Transcript 02-1205 Medication Math

MEDICATION MATH
Jose A. Martinez,MSN,RN
Nursing Instructor
MED MATH / JAM / 2003
OBJECTIVES
• Ability to calculate basic arithmetic
and convert Arabic numerals to
Roman numerals and reverse this
process
• Demonstrate correct use of
symbols and abbreviations
MED MATH / JAM / 2003
OBJECTIVES
• Ability to convert measurements
of weights and volumes in
household, apothecaries’ and
metric systems
MED MATH / JAM / 2003
OBJECTIVES
• Ability to solve for unknowns
using the systems of
measurements listed in the
syllabus and your text book
MED MATH / JAM / 2003
OBJECTIVES
• Ability to solve for unknowns
using the systems of
measurements listed in the
syllabus and your text book
MED MATH / JAM / 2003
Scenes Around Laredo Community College
Laredo, Texas
August 2000
MED MATH / JAM / 2003
INTRODUCTION
Knowledge of basic math is a
necessary component of dosage
calculation that nurses need to
know to prevent medications errors
and ensure the safe administration
of medications.
MED MATH / JAM / 2003
INTRODUCTION
Be Fully Advised:
If given incorrectly, the drug given to
cure or help the client can kill them!
MED MATH / JAM / 2003
Roman Numerals
This system developed by
Romans uses letters to
describe amounts. (there is
no ‘zero’ (0) in this system!)
Used primarily in the
APOTHECARIES’ system:
“gr x” = grains 10
MED MATH / JAM / 2003
Roman Numerals
I or i = one
II or ii = two
III or iii = three
From this point on - working
with Roman Numerals
becomes a little more
complex and certain rules
must be followed!
MED MATH / JAM / 2003
Roman Numerals
V or v = five
IV or iv = four
VI or vi = six
Certain numbers are
immediately subtracted
from other numbers (5 - 1 =
4 or v - i= iv)
Some are added (e.g,, (5 +
1= 6 or v + i = vi [6] ))
MED MATH / JAM / 2003
Roman Numerals
•The only fraction we will
work with is “1/2”.
•The fraction “1/2” is written
as “ss”
•The number “i ss” would be
read as “1 1/2”
MED MATH / JAM / 2003
Roman Numerals
•The only fraction we will
work with is “1/2”.
•The fraction “1/2” is written
as “ss”
•The number “i ss” would be
read as “1 1/2”
MED MATH / JAM / 2003
Scenes Around Laredo Community College
Laredo, Texas
August 2000
MED MATH / JAM / 2003
Arabic Numerals
•These are the numbers
that we used in our every
day activities - 1, 2, 3, 10,
1/3 … etc.
•The Arabic system
developed the ‘zero’ (0).
MED MATH / JAM / 2003
General Review:
Fractions
NUMERATOR:
DENOMINATOR:
How many parts of the
whole you are taking
How many equal parts
the whole is divided into
Remember, the ‘de-nom’ is always below!
MED MATH / JAM / 2003
General Review:
Fractions
Types:
Proper
1/8, 5/6, 7/8
Improper
3/2, 6/5, 8/7
Mixed
3 1/3, 5 1/8, 9 1/2
MED MATH / JAM / 2003
General Review:
Fractions
To do any
operation with
fractions you
must work with
the COMMON
DENOMINATOR
MED MATH / JAM / 2003
ARITHMATIC:
1/4 + 1/3 =
( multiply denominators
[4x3=12] to get com.de.,
then divide individual de.
[4/12=3. So:1/4=3/12 )
1/4= 3/12
1/3= 4/12
7/12
General Review:
Decimals
Most
medications are
ordered in
metric measures
that use
decimals not
fractions.
MED MATH / JAM / 2003
.
Capoten  6 25 mg
.
Digoxin 0 125 mg
Sometimes the decimal is
ignored! This can be a
fatal mistake!
General Review:
Decimals
Do not
underestimate the
power of the
decimal.
Many medications
need only a small
amount to be
effective.
