BEPAA-Integrated Health Sciences (IHS) Curriculum, Fundamentals of Mathematics | Student Version

7/21/2019 BEPAA-Integrated Health Sciences (IHS) Curriculum, Fundamentals of Mathematics | Student Version

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BEPAABoard for the Education of People of African Ancestry

286 Convent Avenue New York, NY 10031Integrated Health Sciences ProgramFor H.S. students interested in pursuing careers in the health professions

MODULE II

Fundamentals of MathematicsWith clinical medicine, nursing and pharmacy application

Designed and Facilitated by

Marc Imhotep Cray, M.D.

[email protected]
mailto:[email protected]:[email protected]


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2

There is an old adage that questions, Is it better to givea poor man a fish, or teach him how to fish?Of course, simply giving him the fish will satisfy his immediatehunger; but he will soon again be hungry. If you teach him how to

fish, on the other hand, he will never be hungry again.

Similarly, it is better to understand how to preform mathematicalfunctions in a general sense, and thereby feed yourself, than it is

to be dependent on someone else should an unfamiliar problem/equation come along.If you learn the basics of solving math problems and

equations, they will all become familiar.


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BEPAA Integrated Health Sciences Program

Fundamentals of Mathematics

3

Math is used extensively to solve problems and equations in the varioushealth professions

A thorough understanding of mathematics will be required as you pursueyour chosen health field

This mathematics review will help prepare you for the upcoming ChemistryModule lessons where math will be applied to understand Chemistry

concepts and principles and solving problems

Finally, this mathematic review module will contribute to your success oncurrent and upcoming high stakes exams, such as ACT, SAT, AP and Statestandardized test

Rational

MODULE II


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Unit Approach and Content

4

These Units/Lessons will review basic math concepts andapply math to the science concepts you have alreadylearned, including: learning dimensional analysis (conversion factor-method) drugs and dosage calculations and solving for physiologic variables like cardiac output,

stroke volume, and mean arterial blood pressure etc.

Companion Workbook/Clinical Calculations Ch. 1 and 2Source: Clinical Calculations Made Easy: Solving Problems Using DimensionalAnalysis, Fifth Edition; LLW 2012- Pg. 2-46
https://drive.google.com/file/d/0B-tlCbPSHvfZUUhjbDA0b3pfODA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZUUhjbDA0b3pfODA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZUUhjbDA0b3pfODA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZUUhjbDA0b3pfODA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZUUhjbDA0b3pfODA/edit?usp=sharing


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Mathematics Units/Lessons

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I. Basic Mathematical Definitions and FractionsII. Decimals, Percents, and Ratios

III. Exponents, Scientific Notation, and the Metric SystemIV.An Introduction to AlgebraV. An Introduction to EquationsVI.More Equation Forms

VII.Statistics and Graphs

Special Reading (cloud folded):Mathematicians of the African Diaspora-49 Special Articles and Web Pages
https://drive.google.com/file/d/0B-tlCbPSHvfZcDBLRlVPS21vYTA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZcDBLRlVPS21vYTA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZcDBLRlVPS21vYTA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZcDBLRlVPS21vYTA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZcDBLRlVPS21vYTA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZcDBLRlVPS21vYTA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZcDBLRlVPS21vYTA/edit?usp=sharing


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Unit I

Basic Mathematical Definitions and Fractions

6

Objectives

Upon completion of this unit, you should be able to

Relate mathematics to everyday activities in the healthsciences and state the importance of a thoroughunderstanding of mathematics to a successful career in thehealth professions

Define basic numerical terms and types of numbersDefine and perform various operations with fractionalnumbers


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Key Terms

7

common denominator

common fraction

denominator

gram (g)improper fraction

least, or lowest, common

denominator (LCD)

liter (L)

meter (m)

metric system

mixed numbers

numerator

ophthalmometer (off-thal-MOM-et-er)proper fractions

reciprocal

respirometer (res-per-OM-et-er)

thermometer



Mathematics in the health field

8

The ability to correctly calculate the dosage of a

drug for a patient may mean the difference betweenlife and death

Relate to mathematics: The vital signs of blood pressure, pulse, temperature, and respirationAll relate in some way to mathematics



Mathematics in the health field (2)

9

Many measurements taken in

the health professions require

mathematical calculations.For example, by measuring theamount of air a patient is breathingover a period of time, you candetermine whether the patient needsto be placed on a breathing machine

(called a ventilator)


