Back to Lesson 9-7
Name
Name
9-7A
Questions on SPUR Objectives
See pages 611–613 for objectives.
PROPERTIES
PROPERTIES
Objective E
3.2
48
__
2. ___
x = 75
Sample: 8x
1. a. Using the Multiplication Property of Equality, by what expression
x
3. __a = _bc
4.2
63
__
can you multiply both sides of ___
n = 78 to eliminate the fractions?
Give the expression, multiply both sides of the equation by the
expression (eliminating common terms), and solve the equation.
Sample: ac
Sample: 75x
Objective E: Recognize the Means-Extremes
Property and know why it works.
In 1–3, by what expression can you multiply both sides of the equation to
eliminate fractions?
5
95
1. __8 = __
x
9-7B
78n; 4.2 · 78 = 63 · n; n = 5.2
In 4–6, solve for x using the Means-Extremes Property. Show your work.
5
95
4. __8 = __
x
b. How would you solve 4.2:n = 63:78 using the Means-Extremes
Property? Write an equation and then solve it.
5:8 = 95:x; 5x = 95 · 8; 5x = 760; x = 152
4.2 · 78 = n · 63; n = 5.2
3.2
48
__
5. ___
x = 75
3.2:x = 48:75; 3.2 · 75 = 48x; 240 = 48x; x = 5
x
6. __a = _bc
c. How can the first two parts of this problem be used to show that the
Means-Extremes Property is related to the Multiplication Property of Equality?
After using the Multiplication Property of Equality to eliminate
ab
x:a = b:c; cx = ab; x = __
c
5
x
2
Sample: __ + __ = __
3
7. Write an equation involving fractions that is not a proportion.
3
USES Objective J
when the Means-Extremes Property is used.
A, D, F, H
2. Which sentences are not proportions?
In 8–10, write a proportion and then answer the question.
8. One copy of War and Peace is 1,134 pages long. Yuko has been
reading __34 of a page per minute. If she continues at this rate, how long
will it take her to finish the book?
__3 page
1134 pages
4
_______
__3
= __________
1,512 minutes
x minutes or 4 : 1 = 1,134:x
1 minute
proportion
13
A __14 = __
39
10
60
B __
= __
3
18
2.5
50
C ___
= ___
15
300
70
D __
= __65
84
1.6
3.3
E ___
= ___
4.8
9.9
51
15
F __
= __
90
24
m
G __
= __12
20
1
H __5 + __35 = __45
3. Rewrite the right side of each sentence as a single fraction, which can
be used as one side in a proportion.
(25.2 hours)
y-2
___
y
a. __23 = __7 - __27
answer
7
20 + 3t
_____
()
b. __49 = 4 + __35 t
9. A 5 __13 -ounce can of olives sells for $1.69. At this rate, how much
should an 8-ounce can cost?
1
5 __
8 oz
3 oz
_________
_______
__1
1.69 dollars = c dollars or 5 3 : 1.69 = 8:c
5
In 4−9, solve the proportion.
$2.54
proportion
x
34
4. __5 = __
85
11
R
5. __
= __
2
18
9
72
6. __e = __
20
500
125
= ___
7. ___
a
62
6
8. ___
= __9s
0.2
2x
8
__
9. __
5 =3
proportion
e = 2.5
R = 99
x=2
answer
10. Last week Sheila earned $22.50 babysitting for 3 hours. At this rate,
how long will she have to work to earn enough to buy a radio that costs $82.50?
$22.50
$82.50
______
______
11 hours
3 hours = x hours or 22.50:3 = 82.50:x
20
_2
x = __
3 , or 6 3
s = 270
a = 15.5
answer
Transition Mathematics
Transition Mathematics
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Name
9-7B
page 2
USES Objective J: Recognize and solve problems involving
proportions in real-world situations.
or 7 :6.2 = (12 ):c
$10
proportion
answer
about 11.3 minutes
proportion
answer
12. Lynelle can do 75 math facts in 3 minutes. At this rate, how long will it
take her to do 240 math facts?
