Transcript 1. Ratio and Proportions

SETTING UP and
SOLVING RATIOS AND
PROPORTIONS
• Ratio – Comparison of 2 numbers by
division.
– Ex. 1:2, ½, 1 to 2
• Proportion – An equation stating that 2
ratios are equal.
– a:b = c:d
• Extremes – The last (or end) terms of a
proportion.
– a and d are the extremes
• Means – The middle terms of the
proportion.
– b and c are the means
Ex 1
A geometry class consists of 13 males and
16 females. Find the ratio of females to males.
16 females
13 males
Find the ratio of females to the entire class.
There are 29 in the class.
16 females
29 class
Ex 2
The male to female ratio in Italy is
46 to 54. Express this ratio as a
fraction in reduced form.
46 males
54 females
To reduce fraction
23 males

27 females
Math
enter
enter
Ex 3
The approximate ratio of the
circumference (distance around) to
diameter (distance across the top)
of an oil barrel is 95.83 inches to
30.5 inches. Express this ratio as
a fraction in reduced form.
95.83 in. circumference
30.5 in. diameter
9583

3050
To reduce fraction
Math enter enter
Ex 4
A manufacturer can produce
1140 parts in 4 hours. What is the unit
rate in parts per hour?
1140 parts
4 hours
285 parts

1 hour
Ex 5
Write the ratio as a rate in lowest terms:
$3.90 for 6 muffins
$3.90
6 muffins
$0.65

1 muffin
Ex 6
There is a law stating the ratio of the width to
length of the American flag should be 10 to
19. Which is not the correct ratio?
A) 20 by 38
20 10
A)

38 19
B) 20 by 44
20 5
B)

(not it)
44 11
C ) 30 by 57
30 10
C)

57 19
D ) 60 by 114
60 10
D)

114 19
Ex 7
Which of the following pairs of ratios do not
form a proportion? Which ones do?
2 10
A)

3 15
30 = 30
16 2
B)

24 3
48 = 48
Cross
Multiply
2 8
C)

3 12
24 = 24
2 8
D)

3 15
30 = 24
Not
a
proportion
Set up and solve this proportion.
8) 5 is to 4 as 45 is to x.
5 = ____
45
____
4
x
5x = 180
5
5
x = 36
First - Set up & solve the proportion.
9) 3 is to 2 as x is to 18.
3 = ____
x
____
2
18
2x = 54
2
2
x = 27
NO set up this time!!
Just solve…..
10)
3 x

6 48
6x = 144
6
6
x = 24
11)
m 4

2 16
16m = 8
16
16
m =
8
16
Now
Reduce
1
m
2
12) Mr. Jones has taken a survey of college
students and found that 40 out of 47 students are
liberal arts majors. If a college has 10,827
students, what is the number of students who are
liberal arts majors, rounded to the nearest whole
number?
First – Set up
Your proportion!
x
40 = _______
____
47
10,827
47x = 433,080
47
47
x = 9214
13) Geothermal energy is heat from inside the
earth. Underground temperatures generally
increase 9°C for every 300 meters of depth. How
deep would a well have to be for the temperature
to reach 216°C ?
First – Set up
Your proportion!
9° = _____
216°
____
300
m
9m = 64800
9
9
m = 7200
14) A map has a scale of 1 cm = 30 km. If two
cities are 11 cm apart on the map, what is the
actual distance between the two cities to the
nearest tenth of a km?
First – Set up
Your proportion!
11cm
1cm = _____
____
30km
x
1x = 330
x = 330 km