Download Pharmacology Chapter 3 Basic Math

Chapter 3
Pharmacology Math
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Objective 1
Describe military time as it compares to civilian
time.
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Objective 1
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Military time uses a 24-hour scale without a.m
or p.m. designations.
It is similar to civilian time from midnight until
noon.
After noon, it increases in 1-hour increments
from 12.
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Objective 1
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To convert military time to civilian time after
noon, subtract 12.
1900 hours becomes 7 p.m.
To convert civilian time to military time after
noon, add 12.
1 p.m. becomes 1300 hours.
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Objective 1
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Military time is pronounced differently than
civilian time.
5 a.m. in civilian time is 0500 military time and
pronounced “Oh-five-hundred.”
4:46 p.m. is 1646 military time and
pronounced “sixteen forty six hours.”
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Objective 2
Understanding Fractions
- A fraction is a number that represents one
or more equal parts of a whole.
a
- It can be written as a/b or
, where b is
b
never equal to zero
- a is the numerator and b is the denominator
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Objective 2
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Addition and subtraction of fractions
- To add (or subtract) a fraction whose
denominators are the same, just add (or
subtract) the numerators and keep the same
denominator
2/5 + 1/5 = 3/5
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Objective 2
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To add (or subtract) fractions which have
different denominators:
- Convert the fractions to equivalent fractions
with the lowest common denominator
1/2 + 1/3 = ?
1/2= 3/6 and 1/3 = 2/6
- Now add: 3/6 + 2/6 = 5/6
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Objective 2
To add (or subtract) mixed numbers
 Convert the mixed numbers to equivalent
improper fractions
 Find the lowest common denominator
 Add (or subtract) as usual
 Note: ALWAYS REDUCE TO LOWEST
TERMS
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Objective 2
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4 2/3 + 1 1/6 = ?
14/3 + 7/6 = ?
28/6 + 7/6 = 35/6 = 5 5/6
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Objective 2
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Multiplication and division of fractions
- To multiply two fractions, multiply the
numerators together and then multiply the
denominators together.
- The result is the new fraction
- Reduce to lowest terms
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Objective 2
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2/3 x 1/4 = ?
2x1=2 =1
3 x 4 12
6
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Objective 3
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Understanding Decimals
- Decimal numbers are written by placing
digits into place value columns that are
separated by a decimal point
-Place value columns are read in sequence
from left to right as multiples of decreasing
powers of 10
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Objective 3
Hundreds tens ones
decimal
point
652.
To the left of the decimal point represents
numbers greater than 1
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Objective 3
decimal tenths hundredths thousandths
point
.345
To the right of the decimal point represents
numbers less than 1
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Objective 3
Addition and Subtraction of decimals
- Line up the decimal points and carry out the
appropriate calculations
24.531
5.040*
+ 2.798
- 1.213
27.329
3.827
*Note: Adding the zero does not change the
value of the number 5.04, yet helps with
subtraction
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Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc.
Objective 3
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Multiplication and division of decimals
- To multiply, carry out the operation, then add the
number of decimal places from the right of the
original two numbers. This is the total number of
decimal places in the answer
- 0.07 x 2.1 = 0.147
- Two places + one place = three places in the answer
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Objective 3
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To divide, carry out the operation align the decimal
point of the answer directly over the dividend (see
text).
If the divisor is a decimal, convert it to a whole
number first. Remember to move the decimal point of
the divisor and that of the dividend the same number
of places to the right so as not to change the value of
your problem (see text).
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Objective 4
The order of operations:
 Parentheses
 Exponents
 Multiplication
 Division
 Addition
 Subtraction
 “Please Excuse My Dear Aunt Sally”
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Objective 5
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Understanding percentages
- Percents are special fractions which mean
“per every hundred”
- The denominator is always understood to
be 100
- It can be shown by the symbol %
- To write a percentage as a fraction, drop the
% and place the number value as the
numerator, such as 25% = 25/100 which =
1/4
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Objective 6
Understanding how to use these operations in
order to convert between fractions, decimals,
and percents
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Objective 6
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To convert fractions to decimals, divide the
numerator by the denominator, as 1/4= 1.00
divided by 4 = 0.25 so 1/4 =0.25
To convert decimals to fractions, the decimal
number expressed becomes the numerator
and the decimal place becomes the
denominator, as 0.95 = 95/100
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Objective 6

To find the percent of a number, change the
percent to a decimal or fraction, replace the
“of” with a times (x) and multiply, as
10% of 100 = 0.10 x 100 = 10
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Objective 7
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Understanding ratios and proportions
- Ratio is a comparison of two numbers
a & b expressed as a:b, a/b or a
b
- Proportion is a statement of equality between ratios
as a:b = c:d, a/b = c/d or a c
b =d
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Objective 7
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Proportions can be used to solve for an
unknown term when the other three terms are
known. Let x = the unknown and remember
that the product of the means equals the
product of the extremes
2:3 = X:9
3×X = 2×9
3X = 18
X =6
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Objective 8
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Temperature conversions
- Celsius (centigrade scale)
- Fahrenheit scale
C = 5/9 (F-32)
F = 9/5 C + 32
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Objective 9
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Measurement systems
- The metric system
*International system of measurement
*Allows ways to calculate small drug
dosages
*In multiples of ten
*Length = the meter
*Volume = the liter
*Weight = the gram
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Objective 9
The metric system prefixes
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micro
.000001
milli
.001
centi
.01
deci
.1
unit
1
deka
10
hecto 100
kilo 1000
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Objective 9
Measurement systems
 Apothecary system
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Used for writing medication orders in ancient
Greece and Rome, Europe of the Middle Ages
Based upon everyday items as a grain
Seldom used today
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Objective 9
Measurement systems
 Household system
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Used in over-the-counter medications and recipes
 Less accurate than the metric so not used in the
surgical setting
 More familiar to the public, so can be used to
compare amounts to those in the metric
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Objective 10
Conversions in the metric system
 Length
1 m = ? cm
Note the prefixes: One centimeter is two
decimal places to the right of the unit (meter),
so move two places to the right for the
answer 1 m = 100 cm
1 cm = ? mm (1 place to the right)
1 cm = 10 mm
Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc.
Objective 10
Conversions in the metric system
 Volume
1L = ? mL
Note the prefixes: milli (Liter) is three decimal
places to the right of the unit, so move three
spaces to the right for the answer 1L = 1000
mL
5000 mL = ? L (three spaces to the left)
5000 mL = 5L
Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc.
Objective 10
Conversions in the metric system
 Weight
1 kg = ? g
note the prefixes, kilo is three spaces to the left
of the unit, so move three spaces to the left
1kg = 1000 g
1 g = ? mg (three spaces to the right)
1 g = 1000 mg
Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc.