Transcript Medical Math

Things to ponder…..
Should students interested in pursuing a
career in health care be proficient in
math?
How does accuracy of mathematical
calculations affect the quality of patient
care?
How will health care workers apply
mathematical concepts?
Are mathematical calculations completed
by humans or machines? Are either one
free of error?
What units of measurement are used in the
health care field?
How is data recorded in health care?
Medical professionals use math
every day while providing health
care for people around the world.
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Write prescriptions
Administer medication
Draw up statistical graphs of epidemics
Figure out the success rates of treatments
Math requires the student to know systems
of measurement (metric, household,
apothecary) and how to convert within
those systems of measurement.
It is essential to understand drug weights
and measures to accurately calculate
medication dosages.
Basic mathematical calculations are
used for:
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Conversions
Charting
Graphing
Dosage calculations
Measurements
Roman numerals vs Arabic numerals
The number system we use daily and are
familiar with is Arabic numerals ( 0 – 9 or
any combination of these digits).
In medication, prescriptions, and other
occasional uses, it is necessary to know
Roman numerals.
Roman numeral system uses letters to
represent numeric values.
Roman
Arabic
I
V
X
L
C
D
M
one
five
ten
fifty
one hundred
five hundred
one thousand
1
5
10
50
100
500
1000
Using Roman numerals…
Rule 1:
 When two Roman numerals of the same
or decreasing value are written beside
each other, the values are added together.
 Examples:
 VI = 5 + 1 = 6
 XX = 10 + 10 = 20
 LX = 50 + 10 = 60

Rule 2
 When Roman numerals of increasing
value are written beside each other, the
smaller value is subtracted from the
larger value.
 Examples:
 IV = 5 – 1 = 4
 XC = 100 – 10 = 90
 LX = 50 – 10 = 40

Rule 3
 No more than three roman numerals of
the same value should be used in a row.
Examples:
To write the number 4, do not write IIII,
instead write it as IV (5-1=4)
To write the number 59, do not write LVIIII,
instead write L for 50, then IX ( 10-1=9)
which is written LIX.

Rule 4
 A line written over a Roman numeral
changes its value to 1,000 times its
original value.
Examples:
_
_
X = 10, 000
L = 50, 000

Convert Roman numerals to Arabic
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Must be able to separate the Roman
numerals into manageable units first.
The easiest way to do this is to make a
distinction between the groups that need to
be added together and the groups that
require subtraction.
1st – scan the Roman numerals looking for
any groups where a smaller value is written
before a larger value. These indicate
subtraction.
2nd – total the values from left to right.
Example 1: convert XCIV to an
Arabic number
 1st
– XC is a subtraction group (100-10=
90).
 2nd – IV is also a subtraction group (51=4)
 Now total the values from left to right.
 90 + 4 = 4
Example 2: convert CDLXXVII to
an Arabic number
1st – CD is a subtraction group (500100=400)
2nd – Add 400+50+10+10+5+1+1= 477
Remember: before you begin conversion, it
is necessary to know the values of the
various Roman numerals so that you can
recognize subtraction groups. Failure to
recognize a small value written before a
larger one will result n an incorrect
answer.
Converting Arabic to Roman
numerals
Must be able to separate the Arabic
numerals into manageable units first.
The easiest way to do this is to make a
distinction among the different place
values in our number system (ones, tens,
hundreds, etc.)
Going from left to right, write each place
value using Roman numerals.
Be sure to follow the four rules for writing
Roman numerals correctly.
Example 1: convert 1,768 to a
Roman numeral
Separate 1,768
Arabic
Roman
◦ 1000
M
◦ 700
DCC
◦ 60
LX
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8
VIII
Write out the Roman numeral as one answer
leaving no spaces between the different parts.
Answer: MDCCLXVIII
Example 2: convert 479 to Roman
numeral
Separate 479
Arabic
400
70
9
Answer: CDLXXIX
Roman
CD
LXX
IX
Military time
Military time works on the premise of a 24-hour
day.
The precise method of measuring time doesn't
require the use of a.m. and p.m. designators to
determine the time of day.
Learning how to convert to military time begins
with an understanding of how individuals express
in different ways from the standard hour and
minute method.
1st - Think in terms of a 24-hour period of time.
Military time begins at midnight with the figure of
00 hours indicating the start of a 24-hour day.
Morning and evening designations aren't
necessary when figuring time in 24-hour
increments.
2nd - Recognize that each hour up to noon is
exactly the same as regular time.
The change occurs at the switch to regular time's
p.m. designation.
Military time denotes 1 p.m. as 1300 and each
hour thereafter counts upward to 23.
3rd - Express minutes and seconds in exactly
the same way as regular time.
Military time uses 60 minutes in an hour and
60 seconds to a minute.
The time of 4:35 in regular time could mean
either morning or afternoon without the
proper designation of a.m. or p.m.
Military time shows 4:35 a.m. as 0435 and
4:35 p.m. as 1635.
4th - Write the correct military time notation
properly.
For example, use 0435:45 hours to express
the time 4:35 and 45 seconds in regular time
(4:35:45).
5th - Recognize that 24 hour clocks may
represent midnight as 0000 hour while
others call midnight 2400 hours.
6th - Remember to always drop the colon to
correctly format military time when writing.
7th - The proper language used for describing
military time refers to hours in terms of
hundreds.
For example, 5 a.m. is referred to O-five
hundred hours.
Five p.m. is referred to as 17 hundreds hours
(1700).
Examples:
1:00 pm will be 1300
2:00 pm will be 1400
3:30 pm will be 1530
4:09 pm will be 1609
11:20 pm will be 2320
12:00 am(midnight)will be 0000 or 2400
12:15 am will be 0015 not 2415
12:01 am will be 0001 not 2401
Percent Base
To find a certain part of a whole, to find
what percent of the whole is being
represented, or to find out what the
whole number is to which you are
comparing, you can work a percent-base
problem.
 The percent represents the part you are
comparing and the base is the whole to
which you are comparing

