Back to Lesson 9-5
Name
Name
9-4B Lesson Master
9-4B
PROPERTIES
SKILLS Objective B: Divide positive and negative numbers.
−125
1. ____
25
−2
___
−5
__
3
3. __
−4
___
−8
6.4
2. ____
−0.8
1
2
3
5. −2 __12 ÷ −7 __12
__1
−3
4. ___
÷ __18
4
3
−14.4
6. _____
−6
PROPERTIES
C
-5 -4 -3 -2 -1
V
A
example, “the product of a positive and a negative number is negative”
3
2
1
-1
-2
x
1 2 3 4 5
-3
-4
becomes “the quotient of a positive and a negative number is negative.”
This is because dividing by a number is equivalent to multiplying by
G
the reciprocal of the number.
R
-5
B
a
, where b ≠ 0?
14. Multiple Choice. Which does not equal __
−b
a
B - __
−a
A ___
b
4 ___
−4 ___
−4
4
−4 , − ___
__4 , − ___
, −4 , − ___
; 4 , ___
, − __
b
−b
−10 ÷ 5 = −2; −10 ÷ −2 = 5
4
__
5
−3
__
4
− ___
−5
5
4
___
−5
REPRESENTATIONS
−1
−1
−3 ; ___ = __
) = __
3(__
3
4
4
4
D −a · __1
C - __a
15. Separate these numbers into two
collections of equal numbers.
8. Write the related facts for: (−2)(5) = −10
4
positive
The rules are identical if “quotient” is substituted for “product.” For
5
4
division.
−3
___
−4
___
5
b
−5 −5
−4
− ___
−5
5 −5 5
related facts with a fact triangle.
−9 · __
3 = −6
2
−6 ÷ __
3 = −9
2
−6 ÷ −9 = __
3
2
2
3
1
5
÷
×
−3
7
18. Draw a fact triangle for ___
÷ __
= n.
12
4
Solve for n.
7
12
−9
25
Transition Mathematics
−3
4
÷
×
−9
___
UCSMP_SMP08_NL_TM1_TR2_C09_405-4417
6/6/07 4:23:43 PM
417
Name
12
___
n = 7 , or −1 7
n
Transition Mathematics
UCSMP_SMP08_NL_TM1_TR2_C09_405-4416 416
417
6/6/07 4:23:44 PM
Name
9-5A Lesson Master
Questions on SPUR Objectives
See pages 611–613 for objectives.
9-5B Lesson Master
SKILLS Objective C: Solve equations and inequalities using the
SKILLS Objective C
Division Property of Equality and the Division
Property of Inequality.
In 1–9, solve and check.
2
2. __3 m = −1.2
3. −15 = 2.5a - 5
m = −1.8;
b = _21 ;
−16 ( _12 ) = −8
4. 16 = 72% of q
200
q = ___
9 ;
200
0.72 ___
9 = 16
a = −4;
_2 (−1.8) = −1.2 2.5(−4) −5 = −15
3
5. −1.2t + 4 = 3.2
n > 5;
8. 56 ≥ −15d + 11
11 ≤ 56
so − _12 (−10)
−1 _34 = 3 _14 > _34
In 10 and 11,
a. Write an equation or inequality to solve the problem.
b. Find the answer.
7
1
4. __
= __
g
10
55
g = 38 _12 ;
(
313 hours or more
3
11. __4 of the students in the drama club went to see a professional
1
125
7. __
k = ___
18
90
k = 25;
1
__
125
___
18 (25) = 90
h > 20.8;
Sample: Let h =
49
52, so __
5.2 (52) =
490 > 196
performance of Hamlet with 5 chaperones. If 29 people went to
Hamlet, how many students are in the drama club?
_3 s + 5 = 29
4
)
1
__
_1
7
__
55 38 2 = 10
49
10. ___
h > 196
5.2
10. Elle is working to save money for college. She wants to have a minimum
of $2,500. If she already has $545 and works at the local bookstore making
$6.25 per hour, how many hours will she need to work?
b.
w = −75;
4
__
15 (−75) = −20
−3
3. ___
y = 12
1.5
n = −14;
45
___
−70 (−14) = 9
y = −6;
−3
__
1.5 (−6) = 12
1
3
5. __
m = __
21
14
121
−1
6. ___
= ___
s
70
210
48
8. __
b = 16
69
1
−0.2
9. __
d < ____
54
0.9
m = 4 _12 ;
1
__
_1
3
__
21 ( 4 2 ) = 14
s = −363;
1
− ___
(−363)
210
3
9. __4 < − __12 g - 1 __34
d ≥ −3 ;
g < −5;
k ≥ −7 ;
Sample: Let k = 0, Sample: Let d = 0, Sample:
so _12(0) = 0 ≥ −3 _12 so −15(0) + 11 = Let g = −10,
545 + 6.25h ≥ 2,500
45
2. ___
n=9
−70
4
1. __
w = −20
15
6. −1.2n < −6
t = _23
Sample: Let
−1.2 ( _23 ) + 4 = 3.2 n = 10,
so (−1.2)(10) =
−12 < −6
7. −3 __12 ≤ __12 k
In 1–12, solve and check.
b.
300
−1
11. ___
< ____
t
227
4.54
d < −12;
Sample: Let d =
1
−54, so __
54 (−54) =
0.2
__
−1 < − 0.9
12.3
12. −8.2 > ____
u
8.4
t < −6;
Sample: Let t =
−1
−9.08, so ___
4.54 (−9.08) =
300
2 > ___
227
u < −5.6;
Sample: Let
u = −8.4,
12.3
so __
8.4 (−8.4) =
−12.3 < −8.2
32 students
Transition Mathematics
UCSMP_SMP08_NL_TM1_TR2_C09_405-4418 418
b = 23;
48
__
69 (23) = 16
Copyright © Wright Group/McGraw-Hill
1. −8 = −16b
A58
÷
×
−5
9
418
−6
−9
−5
−9
17. Draw a fact triangle for __15 ÷ ___
= ___
.
9
25
a.
5
−4
− ___
5
16. What are the related facts given by the fact triangle?
x = −12.6
a.
−5
− __45
−4
___
−5
Objective K: Represent multiplication and division
4
x
10. Solve ___
= −3 for x.
4.2
416
4
− __
7
b
Objective D: Know related facts of multiplication and
4
9. Write the related facts for: __
=3
−1
___
−7
13. Explain how the rules for division of negative numbers compare to the
rules for multiplication of negative numbers.
2.4
__ )
positive and negative numbers.___
4
12. If __a = c, and a and c are negative, is b positive or negative?
y
( __
Objective F: Know the general properties for dividing
−4
11. Write two fractions in lowest terms equal to __
.
7
−6
7. The center of gravity of a polygonal region is the point on
which the region would balance if cut out and placed
horizontally. When placed on a coordinate grid, the mean
of the first coordinates of the polygon’s vertices is the
first coordinate of the center of gravity, and the mean
of the second coordinates of the polygon’s vertices is the
second coordinate of the center of gravity. Find the
coordinates of the center of gravity of CGRAV.
−2 −8
,
5 5
page 2
Transition Mathematics
UCSMP_SMP08_NL_TM1_TR2_C09_405-4419
6/6/07 4:23:45 PM
419
419
6/6/07 4:23:46 PM
Transition Mathematics
SMP08_TM2_TR2_C07-12_A43-A82.indA58 A58
6/6/07 5:40:57 PM
Back to Lesson 9-5
Name
Name
9-5B
page 2
In 13–20,
a. Write an equation or inequality to solve the problem.
b. Find the answer.
13. Valery paid $64.89 for 7 CDs. What was the
14. Box lunches are selling for $8.50 each. Caleb
average price of the CDs?
paid $51.00 for some box lunches. How many
box lunches did Caleb buy?
a.
a.
7p = 64.89
8.50b = 51
$9.27
b.
6 box lunches
b.
15. Matt wants to ship brochures, each weighing
7 grams, in a box that weighs 350 grams.
There is a total shipping weight limit of
1700 grams. What is the greatest number of
brochures Matt can ship?
a.
