Ch. 3 Dosages

1. Chapter 3
Relationships of Quantities:
Percents, Ratios, and Proportions
PowerPoint® Presentation to accompany:
Math and Dosage Calculations for
Healthcare Professionals
Fourth Edition
Booth, Whaley, Sienkiewicz, and Palmunen
© 2012 The McGraw-Hill Companies, Inc. All rights reserved.

2. 3-2
Learning Outcomes
3-1 Convert values to and from a percent.
3-2 Convert values to and from a ratio.
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3-3 Write proportions.
3-4 Use proportions to solve for an unknown
quantity.

3. 3-3
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Key Terms
 Cross-multiplying
 Means and
extremes
 Percent
 Proportion
 Ratio

4. 3-4
Introduction
 For dosage calculation you must:
 understand percents, ratios, and
proportions ;
 be able to find a unknown quantity in a
proportion.
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5. 3-5
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Percents
 Percents provide a way to express the
relationship of parts to a whole.
 Percent is indicated by the symbol %.
 Percent means “per 100” or “divided by 100.”

6. 3-6
Percents (cont.)
 A number < 1 is expressed as less than
100 percent.
 A number > 1 is expressed as greater than
100 percent.
 Any expression of one equals 100 percent.
1.0 = = 100 percent
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5
5

7. 3-7
Converting Values To and From a
Percent
RRuullee 33--11
To convert a percent to a decimal, remove
the percent symbol. Then divide the
remaining number by 100.
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8. 3-8
Converting Values To and From
a Percent (cont.)
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EExxaammppllee
Convert 42% to a decimal:
 Move the decimal point two places to the left.
 Insert the zero before the decimal point for clarity.
 42% = 42.% = .42. = 0.42

9. 3-9
RRuullee 33--22
To convert a decimal to a percent, multiply
the decimal by 100. Then add the
percent symbol.
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Converting Values To and
from a Percent (cont.)

10. 3-10
Working with Percents (cont.)
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EExxaammppllee
Convert 0.02 to a percent:
 Multiply by 100%.
 0.02 x 100% =2.00% = 2%

11. 3-11
Working with Percents (cont.)
RRuullee 33--33
To convert a percent to an equivalent
fraction, write the value of the percent as the
numerator and 100 as the denominator.
Then reduce the fraction to its lowest term.
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12. 3-12
Working with Percents (cont.)
Convert 8% to an equivalent fraction.
8% =
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EExxaammppllee
2
25
8 = 8
=
100
100
2
25

13. 3-13
Converting Values To and from a
Percent (cont.)
RRuullee 33--44 To convert a fraction to a
percent:
1. convert the fraction to a decimal;
2. round to the nearest hundredth;
3. then follow the rule for converting a
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decimal to a percent.

14. 3-14
Converting Values To and from a
Percent (cont.)
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EExxaammppllee
Convert 2/3 to a percent.
 Convert 2/3 to a decimal and round to the
nearest hundredth.
 2/3 = 2 divided by 3 = 0.666 = 0.67
 0.67 x 100% = 67%

15. 3-15
Answer = 75%
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Practice
Convert the
following percents
to decimals:
Convert the
following
fractions to
percents:
Answer = 0.14
14%
300% Answer = 3.00
6/8
4/5 Answer = 80%

16. 3-16
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Ratios
 The relationship of a part to the whole
 relates a quantity of liquid drug to a quantity
of solution;
 is used to calculate dosages of dry
medication such as tablets.

17. 3-17
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Ratios (cont.)
 Like a fraction, a ratio has two parts.
 The first part = numerator.
 The second part = denominator.
 The two parts are separated by a colon.

