Back to Lesson 8-2
Name
Name
8-1B
page 2
8-2A Lesson Master
USES
In 17−20, simplify the expression, . . .
a. retaining the parentheses.
a.
18. 2(m + n) - (m + n)
a.
19. −4(x - y) + (x - y)
a.
20. (3a + b) + 2(3a + b)
a.
5(p + r)
1(m + n)
−3(x - y)
3(3a + b)
5p + 5r
m+n
−3x + 3y
9a + 3b
b.
b.
b.
b.
(4x)(4y) = 4 · 4 · x · y = 16xy; 4(x + y) = 4x + 4y;
16xy ≠ 4x + 4y, since, for example, if x = y = 1, 16 ≠ 8
22. Jean bought 3 pairs of jeans and 4 T-shirts at the mall. Including taxes,
each T-shirt cost $9.71 and each pair of jeans cost $35.53.
1 yard
______
1 yard
In 4 and 5, do the multiplication. Include the rate units in your answer.
13.5 _________
week
hours of practice
days
hours of practice
4. 2.25 _____________ · 6 _____
week
18 ____
day
gallons
gallon
miles
5. 360 _____
· 0.05 _____
mile
day
In 6−10, show your calculation and give your answer.
6. If Marlene runs 4.85 miles an hour and she runs 2 hours each day,
how many miles does she run in 8 weeks?
543.2 miles
answer
7. It takes Sam about one minute to read 500 words. How many hours
will it take him to read a 396-page book with about 450 words per page?
1 minute
450 words
______
______
1 hour
· 396 pages · _______
page
500 words ·
60 minutes
5.94 or about 6 hours
answer
8. If Sharon earns $6.75 an hour and works 20 hours a week, how
much does she earn in a year? (52 weeks in a year.)
a. Use the Multiplicative Identity Property of One to write an
equivalent expression.
b. Simplify the expression.
Sample: 0.79 · 1A
0.79A
25.
w
year
calculation
answer
9. One foot equals how many centimeters? (1 inch = 2.54 cm)
cm
inches
____
2.54 ___
inch · 12 foot
cm
30.48 ___
foot
calculation
w
answer
60 minutes _______
24 hours ____
60 seconds
30 days · _____
1 day · 1 hour · 1 minute
10. How many seconds are there in a 30-day month?
d
v
$7,020
____
$6.75
hours
weeks
____
____
____
hour · 20 week · 52 year
In 24 and 25, give a formula in simplest form for the perimeter of
the polygon.
v
2,592,000 seconds
calculation
d
answer
x
d
x + 2v + 2w
6d
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Name
6/6/07 4:09:27 PM
Name
8-2B
0-0X Lesson Master
8-2B
VOCABULARY
page 2
In 9−16, show your calculation and give the answer.
9. 4 miles equals how many feet? (1 mi = 5,280 ft)
1. a. Explain the relationship between a rate factor and a conversion factor.
A rate is a quantity whose unit contains the phrase “per,” or “for
calculation:
each,” or some synonym. A rate factor is a factor used in solving a
ft
4 mi · 5,280 ___
1 mi
answer:
21,120 ft
answer:
326,700 ft2
10. Convert 7.5 acres to square feet. (1 acre = 43,560 ft2)
ft
7.5 acres · 43,560 ____
1 acre
2
problem. A conversion factor is a rate whose value is 1.
calculation:
b. Give an example of each.
inches
1 inch
_____
Samples: 7 inches per minute, or 7 ____
minute , is a rate factor. 2.54 cm is
a conversion factor.
11. Andrea picked 2 bushels of cherries. How many pints is this?
(1 bushel = 4 pecks; 1 peck = 16 pt)
____
2 bushels · 4 _____
1 bushel · 16 1 peck
pecks
calculation:
pints
128 pints
answer:
12. Convert 20,000 cubic centimeters to quarts. (1 L = 1,000 cm3; 1 L ≈ 1.06 qt)
L
__
20,000 cm3 · 1 ______
1,000 cm · 1.06 1 L
qt
In 2 and 3, write the conversion equation that corresponds to each
conversion factor.
day
24 hours
2. 1 _______
USES
1 day = 24 hours
feet
3. 5,280 _____
1 mile
Copyright © Wright Group/McGraw-Hill
hour
a. Identify the rate factor.
