Transcript Chapter_18x

Chapter 18
Medical Math
© 2009 Delmar Cengage Learning
Introduction
• Math skills are a requirement for working
in a health care occupation
• Calculations are needed for
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Correct medical dosages
Recording height and weight
Intake and output measurement of fluids
Administrative tasks such as bookkeeping and billing
Tests performed in the lab
Mixing of cleaning fluids
• Health care workers must make every effort
(continues)
to achieve 100% accuracy
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18:1 Basic Calculations
• It is necessary to be able to add, subtract,
and divide whole numbers, decimals,
fractions, and percentages
• Understanding of equivalents when using
decimals, fractions, and percentages
• When taking professional exams for
licensure or certification, calculators are
sometimes not allowed
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Whole Numbers
• Do not contain decimals or fractions
• Addition—adding numbers together
to find the total amount
• Several uses in health care
– Inventory records
– Statistical information on patients
• Example: You are to record and total the amount of
fluid intake
– A patient drank 240 ml. milk, 120 ml coffee, 45 ml water, and 60
ml juice…what is the total?
(continues)
– 240+120+45+60=465 ml of fluid
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Whole Numbers
(continued)
• Subtraction—taking a number away
from a number to find the difference
• Several uses
– Weight loss
– Pulse deficit calculation
• Example: A patient with a heart condition is
on a weight reduction plan. Last month he
weighed 214 pounds and now weighs 195
pounds, how much weight was lost? (continues)
• 214-195= 19 pounds.
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Whole Numbers
(continued)
• Multiplication—same as addition or multiplying
to find the quantity
• Several uses include
– Payroll records (salary amount paid for number
of hours worked)
– Microscope power magnification
• Example: You need a total of 24 agar slant tubes,
each tube you need 30ml of broth and 15 ml of
agar, how much of each do you prepare?
• 30ml x 24 = 720
(continues)
• 15 ml x 24=360
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Whole Numbers
(continued)
• Division—finding how many times a number
is contained in another number
– Finding cost of one item
– Determining amount of diet nutrients
• Example: A student doing research learns
that statistics show 526,704 people die of
cancer each year. On average how many
people die of cancer each month?
• 526,704/12=43892
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Decimals
• Decimals—are based on the number 10
• Represent the number of tenths, hundredths,
thousandths, and so on
• Are added, subtracted, multiplied, and divided the
same as whole numbers
• Always check the placement of the decimal point to
avoid mistakes
• Examples (See Table 18-1 in text) A dietician has
you add up the grams of fat you have eaten:
• 44.51 g+18.3 g+13.83 g= 76.64 g fat your
recommended amount is 60g, you went over 16.64
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Fractions
• Fraction—a quantity less than a whole
number expressed as a decimal
• Has a numerator (top number) and a
denominator (bottom number)
• Some fractions need to be reduced to
their lowest term. 4/8 =1/2
• See Table 18-2 in text
• Examples: do example on page 567
(continues)
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Fractions
(continued)
• Improper fractions—numerators are larger than
denominators
• Converting fractions is used for addition
and subtraction: have to have the same
denominator!
• Multiplying fractions
• Dividing fractions—needs to be inverted
(reciprocal) and then multiplied
• Examples : Go over the two examples on page 568
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Percentages
• Percentages—whole or proportion of
a whole (100%)
• Part/whole x 100= %
• Advantage is to convert the percentage
to a decimal before adding, subtracting,
multiplying, and dividing
• Examples: Do examples 1&2 on page 569!!
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Ratios
• Shows relationship between like values
or numbers
• Health care workers use ratios for strengths
of solutions
• 50 percent strength solution is 1:2 ratio
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Converting Decimals, Fractions,
Percentages, and Ratios
• Decimals, fractions, and percentages
represent parts of a whole
• There are specific methods of conversion
from one to another
• See Table 18-3 in text: go over this table
and look at the examples on how to do
each calculation.
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Rounding Numbers
• This requires changing them to the nearest
ten, hundred, thousand, and so on
• Depends on degree of accuracy
• Refer to Table 18-4 in text
• Examples : go over examples on page 571.
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Solving Problems with Proportions
• Proportion—equality between two ratios
(“two is to six as three is to nine”)
• For converting from one unit to another
when three in the proportion are identified
• Examples: Go over examples pg. 572
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18:2 Estimating
• Estimating—a reasonable approximate
calculation of the answer
• Errors can occur with numbers in wrong
order or decimal points misplaced
• Practice and thought is needed when
learning to estimate answers and detecting
incorrect answers
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18:3 Roman Numerals
• Numbers used today are known as Arabic
numerals (1, 2, 3, and so on)
• In the health care field Roman numerals are
used for specific reasons
• Study Table 18-5 in text
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18:4 Angles
• Used in health care for
– Injection of medications
– Description of joint movements
• Indication of bed positions
• Angles are made when two plane surfaces
meet along a line
• The distance between the plane and line
of the angle is measured in degrees
• See Figure 18-6 in text
(continues)
• Do Examples on page 574
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18:5 Systems of Measurement
• Various systems of measurement used in
health care
• Terminology in each system
– Distance (length)
– Capacity (volume)
– Mass (weight)
• Each system has its own method of naming
(nomenclature)
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Household System
• Used in the United States
• Discuss Table 18-6 in text
• With basic equivalents known then
unknown measurements can be found
by using proportions
12in/1ft =144in/x feet 144/12 = 12 feet
• Look at figure 18-9
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Metric System
• More accurate than the household system
• Metric units
– Distance/length: meter (m)
– Capacity/volume: liter (l or L)
– Mass/weight: gram (g or gm)
• See Table 18-7 in text: know prefixes!!
• Metric system based on multiples of tens
• Go over examples 1-3 and 1-2 pg. 577
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Apothecary System
• Oldest and used less than the metric or
household systems
• Still used by some doctors
• Necessary for health care workers to be
able to convert within the system
• See Table 18-8 in text
• Use of lowercase and uppercase Roman
numerals sometimes used along with
this system
(continues)
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Converting Systems of Measurement
• Health care workers need to be aware of
equal values between units
• Not an exact science when converting
• The answer is considered to be
approximately the same
• Discuss Table 18-9 in text
• Go over Examples page 578-579 1-8
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18:6 Temperature Conversion
• Use of the Fahrenheit (F) thermometer scale
in the United States
• Centigrade (Celsius) or C is often used in
health care
• Conversion charts and formulas (using
fractions or decimals) are available
• See Tables 18-10 and 18-11 in text
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18:7 Military Time
• Traditional system of correct time uses
A.M. and P.M. (12 hours)
• Errors can occur if time is misread
• Accuracy of time is critical in health care
• Military time is based on a 24-hour day
• Avoids any confusion
• See Table 18-12 in text
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