192 brochures
b.
17. Leisurely swimming burns around
350 calories an hour. About how many
minutes will it take to burn 150 calories
through leisurely swimming?
208h ≥ 624
__3 hour (between 25 and 26 minutes) b.
7
at least 3 hours
b.
19. Manny wants to invite some friends to a
basketball game on his birthday. Tickets to
the game cost $11.70 and transportation will
cost $60 for the group. If Manny can spend
up to $190, how many friends can he invite
(don’t forget a ticket for Manny)?
a.
20. Brawny-Brats bratwursts are sold in
packages of 10, while buns for them are sold
in packages of 8. If the picnic committee
buys 17 packages of buns, what is the
greatest number of packages of bratwurst
that will allow for a bun for every bratwurst?
11.7 + 11.7f + 60 ≤ 190
10 friends
b.
10p ≤ 8 · 17
a.
2. On the final exam in mathematics, Joanne scored 112 of 125 points.
What was her percent score?
about 1.42 times as many students attended as last year.
b. Last year, about 0.7 times as many students attended as this year.
c. This year’s attendance was about 1.42 percent of the number of
students in attendance last year.
4. Fill in the blank. According to the Consumer Price Index, in July of 1996,
a gallon of gasoline cost $1.57. In July, 2006, it cost $3.20.
3.20
____
1.57
.
about 204 percent of the 1996 price.
5. According to infoplease.com (source: Department of Education, National
Center for Education Statistics), 26,410 students graduated from college
in 1900. In 2000 there were 1,237,875 graduates. To the nearest tenth of a
percent, find the ratio of graduates in 1900 to graduates in 2000.
2.1%
6. The largest state, Alaska, has 571,950 square miles of land. The smallest
state, Rhode Island, has 1,045 square miles of land. To the nearest tenth
of a percent, find the ratio of the land mass of Rhode Island to the land
mass of Alaska.
0.2%
7. The atomic weight of the smallest atom, Hydrogen, is 1.00794. The next
atom listed on the periodic table, Helium, has an atomic weight of 4.002602.
a. To the nearest hundredth of a percent, what is the ratio of the weights
of the hydrogen atom to the helium atom?
25.18%
b. To the nearest hundredth of a percent, what is the ratio of the weights
of the helium atom to the hydrogen atom?
397.11%
Transition Mathematics
420
89.6%
3. Fill in the blank. 320 students attended the school’s Valentine’s Day
dance this year. Last year 225 students attended.
8. At the time of his draft in 1987, “Mugsy” Bogues, 5'3", was the
shortest person ever to play in the National Basketball Association
(NBA). During his rookie year, he was a teammate of Manute
Bol, 7'7", who was the tallest person ever to play in the NBA at
that time. Manute Bol is about how many times as tall as
Mugsy Bogues?
13 packages
b.
6%
1. $2.74 tax was added to a $45.63 dinner bill. Calculate the tax rate.
b. The 2006 price is
a.
See pages 611–613 for objectives.
USES Objective I
a. The ratio of the 2006 price to the 1996 price is
1.16 lb of ham
18. Walking burns about 208 calories an hour.
About how long will it take to burn at least
624 calories through walking?
350h = 150
a.
0.67 + 6.25h = 7.89
b.
Questions on SPUR Objectives
a. This year,
16. Jenna paid $7.89 for lunch materials that
consisted of a loaf of bread that cost $0.67
and deli ham that cost $6.25 a pound. To two
decimal places, how many pounds of ham did
Jenna buy?
350 + 7b ≤ 1700
a.
9-6A Lesson Master
91
___
≈ 1.4
63
times as tall
Transition Mathematics
UCSMP_SMP08_NL_TM1_TR2_C09_405-4420 420
UCSMP_SMP08_NL_TM1_TR2_C09_405-4421
6/6/07 4:23:46 PM
421
Name
6/6/07 4:23:46 PM
Name
9-6B Lesson Master
6-5B
9-6B
USES Objective I: Use the Ratio Comparison Model for Division.