MED MATH / JAM / 2003
Capoten 6.25 mg
Digoxin 0.125 mg
“Capoten 6 and 25
hundredths mg”
“Digoxin zero point one
hundred and twentyfive thousandths mg”
General Review:
Decimals
A decimal error in
giving a med can
mean that the client
gets 10 or 100 or
even 1000 x the
ordered amount of
drug - this can
become toxic in no
time at all!
MED MATH / JAM / 2003
Capoten  6.25 mg
Digoxin 0.125 mg
“Capoten  6 point
25 mg”
“Digoxin zero point
one-two-five mg”
General Review:
Decimals
It is MOST
IMPORTANT to place
a zero (0) in front of
the decimal point to
indicate that it is a
fraction when there is
no whole number
before it.
MED MATH / JAM / 2003
0.11 x 0.33=
0.11
x0.33
33
33
363
The answer requires a
4 decimal number
General Review:
Decimals
In this example a 4
decimal placed
number is required
because there are
2 places (0.11) to
be added to
another 2 places
(0.33)
MED MATH / JAM / 2003
0.11 x 0.33=
The partial answer is
363 and we now add
a “0” to the left most
space and then add
a decimal point.
0.0363 is the
answer
General Review:
Decimals
Three Steps To Correctly Writing a
Decimal:
•1.- The whole number. (If there is no
whole number, write zero [0] ).
•2.- The decimal point to indicate the
place value of the right-most number
•3.- The decimal portion of the
number
MED MATH / JAM / 2003
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Laredo, Texas
August 2000
MED MATH / JAM / 2003
General Review:
Ratio
A ratio is used to
indicate a
relationship
between two
numbers. These
numbers are
separated by a
colon (:), e.g., 3:4
MED MATH / JAM / 2003
In the example
given on the left 3
is the numerator 4
is the denominator
The expression
could be written as
3/4
General Review:
Proportion
A proportion is an
equation of two
ratios. The terms of
the 1st ratio have a
relationship to the
terms of the 2nd
ratio, e.g,: 3:4 :: 6:8
MED MATH / JAM / 2003
Read as follows:
“3 is to 4 equals
6 is to 8”
The two terms in a
proportion are called
means
extremes - Do not
confuse these terms.
General Review:
Proportion
In the example
3:4 :: 6:8
4 and 6 are the
means
3 and 8 are the
extremes
MED MATH / JAM / 2003
The product of the
means = the product of
the extremes:
4 x 6 = 24
3 x 8 = 24
24 = 24 The answer is
verified; the ratios are
equal, the proportion is
true.
General Review:
Proportion
If the example is
written as a
fraction 3/4 = 6/8
4 and 6 are the
means
3 and 8 are the
extremes
MED MATH / JAM / 2003
The product of the
means = the product of
the extremes:
4 x 6 = 24
3 x 8 = 24
24 = 24 The answer is
verified; the ratios are
equal, the proportion is
true.
Solving for x in Ratio &
Proportion
In this example:12 : 9 :: 8 : x
12 : 9 :: 8 : x
“X”
still marks the
spot!
X =6
MED MATH / JAM / 2003
12 x = 72 (multiply the means
and extremes)
72 = 12x (divide both
12 x sides of the equation
by the number in front of the x
to obtain the value for x
Dosage Calculations using
Ratio & Proportion
R-P may be used to represent
the weight of a drug that is in
tablet or capsule form:
1 tab
1 tab : 0.125mg or
0.125mg
This means that 1 tablet
contains 0.125mg of the drug
MED MATH / JAM / 2003
Dosage Calculations using
Ratio & Proportion
R & P may be used to represent
the weight of a drug in a certain
volume of solution:
1 mL
1 mL : 250 mg or
250 mg
This means that 1 mL contains
250 mg of the drug
MED MATH / JAM / 2003
Dosage Calculations using
Ratio & Proportion
The doctor orders 40 mg of a
certain drug. The drug comes in a
vile: “80 mg per 2 mL”. How many
mL does the nurse give?
The most important step
is to set up the equation
correctly.
MED MATH / JAM / 2003
Dosage Calculations using
Ratio & Proportion
The most important step is to set up
the equation correctly.
