 30 yd 41. 3 tr × × = 26,280 hr
1 tr 1 day
× 10 yd × 0.3 yd = 90 yd3 . 1 ft 1 yd 1 mi
42. 26,500 in × × ×
c. The area of the bed is 25 ft × 8 ft = 200 ft , 2 12 in 3 ft 1760 yd
and the volume of soil it holds is 25 ft × 8 ft × ≈ 0.42 mi
1.5 ft = 300 ft 3 . 43. Note that 1 ft = 12 in, and thus (1 ft) 2 = (12 in) 2 ,
26. a. The area of the warehouse floor is 40 yd × 25
which means 1 ft 2 = 144 in 2 . This can also be
yd = 1000 yd 2 , and the volume of the cartons is
1 ft 2 144 in 2
written as = 1 , or = 1.
40 yd × 25 yd × 3 yd = 3000 yd . 3
144 in 2 1 ft 2
b. The area of the bed’s floor is 12 ft × 5 ft = 60
44. Since 1 m = 100 cm, we have (1 m)3 = (100 cm)3 ,
ft 2 , and the volume of the bed is 12 ft × 5 ft ×
which means 1 m3 = 1,000,000 cm3 . This can
3.5 ft = 210 ft 3 .
1 m3
c. The volume of the can is the area of its base also be written as = 1, or
multiplied by its height, which is 6 in × 4 in =
2 1,000,000 cm3
24 in 3 . 1,000,000 cm3
= 1.
27. Speed has units of miles per hour, or mi/hr. 1 m3
28. The price of oranges has units of dollars per 45. The volume of the sidewalk is 4 ft × 200 ft ×
pound, or $/lb.
0.5 ft = 400 ft 3 . Since 1 yd = 3 ft, we know 1 yd3
29. The cost of carpet has units of dollars per square
= 27 ft 3 , and this can be used to convert to cubic
yard, or $/ yd 2 .
yards.
30. The flow rate has units of cubic feet per second, or
1 yd3
cfs (or ft 3 /s). 400 ft 3 × 3
= 14.8 yd3
27 ft
31. The price of rice has units of yen per kilogram, or
yen/kg.
32. The production rate has units of bagels per hour,
or bagels/hr.
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