6. Fill in the blank. The Nile is the longest river in the world, measuring 4,160 miles.
The second longest river is the Amazon, measuring 4,000 miles. The Chang Jiang
(Yangtze) is third longest river, measuring 3,964 miles.
In 1−4, use this table of the heights above sea level of the 121 tallest mountains
on Earth, from infoplease.com.
a. The Nile is about
Elevation
(meters)
Number
of Peaks
>8,500 8,000−8,499 7,500−7,999
4
10
22
7,000−7,499 6,500−6,999
30
20
6,000−6,499
35
1.04
1.01
1.05
b. Compare the numbers of Himalayan and
Karakoram peaks, in both orders.
a. The 2002 grocery bills were about
of their 2007 grocery bills.
71%
a. What percent of the 14 tallest peaks are in the Himalayas?
4 Karakoram __
2 10 Himalayan 5
___________
, ; ___________, __
10 Himalayan 5 4 Karakoram 2
Copyright © Wright Group/McGraw-Hill
a. Find the ratio of Himalayan peaks to all the peaks taller than
6,999 meters.
43
___
times as long as the Amazon.
times as long as the Chang Jiang.
times as long as the Chang Jiang.
71
____
, or 59%
121
3. The Andes mountains have the other 50 peaks whose heights are
between 6,000 meters and 6,999 meters. There are 45 Himalayan
peaks in the entire table.
50
10
___
, or ___;
a. Give the ratio and percent of the number of Andean peaks whose
heights are between 6,000 meters and 6,999 meters compared to
the total number of peaks with those heights.
55
11
91%
50 Andean ___
10 45 Himalayan 9
________
, ; ___________, ___
45 Himalayan
9
4. A tax of $3.99 was added to the $56.99 cost of a pair of shoes. Calculate
the tax rate.
50 Andean
10
7%
1.004 times
as long
a. About how many times as long as the Missouri is the Mississippi?
b. About how many times as long as the Mississippi is the Missouri? 0.996 times
as long
Transition Mathematics
5. The fourteenth and fi fteenth longest rivers are the Mississippi River,
2,350 miles long, and the Missouri River, 2,341 miles long.
71
percent
141
percent
1.41
times
8. Last year 3,041 babies were born at South Side Hospital, and 1,218
were born at Hastings Hospital.
66
b. Find the ratio and percent of the number of Asian peaks
to the number of peaks taller than 5,999 meters.
b. The 2007 grocery bills were about
of their 2002 grocery bills.
c. Their 2007 grocery bills were about
their 2002 grocery bills.
2. Of the peaks taller than 6,999 meters, all are in Asia, and 43 are
in the Himalayas. There are 5 Asian peaks whose heights are between
6,000 meters and 6,999 meters.
UCSMP_SMP08_NL_TM1_TR2_C09_405-4422 422
page 2
7. Fill in the blank. In 2002 a family’s grocery bills averaged $380 per
month. In 2007 they spent an average of $535 per month.
1. Of the 14 tallest peaks, 10 are in the Himalayas and 4 are in
the Karakoram.
b. Compare the numbers of Andean and
Himalayan peaks, in both orders.
b. The Amazon is about
c. The Nile is about
Source: National Geographic Society
422
421
a. Write a sentence comparing the number of births at South Side
Hospital to the number of births at Hastings Hospital.
_1
Sample: There were nearly 2 2 times as many babies
born at South Side Hospital as at Hastings Hospital.
b. Write a sentence comparing the number of births at Hastings
Hospital to the number of births at South Side Hospital.
Sample: Hastings Hospital had about 40 percent of
the number of births that South Side Hospital had.
9. In 2000, three percent of the people living in Ohio were born in another country.
How was the three percent calculated?
The number of foreign-born people living in Ohio in
2000 was divided by total number of people living in
Ohio in 2000.
Transition Mathematics
UCSMP_SMP08_NL_TM1_TR2_C09_405-4423
6/6/07 4:23:47 PM
423
6/6/07 4:23:47 PM
Transition Mathematics
SMP08_TM2_TR2_C07-12_A43-A82.indA59 A59
423
A59
6/6/07 5:41:05 PM