80 mg : 2 mL :: 40 mg : x
LeftThis is what Of
Side is written The
WHAT
PHARMACY
SENT
WHAT
PHARMACY
SENT
This is the way the drug manufacturer
packaged this medication.
MED MATH / JAM / 2003
on the
package
you are
holding in
your hand!
Equation
Dosage Calculations using
Ratio & Proportion
The most important step is to set up
the equation correctly.
80 mg : 2 mL :: 40 mg : x
WHAT
DOCTOR
ORDERED
MED MATH / JAM / 2003
Dosage Calculations using
Ratio & Proportion
The most important step is to set up
the equation correctly.
80 mg : 2 mL :: 40 mg : x
WHAT YOU
NEED TO
GIVE
MED MATH / JAM / 2003
Dosage Calculations using
Ratio & Proportion
The doctor orders 40 mg of a
certain drug. The drug comes in a
vile: “80 mg per 2 mL”. How many
mL does the nurse give?
80 mg : 2 mL :: 40 mg : x
multiply means (2 x 40) = 80
multiply extremes (80 x x ) 80 x
MED MATH / JAM / 2003
Dosage Calculations using
Ratio & Proportion
The doctor orders 40 mg of a
certain drug. The drug comes in a
vile: “80 mg per 2 mL”. How many
mL does the nurse give?
80 x = 80
80 / 80 = 1
x = 1 mL
The nurse gives 1 mL of the drug.
MED MATH / JAM / 2003
Scenes Around Laredo Community College
Laredo, Texas
August 2000
MED MATH / JAM / 2003
The Metric System
THE ONLY ONE
WHO HAS ANYTHING TO WORRY
ABOUT
CONCERNING THE
METRIC SYSTEM IS
THE “INCH” WORM !!!
MED MATH / JAM / 2003
The Metric System
The international decimal system
of weights and measures
Three basic units of measure:
• GRAM: basic unit for weight
• LITER: basic unit for volume
• METER: basic unit for length
You can expect to see more items with
Grams and Liters then with Meters
MED MATH / JAM / 2003
The Metric System
Memorize:
gram = g
milligram = mg
kilogram = kg microgram = mcg
liter = L
milliliter = mL
MED MATH / JAM / 2003
The Metric System
Memorize:
Kilo 1000 one thousand x
Centi 0.01 one hundredth
part
Milli 0.001 one thousandth
part of
Micro 0.000001 one millionth
part of
MED MATH / JAM / 2003
The Metric System
Memorize:
1 kilogram [kg] =1,000 grams [g]
1 gram [g]=1,000 milligrams [mg]
1 milligram [mg] =1,000 micrograms [mcg]
MED MATH / JAM / 2003
The Metric System
Memorize:
1 liter = 1,000 milliliters [mL] or
1,000 cubic centimeters [cc]
1 milliliter [mL] = 1 cubic
centimeter [cc]
MED MATH / JAM / 2003
The Metric System
To convert a smaller
unit to a larger one,
divide by moving the
decimal point 3
places the left
(smaller) (larger)
100mL = __ L
100mL = 0.1 L
MED MATH / JAM / 2003
To convert a larger
unit to a smaller
one, multiply by
moving the decimal
3 places to the right
(larger)
(smaller)
0.75g = ___ mg
0.75g = 750 mg
The Apothecaries’ System
Particulars
• 1.- The measures used are
approximations
• 2.- Roman and Arabic numerals are
used in this system
MED MATH / JAM / 2003
The Apothecaries’ System
Particulars
• 3.- Fractions are used to express a
quantity less then one
• 4.- The symbol ss is used for the
fraction 1/2
MED MATH / JAM / 2003
The Apothecaries’ System
Memorize:
1 grain [gr] = 60 or 65 milligrams [mg]
gr 15 = 1 g
[15 grains = 1 gram] 1 fluid dram = 60
minims
1 fluid dram - 4 or 5 mL
1 fluid ounce = 30 mL
1 fluid ounce = 8 fluid drams
MED MATH / JAM / 2003
The Household System
The household system is used for doses
given primarily at home.