In a % base problem, there are 3
parts:

The percent

The base

The part (or percentage)
16
x
.25
=
4
16 is the base
.25 is the %
4 is the part
(whole)
(changed to a decimal)
(percentage)
This problem indicates that 25% (.25) of 16
is 4. Multiplication is used in the problem
with the multiplication and equal signs is
an important part of being able to solve
it.
It will be necessary to solve a percentbase problem looking for each of the
three guidelines:
Noticing the words “of” and “is” will help in
setting up the problem and solving it.
The word “what” indicates the missing answer.
If the unknown answer is not alone on the left
or right side of the equal sign, you must
multiply to find the solution.
What is 15% of 200?
1. Put the problem into symbols and numbers.
“what” = 15% x 200
2. Change the percent to decimal and solve.
“what” = .15 x 200
3. Decide whether to multiply or divide
(multiply because the unknown part is alone.)
200
x .15
30.00
Answer:
30 is 15% of 200
Forty is 20% of what number?
1. Put the problem into symbols and numbers.
40
=
20%
x
“what”
2. Change the percent to decimal and solve.
40
=
.20
x
“what”
3. Decide whether to multiply or divide.
(divide because the unknown part is not alone)
40 divided by .20 = 200
Answer:
40 is 20% of 200
What percent of 80 is 24?
1. Put the problem into symbols and numbers.
“what” % x 80 = 24
2. Change the percent to decimal and solve
(we are looking for the percent…we can’t change it
now, but we must once we find it)
3. Decide whether to multiply or divide
(divide because the unknown part is not alone.)
24 divided by 80 = .3
4. Change .3 to a percent (.3 = 30%)
Answer:
30% of 80 is 24
Proportion:
Expresses the relationship between two
ratios.
It is written as two ratios with an equal sign
between.
Example:
3:4 = 1:5
The four numbers in the proportion have
special names
3:4 = 1:5
The two outer numbers in this case 3 and 5 are
called the Extremes.
The two inner numbers in this case 4 and 1 are
called Means.
In a true (equal) proportion, the product of the
means should equal the product of the extremes.
3:4 = 1:5
Means
Extremes
4x1=4
3x5=15
4 doesn’t equal 15 which means this is not a true
proportion.
Solving Proportions
If you know that a proportion is true (that
the ratios are equal), you can solve for a
missing part.
This is very useful because it helps you
solve problems based on another
problem as your model.
For example: if you know a patient should
get 1ounce of medicine for every 20
pounds of body weight, you can use a
proportion to determine how much to
give a 180 lb man.
Example: you can compare ounces to
pounds in two rations and set them equal.
oz
1 oz
=
# of oz to give
lb
20lb
180 lb
oz
1 oz
=
# of oz to give
lb
20lb
180 lb
Since this is a true proportion, the product
of the means equals the product of the
extremes. 1:20 = ?:180
Means = Extremes
20 x ?oz =
1 x 180
20 x ?oz =
180
20
20
oz = 9
A 180lb man needs 9oz of medicine.
Proportions do not always contain just
whole numbers as the means and
extremes.
Occasionally they may contain fractions,
decimals, or more complicated
expressions.
These two can be solved by the unknown
amount.
Example 1
Halterol is administered by the following
formula: ½ tablet per blood lost. Josie
recently lost three pints of blood.
How much Halterol should be
administered?
Tablets
Pints
½ =
unknown “x”
1
3
½ : 1 = x:3
Means = Extremes
1x
=
½ (3)
x
=
1½
Josie needs 1 ½ tablets
Example 2
Solve the following:
5 : (x-2) = 10 : 6
Means
=
10 (x – 2) =
Extremes
5x6
10x – 20
30
=
(multiply everything in the parentheses by 10)
10x – 20 + 20 = 30 +20
10x
10
=
Answer: x = 5
50
10
(add 20 to both sides)
(-20 + 20 = 0)
( divide both sides by 10)
Remember:
It is wise to check your answers when you
have solved a proportion
You should be able to replace the answer
you found back into the original
proportion, multiply the means and
extremes, and the result will be a true
proportion.
If it is not, recheck your work.
Measurement
The three main types of measurements:
volume
length
mass
English system and Metric system
English system
English system is the most common
system used in the U.S.
 Learn the abbreviations and equivalent
measures.
 To convert from one measurement to
another, you must multiply or divide by
different numbers for each different
conversion. (Conversion Number)

