Things to ponder….. Should students interested in pursuing a career in health care be proficient...
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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?
Things to ponder….. Should students interested in pursuing a career in health care be proficient in math? How does accuracy of mathematical calculations
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?
Slide 2
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?
Slide 3
Medical professionals use math every day while providing health
care for people around the world. Write prescriptions Administer
medication Draw up statistical graphs of epidemics Figure out the
success rates of treatments
Slide 4
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.
Slide 5
Basic mathematical calculations are used for: Conversions
Charting Graphing Dosage calculations Measurements
Slide 6
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.
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
Slide 9
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
Slide 10
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.
Slide 11
Rule 4 A line written over a Roman numeral changes its value to
1,000 times its original value. Examples:_ X = 10, 000L = 50,
000
Slide 12
Convert Roman numerals to Arabic 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. 1 st scan
the Roman numerals looking for any groups where a smaller value is
written before a larger value. These indicate subtraction. 2 nd
total the values from left to right.
Slide 13
Example 1: convert XCIV to an Arabic number 1 st XC is a
subtraction group (100-10= 90). 2 nd IV is also a subtraction group
(5- 1=4) Now total the values from left to right. 90 + 4 = 4
Slide 14
Example 2: convert CDLXXVII to an Arabic number 1 st CD is a
subtraction group (500- 100=400) 2 nd 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.
Slide 15
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.
Slide 16
Example 1: convert 1,768 to a Roman numeral Separate 1,768
ArabicRoman 1000M 700DCC 60LX 8VIII Write out the Roman numeral as
one answer leaving no spaces between the different parts. Answer:
MDCCLXVIII
Slide 17
Example 2: convert 479 to Roman numeral Separate 479
ArabicRoman 400CD 70LXX 9IX Answer: CDLXXIX
Slide 18
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.
Slide 19
1 st - 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. 2 nd -
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.
Slide 20
3 rd - 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. 4 th - 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).
Slide 21
5 th - Recognize that 24 hour clocks may represent midnight as
0000 hour while others call midnight 2400 hours. 6 th - Remember to
always drop the colon to correctly format military time when
writing. 7 th - 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).
Slide 22
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
Slide 23
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
Slide 24
In a % base problem, there are 3 parts: The percent The base
The part (or percentage)
Slide 25
16x.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.
Slide 26
It will be necessary to solve a percent- base 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.
Slide 27
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
Slide 28
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
Slide 29
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 percentwe cant 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
Slide 30
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
Slide 31
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 MeansExtremes
4x1=43x5=15 4 doesnt equal 15 which means this is not a true
proportion.
Slide 32
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.
Slide 33
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 lb20lb180 lb
Slide 34
oz 1 oz= # of oz to give lb20lb180 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
= 18020 oz = 9 A 180lb man needs 9oz of medicine.
Slide 35
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.
Slide 36
Example 1 Halterol is administered by the following formula:
tablet per blood lost. Josie recently lost three pints of blood.
How much Halterol should be administered?
Slide 37
Tablets =unknown x Pints13 : 1 = x:3 Means = Extremes 1x = (3)
x = 1 Josie needs 1 tablets
Slide 38
Example 2 Solve the following: 5 : (x-2) = 10 : 6
Slide 39
Means = Extremes 10 (x 2)= 5 x 6 (multiply everything in the
parentheses by 10) 10x 20 = 30 (add 20 to both sides) 10x 20 + 20 =
30 +20 (-20 + 20 = 0) 10x= 50 ( divide both sides by 10)10 Answer:
x = 5
Slide 40
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.
Slide 41
Measurement The three main types of measurements: volume length
mass English system and Metric system
Slide 42
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)
Slide 43
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
Slide 44
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
= 3tsp1oz = 2 Tbsp 1ft = 12 inches1 yd = 3 ft 1lb = 16 oz
Slide 45
Metric System Based on the number 10 Learn the prefixes kilo
(k) = 1,000deci (d) 0.1 hecto (h) = 100centi (c) 0.01 deka (dk) =
10milli(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.
Slide 46
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
Slide 47
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
Slide 48
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)dk (10)Basic Unit d (0.1) c (0.01) m (0.001) kl hl
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)
Slide 49
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.
Slide 50
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
Slide 51
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
Slide 52
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
Slide 53
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.
Slide 54
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? 1 st - 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) 2 nd complete the proportion Known unit on hand = dose
ordered Known dosage formunknown amount to be given 125mg = 500mg
5ml ?ml Cross multiply: 125(?) = 5x500 becomes 125(?ml) = 2500
Divide by 125: 125(?) = 2500 becomes (?) = 20ml every 4 hours
125(?) 125
Slide 55
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 = dose ordered Known dosage form 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
Slide 56
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?
Slide 57
Answer: 1. 10 ml 2. 2 tablets
Slide 58
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.
Slide 59
Example 1 The physician ordered Delalutin 150mg IM. Delalutin
is available as 0.45g/ml. How many ml should be given? 1 st 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) 2 nd 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
Slide 60
Example 2 The physician ordered 0.5g of Robaxin IM. It is
available in 50mg/ml. How many ml should be given? 1 st convert
0.5g to mg 0.5g = 500mg 2 nd complete the proportion 50mg = 500mg
1ml ?ml Cross multiply: 50 x ? = 1x500 50(?) = 500 Divide by 50: 50
(?) = 500 5050 Answer: 10ml
Slide 61
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?
Slide 62
Answers 3.75ml 6.25ml
Slide 63
Adult dosages are very different than dosages for children.
Various methods used to calculate childrens dosages: Youngs Rule:
age of child x average adult dosage = childs dose age of child +12
Frieds Rule: age in months x adult dose = infant dose 150 Clarks
Rule: childs weight (lb) x adult dose = childs dose 150
Slide 64
Dosage per kilogram of body weight: This rule uses the childs
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
Slide 65
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.