This is the least accurate of the
three system because of different
sizes of measuring instruments
used -
MED MATH / JAM / 2003
The Household System
Memorize:
Drop (gtt)
Teaspoon (t, tsp.) [60 gtt = 1 tsp]
Tablespoon (T, tbs) [3 tsp = 1 tbs]
Cup (C)
[16 tbs = 1C]
Pint (pt) [2C = 1 pt]
Quart (qt) [2pt = 1 qt]
MED MATH / JAM / 2003
Scenes Around Laredo Community College
Laredo, Texas
August 2000
MED MATH / JAM / 2003
The Systems
Approximate Equivalents of Household,
Apothecaries’ and Metric
Measurements
Household
Apothecaries’
Metric
60 dr ops ( gt t )
1 t easpoon ( t )
5 mL ( or cc)
1 t easpoon ( t )
1 f luidr am ( f 3) 5 mL
This symbol is NOT the number “3” it is the DRAM sign
MED MATH / JAM / 2003
Approximate Equivalents of Household,
Apothecaries’ and Metric
Measurements
Household
Apothecaries’
Metric
1 t ablespoon
4 f luidr ams
15 mL
2 t ablespoon
8 f luidr am ( f 3) 30 mL
or 1 ounce
Don’t confuse these symbols:  and =
fluid ounce, = dram
MED MATH / JAM / 2003
Approximate Equivalents of Household,
Apothecaries’ and Metric
Measurements
Household
Apothecaries Metric
’
1 measuring
cup
1 pint
8 ounces
240 mL
16 ounces
500 mL
MED MATH / JAM / 2003
Approximate Equivalents of Household,
Apothecaries’ and Metric
Measurements
Household
MED MATH / JAM / 2003
Apothecaries’
Metric
m 15 or 16
1 mL ( cc)
i dr am ( 3i)
4 or 5mL ( cc)
Approximate Equivalents of Household,
Apothecaries’ and Metric
Measurements
Household
Apothecaries’
Metric
1 T, 1 t bs
3 iv
15 or 16mL
( cc)
1 g ( 1000mg)
gr 15
“grains 15”
MED MATH / JAM / 2003
Approximate Equivalents of Household,
Apothecaries’ and Metric
Measurements
Household
MED MATH / JAM / 2003
Apothecaries’
Metric
1 oz
1 pt ( 16 oz)
1 qt ( 32 oz)
2.2 lb
30 mL
500 mL
1000mL, 1L
1k g ( 1000 g)
Approximate Equivalents of Household,
Apothecaries’ and Metric
Measurements
Household
Apothecaries’
Metric
1 quar t
32 ounces
m 15 or 16
1000 mL
1 mL ( cc)
MED MATH / JAM / 2003
Scenes Around Laredo Community College
Laredo, Texas
August 2000
MED MATH / JAM / 2003
CONVERTING - Within
and Between Systems
It is very important that every
nurse is proficient in converting
between all three systems of
measure. Your
client’s life
depends on your
accuracy!
MED MATH / JAM / 2003
CONVERTING - Within
and Between Systems
The nurse has a
professional, ethical
and legal responsibility
to ensure safe practice.
HOW WOULD YOU FEEL IF ONE OF
YOUR FAMILY WAS GIVEN THE
WRONG DOSE OF A DRUG?
MED MATH / JAM / 2003
CONVERTING - Within
and Between Systems
POINTS FOR CONVERTING
•
•
•
•
1- Memorize the equivalents
2- Use these as conversion factors
3- Follow basic math principles
4- Follow the system used
(metric uses decimals,
Apothecaries’ uses fractions)
MED MATH / JAM / 2003
CONVERTING - Within
and Between Systems
RULES FOR R & P
• 1- State known equivalent 1st
• 2- Add incomplete ratio on the
other side of = sign
• 3- Units written in same
sequence (mg : g = mg : g)
• 4- Label terms accurately
MED MATH / JAM / 2003
CONVERTING - Within
and Between Systems
Example:
8mg = _____ g
(How many grams are in 8
milligrams?)