Conversion numbers:
Three basic group of conversion numbers:
Volume - gallon, half gallon, quart, pint, cup,
ounce, Tbsp, and tsp
Length - mile, yard, foot, and inch
Mass - pounds and ounces
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When converting from a large unit to a
smaller one, multiply by the conversion
number.
When converting from a small unit to a
larger one, divide by the conversion number.
Hint: you will need to memorize the
conversion numbers for volume, length, and
mass.
◦ 1Tbsp = 3tsp
◦ 1ft = 12 inches
◦ 1lb = 16 oz
1oz = 2 Tbsp
1 yd = 3 ft
Metric System
Based on the number 10
 Learn the prefixes
kilo (k) = 1,000
deci (d) 0.1
hecto (h) = 100
centi (c) 0.01
deka (dk) = 10
milli (m) 0.001

A prefix can never be used alone.
It must have a base unit with it to indicate
whether you are measuring length, volume,
or mass.
Three basic units:
◦ Gram (g) – measures mass or weight (solid)
◦ Liter (l) – measures volume or liquid (fluid)
◦ Meter (m) – measures length or distance
*___*___*___One___*___*___*
k(1000)
h (100)
dk (10)
Basic Unit
d (0.1)
c (0.01)
m (0.001)
kl
hl
dkl
Liter(l)
dl
cl
ml
kg
hg
dkg
Gram(g)
dg
cg
mg
km
hm
dkm
Meter(m)
dm
cm
mm
Each unit can be multiplied by 10 to
produce increasingly larger units or
divided by 10 to produce smaller units.
 Length – kilometer, hectometer,
dekameter, meter, decimeter, centimeter,
millimeter
 Volume – kiloliter, hectoliter, dekaliter,
liter, deciliter, centiliter, milliliter
 Mass – kilogram, hectogram, dekagram,
gram, decigram, centigram, milligram

Rule of thumb using metric system
Because all of the measurements are related by the
number ten, you convert measurements by the
moving the decimal either to the left or right.
Example: 6.9 liters (l) = ____ ml
*___
*___
k(1000)
h (100)
kl
hl
*___
*
*___
*___
*____
dk (10)
Basic Unit
d (0.1)
c (0.01)
m (0.001)
dkl
Liter(l)
dl
cl
ml
6.9 liters
6900ml
The decimal was moved 3 units to the right to go
from liters(l) to milliliters(ml)
Converting Rules of thumb…
It is helpful to know the relationship of
metric measurements to their English
counterparts.
 All units of measurement must be in the
same system, that is, volume to volume,
weight to weight, and length to length.
 Label all units of measurement.