75
240
__
___
m
3
or 75:3 = 240:m
9.6 minutes
proportion
answer
13. If pizza sauce costs $1.35 for 4 cans, how many cans can be bought for $12?
c
4
___
__
1.35
12
=
or 4:1.35 = c:12
35 cans
proportion
answer
14. It takes Ed 5 minutes to wash 4 windows. At this rate, how long will it
take him to wash 35 windows?
35
_4
__
m
5
=
or 4:5 = 35:m
43.75 minutes
proportion
answer
15. A model of a car is built to a scale of 1:20. If the model is 23.5 centimeters
long, how many meters long is the car?
23.5
1
__
___
c
20
=
or 1:20 = 23.5:c
proportion
4.7 meters
answer
16. Sliced ham sells for $2.09 a half pound. How much will 1.62 pounds of
ham cost? Round your answer up to the nearest cent.
p
2.09
___
___
_1
_1
2
1.62
2
=
or 2.09: = p:1.62
proportion
q = 10
p
9
2. __
= __
10
15
p = 13.5
3
x
3. __
= __
50
25
x = 1.5
In 4–9, write a proportion(s). Then answer the question.
4. A photograph 3 cm wide and 12 cm long is proportionately enlarged to a
width of 12 cm. What is the new length of the photo?
3 cm
12 cm
____
____
12 cm = x cm ; x = 48 cm
11. A copier makes 530 copies in 5 minutes. At this rate, how long will it
take to make 1,200 copies?
1,200
530
___
t
5
=
See pages 611–613 for objectives.
USES Objective J
3
15
1. __2 = __
q
10. If 73 __34 yards of
ribbon costs $6.20, how much do 12 __12 yards cost?
7 _4
12 _12
__
___
_3
_1
c
6.2
2
4
= ___ or 530:5 = 1,200:t
Questions on SPUR Objectives
In 1–3, solve each proportion mentally.
In 10–16, write a proportion and then answer the question.
=
9-8A
$6.78
answer
5. Manuel completed 6 math problems in 12 minutes. At this rate, how long
will it take him to finish the entire 28-problem assignment?
6 problems
28 problems
_______
_______
12 minutes = x minutes ; x = 56 min
1
the size of a real house and
6. A dollhouse and its furniture is usually __
12
furniture. If a real dining-room table is about 72 inches long, 48 inches
wide, and 36 inches high, what would be the dimensions of a dollhouse table?
12 in.
____
1 in. =
48 in.
36 in.
72 in.
___
= ____
= ____
; 6 in. long, 4 in. wide, 3 in. high
in.
w in.
h in.
7. One cow requires 2 __12 acres of land for grazing. How many cows can be
supported on a 300-acre pasture?
Copyright © Wright Group/McGraw-Hill
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the fractions, you get the same simplified equation as you do
8
1 cow
x cows
_____
______
2.5 acres = 300 acres ; x = 120 cows
8. At a deli, sliced turkey sells for $3.29 a half pound. How much will
1.50 pounds of sliced turkey cost?
3.29 dollars
x dollars
_______
______
0.5 pounds = 1.5 pounds ; x = $9.87
9. On a map with a scale of 1 inch = 60 miles, it is about 3 __14 inches from
Boston to New York City. If Harry averages 30 miles per hour, how long
will it take him to make the trip?
3.25 in.
30 mi
195 mi
1 in.
___
= ____
; x = 195; ___
= ____
; 6 _1 hours
60 mi
x mi
1 hr
x hr
2
10. In 2006, the world record for the 100 m dash was 9.77 seconds. If this
pace could be maintained, estimate the time for the 1,600 m run
(the metric mile) using proportional thinking. Then write and solve a
proportion. Give your answer in minutes and seconds.
100 m
____
about 160 sec; ____
9.77 sec = x sec ;
156.32 sec = 2 min, 36.32 sec
1,600 m
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