MED MATH / JAM / 2003
CONVERTING - Within
and Between Systems
8mg = _____ g
1000mg : 1 g :: 8 mg : xg
[Known equiv.]
[Unknown equiv.]
1 x 8 = 1000 x (x)
8/1000 = 1000 x /1000
x = 8/1000
x = 0.008 g
MED MATH / JAM / 2003
CONVERTING - Within
and Between Systems
Example:
gr 1/100 = _____ mg
(How many milligrams are in 1/100
grains?)
MED MATH / JAM / 2003
CONVERTING - Within
and Between Systems
Example: The doctor orders,
“gr 1/100” of a certain drug.
The drug comes as 0.3mg per
tablet. The nurse will
administer ___ tablet(s).
This is a typical type of drug conversion
problem that nurses respond to every day.
MED MATH / JAM / 2003
CONVERTING - Within
and Between Systems
gr 1/100 = _____ mg
STEP
#1
(This is a conversion between systems)
[Apothecaries’]
[Metric]
Equivalent: gr 1 = 60mg
gr 1 : 60mg :: gr 1/100 : x mg
60 x 1/100 = x
60/100 - x
x = 0.6 mg - This is how much we need
MED MATH / JAM / 2003
CONVERTING - Within
and Between Systems
x = 0.6 mg - this is how much we need
Now we need to know how many
tablets of 0.3mg strength the
nurse will give:
0.3 : 1(tablet) :: 0.6 : x
0.3x = 0.6 or 0.6 / 0.3 =
2 tablets
MED MATH / JAM / 2003
STEP
#2
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MED MATH / JAM / 2003
Converting Between
Temperature Systems
Two more items before
we leave the area - since
there are 2 scales that
can be used to measure a
client’s temperature we
need to know how this is
done
MED MATH / JAM / 2003
Converting Between
Temperature Systems
There is an easy way to remember
which system to use:
°F
°C
WATER BOILS
212
100
WATER FREEZES 32
0
THE FAHRENHEIT SCALE HAS MORE
NUMBERS - IT COVERS MORE AREA
MED MATH / JAM / 2003
Converting Between
Temperature Systems
SO - IF YOU HAVE A TEMPERATURE IN
FAHRENHEIT AND WANT TO CONVERT
TO CENTIGRADE - YOU
AUTOMATICALLY KNOW YOUR
ANSWER WILL BE A SMALLER
NUMBER
MED MATH / JAM / 2003
Converting Between
Temperature Systems
LET’S WORK WITH 2 EXAMPLES OF
TEMPERATURE CONVERSION
°F
°C
100.4 °F = ? °C
? °F = 37.3 °C
MED MATH / JAM / 2003
Converting Between
Temperature Systems
LET’S LOOK AT THE FORMULA
CELCIUS TO FAHRENHEIT
°F = (°C X 1.8) + 32
°F = 37.3 °C = ? °F
°F = (37.3 X 1.8) + 32 =
°F = 67.14 + 32 =
°F = 99.14
MED MATH / JAM / 2003
Converting Between
Temperature Systems
LET’S LOOK AT THE FORMULA
FAHRENHEIT TO CELCIUS
°C = (°F - 32) X 0.55
°C = 100.4 °F = ? °C
°C = (100.4 - 32) X 0.55 =
°C = 68.4 X 0.55 =
°C = 37.6
MED MATH / JAM / 2003
Standard and
Military Time Systems
Last item:
•For military time do not use a.m. or
p.m.
•For times after 12noon on standard
time simply add 12 to the time.
•1:00pm + 12 = 1300hrs
•5:00pm + 12 = 1700hrs ETC.
