SETTING UP and SETTING UP and SOLVING RATIOS AND SOLVING RATIOS AND

PROPORTIONSPROPORTIONS

SETTING UP and SETTING UP and SOLVING RATIOS AND SOLVING RATIOS AND

PROPORTIONSPROPORTIONS

• 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.

Find the ratio of females to the entire class.There are 29 in the class.

16

13

females

males

16

29 clas

females

s

Ex 2 The male to female ratio in Italy is

46 to 54. Express this ratio as a fraction in reduced form.

46

54 fe

males

males

23

27 fe

males

males

To reduce fraction 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?

) 20 by 44B

) 30 by 57C

) 20 by 38A

) 60 by 114D

20 10)

38 19A

30 10)

57 19C

5 (not it)

1

20)

44 1 B

60 10)

114 19D

Ex 7 Which of the following pairs of ratios do not

form a proportion? Which ones do?

24 = 24

48 = 48

30 = 30

30 = 24

2 10)

3 15A

16 2)

24 3B

2 8)

3 12C

2 8)

3 15D Not

aproportion

CrossMultiply

8) 5 is to 4 as 45 is to x.

Set up and solve this proportion.

____ = ____54

45x

Now cross

multiply

5x = 1805 5

x = 36

First - Set up & solve the proportion.

9) 3 is to 2 as x is to 18.

____ = ____32

x18

Now cross

multiply

2x = 542 2x = 27

NO set up this time!! Just solve…..

3

6 48

x10

)

6x = 1446 6

x = 24

11)4

2 16

m

16m

= 8

16 16

m =8

16

NowReduce

1

2m

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!

40

47 10,827

x

Now cross

multiply

47x =433,08047 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 upYour proportion!

____ = _____9°

300 m216°

9m =64800

9 9m = 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 upYour proportion!

____ = _____1cm30k

m

11cm x

1x = 330

330 kmx =

Ex 6 Set up & Solve proportions

A regional forestry division wanted to estimate the number of deer in a particular national park. They caught and tagged 76 deer and released them back into the park. Later they selected a sample of 225 deer. Of these 225 deer, 15 were tagged. What is the best estimate of the number of deer in

the park? 76

tagged deer

x total population

15x 15 15

1140x

15 tagged

225 sample population

17,100