18. 3-18
Converting Values To and
From a Ratio
RRuullee 33--55
Reduce a ratio as you would a fraction.
Reduce 2:12 to its lowest terms.
Both values 2 and 12 are divisible by 2.
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2:12 is written 1:6
EExxaammppllee

19. Converting Values To and
From a Ratio. (cont.)
RRuullee 33--66
To convert a ratio to a fraction, write value A (1st
3-19
number) as the numerator and value B (2nd
number) as the denominator, so that A:B =
Convert the following ratio to a
fraction:
A
4
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4:5 =
B
5
EExxaammppllee

20. 3-20
Converting Values To and
From a Ratio.(cont.)
RRuullee 33--77
To convert a fraction to a ratio, write the
numerator as the 1st value A and the
denominator as the 2nd value B.
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A
= A:B B

21. 3-21
Converting Values To and
From a Ratio (con’t)
Convert the following into a ratio:
11
3 = 47:12
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7
12 = 7:12
12
EExxaammppllee
47
=
12

22. 3-22
Converting Values To and
From a Ratio. (cont.)
RRuullee 33--88 To convert a ratio to a decimal:
1. write the ratio as a fraction;
2. convert the fraction to a decimal.
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23. 3-23
Converting Values To and From
a Ratio (cont.)
Convert the ratio 1:10 to a decimal.
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1. Write the ratio as a fraction.
1
1:10 = 10
EExxaammppllee
2. Convert the fraction to a decimal.
1
10
= 1 divided by 10 = 0.1
1 = 0.1
Thus, 1:10 = 10

24. 3-24
Converting Values To and
From a Ratio (cont.)
RRuullee 33--99 To convert a decimal to a ratio:
1. write the decimal as a fraction;
2. reduce the fraction to lowest terms;
3. restate the fraction as ratio.
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25. 3-25
Converting Values To and From a
Ratio (cont.)
1. Write the decimal 0.25 as a fraction.
25
100
2. Reduce the fraction to lowest terms.
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1
25
3. Restate the number as a ratio.
1:4
4
100
=
EExxaammppllee

26. 3-26
Converting Values To
and From a Ratio (cont.)
RRuullee 33--1100 To convert a ratio to a percent:
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1. convert the ratio to a decimal;
2. write the decimal as a percent by multiplying
the decimal by 100 and adding the %
symbol.

27. 3-27
Converting Values To and
From a Ratio (cont.)
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Convert 2:3 to a percent.
1. 2:3 =
2 = 0.67
3
2. 0.67 X 100% = 67%
EExxaammppllee

28. 3-28
Converting Values To and From
a Ratio (cont.)
RRuullee 33--1111 To convert a percent to a ratio:
1. write the percent as a fraction;
2. reduce the fraction to lowest terms;
3. write the fraction as a ratio.
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 Numerator = value A
 Denominator = value B
 A:B

29. 3-29
Converting Values To and
From a Ratio (cont.)
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Convert 25% to a ratio.
1. 25% =
25
100
2. 25 = = =
1 : 4 25%
1
4
100
EExxaammppllee

30. 3-30
Practice
Convert the following ratios to a fraction or mixed
numbers:
3:4 5:3
1 2
5 =
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Answer =
3
4
Answer =
3
3

31. 3-31
Practice
Convert the following decimals to ratios:
0.9 8
Answer = 9 : 10
8 =
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9 =
10
Answer = 8 : 1
1

32. 3-32
Writing Proportions
 A proportion is a mathematical statement that
two ratios or two fractions are equal.
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 2:3 is read “two to three”
 2:3 = 4:6 is read “two is to three as four is to
six”

33. 3-33
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Writing Proportions (cont.)
RRuullee 33--1122
To change a proportion from
ratios to fractions, convert both
ratios to fractions.

34. 3-34
50
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Writing Proportions (cont.)
Write 5:10 = 50:100 as a proportion using
fractions.
100
5
5:10 = 50:100 same as =
10
EExxaammppllee

35. 3-35
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Writing Proportions (cont.)
RRuullee 33--1133
To change a proportion from
fractions to ratios, convert each
fraction to a ratio.

