SETTING UP and SOLVING RATIOS AND PROPORTIONS

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SETTING UP and SOLVING RATIOS AND PROPORTIONS
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• Ratio Comparison of 2 numbers by division.
• Example 12, ½, 1 to 2
• Proportion An equation stating that 2 ratios
  are equal.
• Example ab cd

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Example 1
A geometry class consists of 13 males and
16 females. Find the ratio of females to
males. Find the
ratio of females to the entire class. There are
29 in the class.
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Example 2
The male to female ratio in Italy is
46 to 54. Express this ratio as a fraction in
reduced form.
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Example 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.
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Example 4
A manufacturer can produce 1140 parts in 4
hours. What is the unit rate in parts per
hour?
Example 5
Write the ratio as a rate in lowest terms 3.90
for 6 muffins
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Example 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?
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Example 7
Which of the following pairs of ratios do not
form a proportion? Which ones do?
Cross Multiply
Yes
Yes
Not a proportion
Yes
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Set up and solve this proportion.
8) 5 is to 4 as 45 is to x.
5
45
Now cross multiply
____ ____
x
4

180
5x
5
5
36
x

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First - Set up solve the proportion.
9) 3 is to 2 as x is to 18.
3
x
Now cross multiply
____ ____
18
2

54
2x
2
2
x

27
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NO set up this time!!
Just solve..
10)
6x
144

6
6
x
24

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You try it!!
11)
Now Reduce
16m
8

16
16
m

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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
____ _______
10,827
47
433,080
47x

Now cross multiply
47
47
x

9214
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13) Geothermal energy is heat from inside the
earth. Underground temperatures generally
increase 9C for every 300 meters of depth. How
deep would a well have to be for the temperature
to reach 216C ?
First Set up Your proportion!
9
216
____ _____
m
300

64800
9m
9
9
m

7200
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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
____ _____
x
30km
330
1x

330 km
x