Name ________________________________________ Date __________________ Class __________________
LESSON
1-2
Modeling Quantities
Reteach
Multiplying by 1 does not change the value of a number: 33 • 1 = 33
So, multiplying by a fraction equal to 1 does not change the value either: 33 •
5
= 33
5
Multiplying by 1 is like converting rates.
Example
Convert 150 feet per minute to miles per hour.
Step 1 Convert feet to miles.
150 ft
•1
1 min
1 mile = 5280 ft
150 ft
1 mi
150 mi
•
=
1 min 5280 ft 5280 min
Step 2 Convert minutes to hours.
150 mi
•1
5280 min
150 mi
60min 9000 mi
mi
•
=
= 1.7
5280 min
1h
5280 h
h
Write a fraction equal to 1 for the relationship between these units.
1. feet and yards
ft
=1
yd
2. meters and centimeters
3. fluid ounces and cups
m
=1
cm
fl oz
=1
c
Solve each proportion.
4. The 2004 Tour de France was 3391.1 kilometers. The winner
won the race in a little over 83.5 hours. Fill in the blanks to find the
winner's average speed in meters per hour.
3391.1 km
3391.1 km
•1=
•
83.5 h
83.5 h
=
m
=
h
m
h
5. A soft-serve ice cream machine makes 1200 gallons per hour.
Convert this rate to cups per minute.
(Hint: 1 gallon = 16 cups) ____________________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
74
Answer Key
Reteach 2-2: Creating and Solving
Equations
Reteach 1-1: Solving Equations
1. x + (−7) = 12; x = 19
2. y + 1 = −5; y = −6
1. m + 2 m = 18; Mako runs 6 miles.
3. −4 = p + (−2); p = (−2)
2. 18 + 0.15 m = 29.25; 75 min
4. −7 = 4 + (−a); a = 11
3.
5. k = −16
6. g = −6
e + (3e − 20)
= 50; Eric collected $30,
2
and Charlotte collected $70.
Reteach 2-3: Solving for a Variable
7. h = −3
8. d = 19
Reteach 1-2: Modeling Quantities
3 ft
1.
1 yd
1m
2.
100 cm
1. b =
2A
h
2. l =
A
w
3. s =
2R + 6t − 5
2
4. c = P −a −b
3.
8 fl oz
1c
5. t =
4.
1000 m 3,391,100 m
m
;
; 40612
1 km
83.5 h
h
6. H =
5. 320
2I
pr
GK
J
7. n = 360 −m − p −q
c
min
Reteach 1-3: Reporting with Precision
and Accuracy
1. 180 min
2. 7.65 g
8. s =
t
r +1
9. a =
bc
d
Reteach 2-4: Creating and Solving
Inequalities
3. 2.50 in.
1. −3e − 10 ≤ −4
−3e − 10 + 10 ≤ −4 + 10
−3e ≤ 6
−3e 6
≤
−3 −3
e ≥ −2
4. 7.203 qt
5. 3 c
6. 35.4 yd
7. 4.9 oz
8. 42 mi
Reteach 2-1: Modeling with
Expressions
1. 2b + 7
2. 3b + 4p
3. 1 + 2m
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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