36. 3-36
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Writing Proportions (cont.)
10
5 =
Write using ratios.
12
6
10 : 12
5 : 6 10
12
6 5
= and =
5:6 = 10:12
EExxaammppllee

37. 3-37
Write the following as proportions using
fractions:
10
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Practice
4:5 = 8:10 Answer
50:25 = 10:5
8
10
4 =
5
Answer
5
50 =
25

38. 3-38
Using Proportions to Solve for
an Unknown
 Proportions are used to calculate
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dosages.
 If three of four of the values of a proportion
are known, the unknown quantity can be
determined by using:
 ratios; or
 fractions.

39. 3-39
Using Proportions to Solve for an
Unknown (cont.)
A proportion as the ratio – A:B = C:D.
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Extremes
A : B = C : D
Means

40. 3-40
Using Proportions to Solve for an
Unknown (cont.)
RRuullee 33--1144 To determine if a proportion is
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true:
1. multiply the means;
2. multiply the extremes;
3. compare the product of the means and the
product of the extremes.

41. 3-41
Using Proportions to Solve for an
Unknown (cont.)
Is 1:2=3:6 a true proportion?
1. Multiply the means: 2 X 3 = 6
2. Multiply the extremes: 1 X 6 = 6
3. Compare the products of the means and the
extremes: 6=6
1:2=3:6 is a true proportion.
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EExxaammppllee

42. 3-42
Using Proportions to Solve for an
Unknown (con’t)
RRuullee 33--1155 To find the unknown quantity in
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a proportion:
1. Write an equation:
product of the means = product of the
extremes
2. Solve for the unknown quantity.

43. 3-43
Using Proportions to Solve for
an Unknown (con’t)
RRuullee 33--1155 (cont.)
3. Restate the proportion, inserting the unknown
quantity.
3. Check your work. Determine if the ratio
proportion is true.
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44. 3-44
Using Proportions to Solve for an
Unknown (cont.)
Find the unknown quantity in 25:5=50:x
250 x = x = 10
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1. Write the equation:
5 x 50 = 25 X x becomes 250 = 25x
1. Solve the equation by dividing both sides by
25.
25
25
25
EExxaammppllee

45. 3-45
Using Proportions to Solve for
an Unknown (cont.)
EExxaammppllee ((ccoonntt..))
3. Restate the proportion, inserting the
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unknown quantity. 25:5=50:10
3. Check your work.
5 X 50 = 25 X 10
250 = 250
The unknown quantity is 10.

46. 3-46
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EERRRROORR AALLEERRTT!!
 Do not forget the units of measurement.
 Including units in the dosage strength will help
you avoid errors.

47. 3-47
Canceling Units in Proportions
(cont.)
RRuullee 33--1166
1. If the units in the first part of the ratio in
a proportion are the same, they can be
canceled.
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48. 3-48
Canceling Units in Proportions
(cont.)
RRuullee 33--1166 (cont.)
2. If the units in the second part of the ratio
in a proportion are the same, they can
be canceled.
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49. 3-49
Canceling Units in Proportions
(cont.)
If 100 mL of solution contains 20 mg of
drug, how many milligrams of the drug will
be in 500 mL of the solution?
20 mg:100 mL=x:500 mL 20mg X 500 = 100 X x
x = 100mg
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10000 mg x =
100 X
100
100
EExxaammppllee

50. 3-50
Practice
Determine whether the following proportions
6:12=12:24 Answer = True
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are true:
3:8=9:32
Answer = Not true

51. 3-51
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Practice
Use the means and extremes to find the
unknown quantity.
10:4=20:x Answer = 8
3:12=x:36
Answer = 9

52. 3-52
Using Proportions to Solve for an
Unknown (cont.)
RRuullee 33--1177 To determine if a proportion written
C
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as fractions is true:
1. Cross-multiply
A =
1. Compare the products. The products must
be equal.
D
B

53. 3-53
Using Proportions to Solve for
an Unknown (cont.)
2 =
Determine if 2 5 is a true proportion.
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10
5
1. Cross-multiply. 2 X 25=5 X 10
2. Compare the products on both sides of the
equal sign. 50 = 50
2 Therefore, =
10
5
25 is a true proportion.
EExxaammppllee

54. 3-54
Using Proportions to Solve for
an Unknown (cont.)
RRuullee 33--1188 To find the unknown quantity
in a proportion written as fractions:
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1. Cross-multiply.
 Write an equation setting the products equal to
each other.
2. Solve the equation to find the unknown
quantity.