5,280 feet = 1 mile
hour
c. Do the multiplication.
125 miles
calculation:
drive?
Sample: Let r be the rate, and t be the time. Then D = rt.
answer:
20
dollars
lawns
____
7.5 ____
lawn · 6 week · 7 weeks
answer:
$7.98
1 lb
4 oz
____
____
______
1 lb · 16 oz · 1 sandwich · 30 sandwiches
calculation:
students
______
field trip
field trip
198 pencils
buns
400 ____
picnic
answer:
17. Maliha, an Asian elephant at the St. Louis Zoo, weighed 341 pounds
at birth. Then she lost 30 pounds due to an illness. However, over the
next 3 weeks, she gained 11 pounds each week. How much did she
weigh at that point?
2,800 pages
315 dollars
$59.85
344 lb
600 points
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days
16. As part of the buffet for her family reunion, Anna is making
sliced-turkey sandwiches. Sliced turkey costs $7.98 per pound
at a local store. If Anna decides to use 4 ounces per sandwich
and wants to make 30 sliced-turkey sandwiches, how much will
she spend on sliced turkey?
e. Write a general formula for the distance D, clearly identifying
any other variables.
pencils
class
student
hot-dog buns
packages
picnic
package
points
items
8. 5 _____ · 20 _____
· 6 tests
test
item
3,120 wing-beats
15. Kim earns 7.5 dollars for each lawn she cuts. If she cuts 6 lawns
each week, how much will she earn in 7 weeks?
mi
_1
Sample: Isaiah drove at 50 __
h for 2 2 hours. How far did he
cases
_____
7. 8 __________ · 10 _______
case · 5
h
___
· 2 __
40 ____
h
day · 5 wk · 7 wk
pages
calculation:
d. Make up a question that leads to the multiplication.
students
6. 3 classes · 22 _______
· 3 _______
answer:
14. If Donald reads 40 pages per hour and he reads 2 hours each day,
how many pages will he read in 5 weeks?
miles
___
students
cars
5. 5 _______
· 4 _______
car
52 ______
second · 60 seconds
wing-beats
miles
50 ___
hour
≈ 21.2 qt
answer:
13. A Ruby-throated hummingbird, on average, makes 52 wing-beats
per second during flight. How many wing-beats will the hummingbird
make during one minute of flight?
calculation:
b. Identify the rate unit.
In 5−8, do the multiplication. Include units in all answers.
3
calculation:
Objective F: Apply the Rate Factor Model for Multiplication.
miles
4. Consider the expression 2.5 hours · 50 _____
.
382
36 inches
and
calculation
23. Consider the expression 0.79 · 100%(A).
380
1,000 m
and
36 inches
______
3. 36 inches = 1 yard
days
3($35.53) + 4($9.71) = $145.43
d
1 km
_____
calculation
b. Use the Distributive Property to find the total bill.
2 pints
and
1,000 m
_____
1 km
2. 1,000 meters = 1 kilometer
a. Use the Repeated Addition Property of Multiplication to find the total bill.
d
1 quart
miles
hours
____
___
4.85 ___
hour · 2 day · 7 week · 8 weeks
$35.53 + $35.53 + $35.53 + $9.71 + $9.71 + $9.71
+ $9.71 = $145.43
1 quart
____
2 pints
____
1. 2 pints = 1 quart
day
21. Show why (4x)(4y) ≠ 4(x + y)
d
See pages 549–551 for objectives.
Objective F
In 1−3, give two conversion factors that could be derived from the equality.
b. without the parentheses.
17. 3(p + r) + 2(p + r)
24.
Questions on SPUR Objectives
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