Be sure that the relationship between
units is the same on both sides of the
equation.
 When changing English units to metric ,
multiply by the appropriate number.
 When changing Metric to English divide
by the appropriate number.
 Hint:

◦ English to Metric = multiply
◦ Metric to English = divide
Medication dosages (Rx)
The use of proportions is especially
important in computing drug dosages.
The proportion used is the following:
Known unit on hand = dose ordered
Known dosage form
unknown amount to be given
Memorize this proportion and be able
to use it in all dosage situations.
Known unit on hand: amount of grams or milligrams
that the selected drug contains in the known dosage
form.
Known dosage form: typical amount of the medicine
that you are given gram or milligram equivalents for
(125mg/5ml the known dosage form is 5ml)
Dose ordered: amount of grams or milligrams
ordered.
Unknown amount to be given: what you are trying
to determine – what amount of the medication
should be given
At times, the known unit on hand and the
dose ordered may not be available in the
same unit of measure (both grams and
milligrams).
It is necessary to change the dose ordered
to the same unit of measure as the
known unit on hand.
Example 1
The doctor orders 0.5g of Robitussin liquid every 4 hours for cough.
The liquid is available in 125mg/5ml.
How many ml will you give the patient every 4 hours?
1st - convert 0.5g to mg (because the dose ordered must be in the same
unit of measure as the known unit on hand).
0.500g = 500mg (move the decimal 3 to the right)
2nd – complete the proportion
Known unit on hand
Known dosage form
125mg
5ml
=
= dose ordered
unknown amount to be given
500mg
?ml
Cross multiply: 125(?) = 5x500 becomes 125(?ml) = 2500
Divide by 125: 125(?) = 2500
125(?)
125
becomes (?) = 20ml every 4 hours
Example 2
The doctor ordered Sinemet 300mg three times a day. Available is
Sinemet tabs 100mg.
How many tablets will you give?
Known unit on hand
Known dosage form
=
dose ordered
unknown amount to be given
100mg = 300mg
1 tablet
? Tablets
Cross Multiply: 100mg(?tab) = 1 x 300mg becomes 100mg = 300mg
Divide by 100mg: 100mg(?tab) = 300mg
100mg
100mg
? – 3 tablets three times a day
Solve the following:
1. The physician ordered Diamox 0.25g
every morning. It is available in
125mg/5ml.
How many ml should be given?
2. The physician ordered Bucladin-S softabs
50mg every six hours. They are available
in 25mg tablets.
How many tablets should be given?
Answer:
1.
2.
10 ml
2 tablets
Parenteral dosages: medication
injected into either the skin, muscle,
or a vein.
These medications may be premeasured
into single doses or may need to be
measured from a multi-use container.
 Use the proportion method to determine
how much medication to administer.

Example 1
The physician ordered Delalutin 150mg IM. Delalutin is available as
0.45g/ml.
How many ml should be given?
1st – convert 0.45g to mg (because the dose ordered must be in the
same unit of measure as the known unit on hand).
0.45g = ?mg
0.45g = 450mg
(since going from larger to smaller unit, move the decimal
to the right 3 places to become milligrams)
2nd – complete the proportion
150mg = 450mg
1ml
?ml
Cross multiply: 150 (?ml) = 1x450 becomes 150(?ml) = 450
Divide by 150: 150 (?ml) = 450
150
150
Answer: 3ml
Example 2
The physician ordered 0.5g of Robaxin IM. It is available in 50mg/ml.
How many ml should be given?
1st – convert 0.5g to mg
2nd complete the proportion
50mg = 500mg
1ml
?ml
Cross multiply: 50 x ? = 1x500
Divide by 50: 50 (?) = 500
50
50
Answer: 10ml
0.5g = 500mg
50(?) = 500
Solve the following:
1. The physician ordered Streptomycin
75mg IM. On hand is Streptomycin
100mg/5ml.
How much Streptomycin should be given?
2. The physician ordered Dramamine 50mg
IM. It is available in 40mg/5ml.
What is the correct dosage?
Answers
3.75ml
6.25ml
Adult dosages are very different
than dosages for children.
Various methods used to calculate
children’s dosages:
Young’s Rule:
age of child
age of child +12
x average adult dosage = child’s dose
Fried’s Rule:
age in months x adult dose = infant dose
150
Clark’s Rule:
child’s weight (lb) x adult dose = child’s dose
150
Dosage per kilogram of body weight:
This rule uses the child’s weight in
kilograms (kg).
1. Be sure that the weight is given in kg. ( if
it is in lbs the divide by 2.2kg).
2. Multiply the number of kilograms by the
dosage prescribed for each kilogram
Reflections….
Memorize, Memorize, Memorize
 Practice, Practice, Practice
 Proficiency in math computation skills
(addition, subtraction, division,
multiplication, fractions, converting, etc.)
are necessary in health care.
 Sometimes it is necessary to convert
before one can calculate a problem.