55. 3-55
Using Proportions to Solve for
an Unknown (cont.)
RRuullee 33--1188 (cont.)
3. Restate the proportion, inserting the unknown
quantity.
3. Check your work.
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56. 3-56
Using Proportions to Solve for
an Unknown (cont.)
Find the unknown quantity in
6
x
3 =
5
EExxaammppllee
1. Cross-multiply.
3 X x = 5 X 6
2. Solve the equation by dividing both sides by
three.
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30
3 x = 10
3 X x =
3

57. 3-57
Using Proportions to Solve for
an Unknown (cont.)
EExxaammppllee ((ccoonntt.).)
3. Restate the proportion, inserting the unknown
quantity.
6
10
3
=
5
4. Check your work by cross-multiplying.
3 X 10 = 5 X 6
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30 = 30
The unknown quantity is 10.

58. 3-58
Using Proportions to Solve for an
Unknown (cont.)
RRuullee 33--1199
If the units of the numerator of the two
fractions are the same, they can be
dropped or canceled before setting up a
proportion.
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10mg X ?
10
75mg
10mL
=

59. 3-59
Using Proportions to Solve for
an Unknown (cont.)
RRuullee 33--1199 (cont.)
Likewise, if the units from the denominator
of the two fractions are the same, they
can be canceled.
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5 ?
5mL
25mg =
5mL

60. 3-60
Using Proportions to Solve for an
Unknown (cont.)
You have a solution containing
200mg drug in 5mL. How many
milliliters of solution contain
500mg drug?
mg
mg 500
5
x
200 =
mL
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EExxaammppllee
Set up the fractions.
Cross-multiply to solve the equation.

61. 3-61
Using Proportions to Solve for an
Unknown (cont.)
If 100 mL of solution contains 20mg of
drug, how many milligrams of the drug
will be in 500mL of solution?
mg x
mL mL
100 500
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EExxaammppllee
Set up the fraction. 20 =
Cross-multiply to solve the equation.

62. 3-62
Practice
Determine if the following proportions are true:
Answer = Not true
Answer = Not true
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28
48
7 =
16
125
300
50 =
125

63. 3-63
Practice
Cross-multiply to find the unknown quantity.
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Answer = 1
Answer = 2
3 x =
15 5
25 = 75 x
6

64. 3-64
Practice
If 250 mL of solution contains 90 mg of drug, there
would be 450 mg of drug in how many mL of
solution?
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mg
mg 450
x
90 =
mL
250
Answer = 1,250 mL

65. 3-65
In Summary
 In this chapter you learned to:
 convert values to and from a percent;
 convert values to and from a ratio.
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66. 3-66
In Summary (cont.)
 In this chapter you learned to:
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 write proportions;
 use proportions to solve for an unknown
quantity.

67. 3-67
ANSWER: 145% ANSWER: 5.6%
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Apply Your Knowledge
Convert to percent:
1.45 0.056
Convert to a decimal:
15.6 % 0.89%
ANSWER: 0.156 ANSWER: 0.0089

68. 3-68
75 ANSWER: 75:125
4
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Apply Your Knowledge
Convert to a ratio:
125
Convert to a fraction:
78:10
5
ANSWER: 7

69. 3-69
Apply Your Knowledge
Determine if the following are true proportions:
45:90 = 15:30
ANSWER: True proportion
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6/7 = 3/4
ANSWER: Not a true proportion

70. 3-70
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Apply Your Knowledge
Solve for the unknown:
25mg:6mL=x:12mL
ANSWER: 50mg
22/x=12/18
ANSWER: 33

71. 3-71
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End of Chapter 3
If what you're
working for
really matters,
you'll give it all
you've got.
~ Nido Qubein