Chapter 3 Dosages and Calculations

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.

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

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

3-4
Introduction
 For dosage calculation you must:
 understand percents, ratios, and
proportions ;
 be able to find a unknown quantity in a
proportion.

3-5
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.”

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
5
5

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.

3-8
Converting Values To and From
a Percent (cont.)
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

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

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

3-11
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.

3-12
Convert 8% to an equivalent fraction.
8% =
EExxaammppllee
2
25
8 = 8
=
100
100
2
25

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
decimal to a percent.

3-14
Converting Values To and from a
Percent (cont.)
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%

3-15
Answer = 75%
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%

3-16
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.

3-17
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.

3-18
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.
2:12 is written 1:6
EExxaammppllee

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
4:5 =
B
5
EExxaammppllee

3-20
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.
A
= A:B B

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

3-22
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.

3-23
a Ratio (cont.)
Convert the ratio 1:10 to a decimal.
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

3-24
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.

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.
1
25
3. Restate the number as a ratio.
1:4
4
100
=
EExxaammppllee

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

3-27
Convert 2:3 to a percent.
1. 2:3 =
2 = 0.67
3
2. 0.67 X 100% = 67%
EExxaammppllee

3-28
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.
 Numerator = value A
 Denominator = value B
 A:B

3-29
Convert 25% to a ratio.
1. 25% =
25
100
2. 25 = = =
1 : 4 25%
1
4
100
EExxaammppllee

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

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

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

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

3-34
50
Write 5:10 = 50:100 as a proportion using
fractions.
100
5
5:10 = 50:100 same as =
10
EExxaammppllee

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

3-36
10
5 =
Write using ratios.
12
6
10 : 12
5 : 6 10
12
6 5
= and =
5:6 = 10:12
EExxaammppllee

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

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

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

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

3-41
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.
EExxaammppllee

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

3-43
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.

3-44
Unknown (cont.)
Find the unknown quantity in 25:5=50:x
250 x = x = 10
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

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

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

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.

3-48
(cont.)
2. If the units in the second part of the ratio
in a proportion are the same, they can
be canceled.

3-49
(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
10000 mg x =
100 X
100
100
EExxaammppllee

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

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

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

3-53
an Unknown (cont.)
2 =
Determine if 2 5 is a true proportion.
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

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

3-55
an Unknown (cont.)
quantity.
3. Check your work.

3-56
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.
30
3 x = 10
3 X x =
3

3-57
an Unknown (cont.)
EExxaammppllee ((ccoonntt.).)
quantity.
6
10
3
=
5
4. Check your work by cross-multiplying.
3 X 10 = 5 X 6
30 = 30
The unknown quantity is 10.

3-58
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.
10mg X ?
10
75mg
10mL
=

3-59
an Unknown (cont.)
Likewise, if the units from the denominator
of the two fractions are the same, they
can be canceled.
5 ?
5mL
25mg =
5mL

3-60
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
EExxaammppllee
Set up the fractions.
Cross-multiply to solve the equation.

3-61
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
EExxaammppllee
Set up the fraction. 20 =
Cross-multiply to solve the equation.

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

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

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?
mg
mg 450
x
90 =
mL
250
Answer = 1,250 mL

3-65
In Summary
 In this chapter you learned to:
 convert values to and from a percent;
 convert values to and from a ratio.

3-66
In Summary (cont.)
 In this chapter you learned to:
 write proportions;
 use proportions to solve for an unknown
quantity.

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

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

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

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

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

Chapter 3 Dosages and Calculations

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