MED MATH / JAM / 2003
Standard and
Military Time Systems
Last item:
•For converting from military time
to standard time just subtract:
•1300hrs - 12 = 1:00pm
•1700hrs - 12 = 5:00pm
MED MATH / JAM / 2003
Scenes Around Laredo Community College
Laredo, Texas
August 2000
MED MATH / JAM / 2003
TEST TAKING SKILLS
The nurse has a medication calculation to make: Drug
Order: gr 1/4 po of phenobarbital t.i.d. The Supply is:
phenobarbital 15mg scored tablets. The most appropriate
nursing action is to:
A. Verify the order
B. Administer 1/2 tablet
C. Administer 1 tablet
D. Administer 1 1/2 tablets
MED MATH / JAM / 2003
TEST TAKING SKILLS
The nurse has a medication calculation to make: Drug
Order: gr 1/4 po of phenobarbital t.i.d. The Supply is:
phenobarbital 15mg scored tablets. The most appropriate
nursing action is to:
A. Verify the order
This response means that there is something wrong with the
question: the wrong drug was supplied by pharmacy - or, they
sent the right drug but the wrong dosage form (e.g., liquid form
rather than solid), or unscored tablets when the nurse would
need scored tablets, or the physician made an error, or the
client’s condition has changed and giving the med at this time
would be dangerous. MED MATH IS NOT JUST MATH - you
have to exercise proper judgment before administering a med.
There are no errors with this question.
MED MATH / JAM / 2003
TEST TAKING SKILLS
The nurse has a medication calculation to make: Drug
Order: gr 1/4 po of phenobarbital t.i.d. The Supply is:
phenobarbital 15mg scored tablets. The most appropriate
nursing action is to:
B. Administer 1/2 tablet
You recall that 1 grain = 60mg. So now we set up the ratio:
gr 1 : 60mg :: gr 1/4 : x
1x = (60 x 1/4)
(Set it us then cross multiply.)
1x = (60 / 4)
1x = 15mg
If we need 15mg and the tablet is 15mg, 1/2 of this amount
would not give the correct dosage. Go to the next Choice.
MED MATH / JAM / 2003
TEST TAKING SKILLS
The nurse has a medication calculation to make: Drug
Order: gr 1/4 po of phenobarbital t.i.d. The Supply is:
phenobarbital 15mg scored tablets. The most appropriate
nursing action is to:
C. Administer 1 tablet
You recall that 1 grain = 60mg. So now we set up the ratio:
gr 1 : 60mg :: gr 1/4 : x
1x = (60 x 1/4)
(This is where the action is!)
1x = (60 / 4)
1x = 15mg
If we need 15mg and the tablet is 15mg, 1 tablet will give
us the amount we need. Let’s complete the exercise and
look at the last Choice.
MED MATH / JAM / 2003
TEST TAKING SKILLS
The nurse has a medication calculation to make: Drug
Order: gr 1/4 po of phenobarbital t.i.d. The Supply is:
phenobarbital 15mg scored tablets. The most appropriate
nursing action is to:
D. Administer 1 1/2 tablets
You recall that 1 grain = 60mg. So now we set up the ratio:
gr 1 : 60mg :: gr 1/4 : x
1x = (60 x 1/4)
(This is where the action is!)
1x = (60 / 4)
1x = 15mg
If we need 15mg and the tablet is 15mg, 1 1/2 tablets will give
us too much. Choice “C” is the most appropriate nursing
action.
MED MATH / JAM / 2003
TEST TAKING SKILLS
The nurse has a medication calculation to make: Drug
Order: gr 1/4 po of phenobarbital t.i.d. The Supply is:
phenobarbital 15mg scored tablets. The most appropriate
nursing action is to:
C. Administer 1 tablet
If you got this sample question correct congratulations! If not, take a look at the way
this question was constructed and why you
chose the answer you did.
If you would like additional information on this
topic go to page 111 of your Calculate With
Confidence textbook.
MED MATH / JAM / 2003
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MED MATH / JAM / 2003
CONCLUSION
It is simply impossible to
overestimate the REAL
importance of giving drugs
in a safe and appropriate
manner as ordered by the
doctor. Your knowledge of
medication math will help
you to fulfill this vital
nursing responsibility.
MED MATH / JAM / 2003
PRACTICE YOUR
SKILLS
Do the practice exercise to see how well you
have mastered the skills.
By next class be sure to have completed all
the fill in exercises in the 1st 13 chapters.
Complete chapters 14 - 26 before
end of RNSG 1205
MED MATH / JAM / 2003