Ratios and Proportion

1
Ratios and Proportion
ALGEBRA 1 LESSON 4-1
(For help, go to Skills Handbook pages 724 and
727.)
Write each fraction in simplest
form. 1. 2. 3. Simplify each
product. 4. 5. 6.
49 84
24 42
135 180
35 25
99 144
21 81
40 14
96 88
108 56
?
?
?
7-1
2
Ratios and Proportion
ALGEBRA 1 LESSON 4-1
1. 2. 3. 4. 5. 6.
Solutions
49 7 7 7 84 7 12 12


24 6 4 4 42 6 7 7


135 45 3 3 180 45 4 4


35 40 5 7 5 8 5 7 5 8 8 25 14 5 5 7
2 5 5 7 2 2
?
?



4
99 96 9 11 8 12 9 11 8 12 9
3 144 88 12 12 8 11 12 12 8 11 12 4
?
?




21 108 3 7 3 3 3 4 3 7 4
4 1 81 56 3 3 3 3 7 8 3 7 8
8 2
?
?
4




4
7-1
3
Ratios and Proportion
ALGEBRA 1 LESSON 4-1
Another brand of apple juice costs 1.56 for 48
oz. Find the unit rate.
The unit rate is 3.25/oz.
7-1
4
Ratios and Proportion
ALGEBRA 1 LESSON 4-1
The fastest recorded speed for an eastern gray
kangaroo is 40 mi per hour. What is the
kangaroos speed in feet per second?
The kangaroos speed is about 58.7 ft/s.
7-1
5
Ratios and Proportion
ALGEBRA 1 LESSON 4-1
y 3
3 4
Solve .
7-2
6
Ratios and Proportion
ALGEBRA 1 LESSON 4-1
w 4.5
6 5
Use cross products to solve the proportion
.
7-2
7
Ratios and Proportion
ALGEBRA 1 LESSON 4-1
In 2000, Lance Armstrong completed the 3630-km
Tour de France course in 92.5 hours. Traveling at
his average speed, how long would it take Lance
Armstrong to ride 295 km?
Traveling at his average speed, it would take
Lance approximately 7.5 hours to cycle 295 km.
7-2
8
Ratios and Proportion
ALGEBRA 1 LESSON 4-1
z 3 4
z 4 6
Solve the proportion .
7-2
9
Ratios and Proportion
ALGEBRA 1 LESSON 4-1
Solve. 1. Find the unit rate of a 12-oz bottle
of orange juice that sells for 1.29. 2. If you
are driving 65 mi/h, how many feet per second are
you driving? Solve each proportion. 3. 4.
5. 6.
10.75/oz.
about 95.3 ft/s
c 6
12 15
21 12
7 y
4.8
4


1 2
3 x 7
4 8
2 x x 4
25 35
17


7-2
10
Proportions and Similar Figures
ALGEBRA 1 LESSON 4-2
(For help, go to Skills Handbook and Lesson 4-1.)
Simplify 1. 2. 3. Solve each
proportion. 4. 5. 6. 7. 8. 9.
36 42
81 108
26 52
x 12
7 30
y 12
8 45
w 15
12 27



n 1 24
9 a
81 10
25 75
z 30
n 9



7-2
11
Proportions and Similar Figures
ALGEBRA 1 LESSON 4-2
1. 5. 7. 9. 2. 3. 4. 6. 8.
Solutions
y 12
8 45
9 a
81 10
n 9
n 1 24
36 42
6 6 6 6 7 7





45y 12(8)
81a 9(10)
24n 9(n 1)
81 108
27 3 3 27 4 4


45y 96
81a 90
24n 9n 9
26 52
26 1 1 26 2 2
15n 9


9 15
2 15
1 9
n
y 2
a 1
3 5
n
30x 12(7)
w 15
12 27
25 75
z 30


30x 84
27w 15(12)
75z 25(30)
27w 180
75z 750
2 3
w 6
z 10
7-2
12
Proportions and Similar Figures
ALGEBRA 1 LESSON 4-2
In the figure below, ABC DEF. Find AB.
AB is 12 mm.
7-2
13
Proportions and Similar Figures
ALGEBRA 1 LESSON 4-2
A flagpole casts a shadow 102 feet long. A 6 ft
tall man casts a shadow 17 feet long. How tall is
the flagpole?
The flagpole is 36 ft tall.
7-2
14
Proportions and Similar Figures
ALGEBRA 1 LESSON 4-2
The scale of a map is 1 inch 10 miles. The map
distance from Valkaria to Gifford is 2.25 inches.
Approximately how far is the actual distance?
The actual distance from Valkaria to Gifford is
approximately 22.5 mi.
7-2
15
Proportions and Similar Figures
ALGEBRA 1 LESSON 4-2
1. In the figure below, ABC DEF. Find
DF. 2. A boy who is 5.5 feet tall casts a
shadow that is 8.25 feet long. The tree next to
him casts a shadow that is 18 feet long. How
tall is the tree? 3. The scale on a map is 1
in. 20 mi. What is the actual distance between
two towns that are 3.5 inches apart on the map?
About 19.7 cm
12 ft
70 mi
7-2