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Mathematics in the health field(3)

10

Many medical instruments are used tomeasure patient parameters and, thus,require the user to understandmathematicsFor example,

thermometer(thermos meaningtemperature, meter meaning to

measure) is used to measure

temperature; ophthalmometer(ophthalmus meaning

eyes) is used to measure eyes; and

spirometeris used to measure

breathing


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BEPAA Integrated Health Sciences Program 11

The Nurse and MathematicsEvery nurse must know and practice the six rights ofmedication administration including the

1. Right drug2. Right dose3. Right route4. Right time5. Right patient

6. Right documentation


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The Nurse and Mathematics (2)

Although the right drug, route, time, patient, and documentation maybe readily identified, the right dose requires arithmetic skills thatmay be difficult for you

This lesson reviews the basic arithmetic skills (multiplication anddivision) necessary for calculating medication dosage problemsusing the problem-solving method of dimensional analysis

Calculating the right dose of medication to be administered to apatient is one of the first steps toward preventing medication errors


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Basic ArithmeticReview

13


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ObjectivesAfter completing this lesson, you will successfully be able to:

1. Express Arabic numbers as Roman numerals.

2. Express Roman numerals as Arabic numbers.3. Identify the numerator and denominator in a fraction.4. Multiply and divide fractions.5. Multiply and divide decimals.6.

Convert fractions to decimals.


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Most medication dosages are ordered by the physician in metricand household systems for weights and measures usingtheArabic number system with symbols called digits (i.e., 1, 2, 3, 4,5)

Occasionally, orders are received in the apothecaries system ofweights and measures using the Roman numeral system withnumbers represented by symbols (i.e., I, V, X)

The Roman numeral system uses seven basic symbols, andvarious combinations of these symbols represent all numbers in theArabic number system

Arabic Numbers and Roman Numerals


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Arabic Numbers and Roman Numerals (2)

Correctly identifying Roman numerals will assist in preventingmedication errors

Some medication orders may include a Roman numeral.Example: Administer X gr of aspirin, which is correctly

interpreted as administer 10 gr of aspirin

However, according to the Institute for Safe Medication Practices(ISMP), abbreviations increase the risk of medication errors

While some health care providers may still use roman numerals andthe apothecaries system, the ISMP recommends using the metricsystem
http://ismp.org/http://ismp.org/http://ismp.org/


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Arabic Numbers and Roman Numerals (3)Table includes the seven basic Roman

numerals and the corresponding

Arabic numbers

The combination of Roman numeralsymbols is based on three specific

principles:1. Symbols are used to construct a

number, but no symbol may be usedmore than three times

2. The exceptionis the symbol for five(V),which is used only once becausethere is a symbol for 10 (X) and acombination of symbols for 15 (XV)

Also see Cloud Folder Notes:More RN Rules The Romannumerals controversy
https://drive.google.com/file/d/0B-tlCbPSHvfZOVZYcnEzRUxPaUE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZOVZYcnEzRUxPaUE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZOVZYcnEzRUxPaUE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZOVZYcnEzRUxPaUE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZOVZYcnEzRUxPaUE/edit?usp=sharing


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Roman Numerals Subtractive Principle

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Any numeral is counted positively unless there's a larger numeralanywhere to its right, in which case it is counted negatively

However, proper Roman numbers are subject to the followingrestrictions about the applicability of the subtractive principle

The use of the subtractive principle has always been optional. Its

systematic use is fairly modern

For example, it's acceptable to use IIII instead of IV, as is usuallydone on clockfaces (to "balance" their left and right halves, so

we're told).Source: Final Answers 2000-2014, Grard P. Michon, Ph.D.http://www.numericana.com/answer/roman.htm#convert
http://www.numericana.com/answer/roman.htmhttp://www.numericana.com/answer/roman.htmhttp://www.numericana.com/answer/roman.htm


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Roman Numerals Subtractive Principle

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The subtractive principle (asubtrahend preceding a minuend) may apply:

Only to a numeral (the subtrahend) that is a power of ten (I, X or C).For example, "VL" is not a valid representation of 45 (XLV is correct)

Only when the subtrahend precedes a minuend no more than ten times larger

For example, "IL" is not a valid representation of 49 (XLIX is correct)

Only if any numeral preceding the subtrahend is at least ten times largerFor example, "VIX" is not a valid representation of 14 (XIV is correct), and

"IIX" is not correct for 8 (VIII is correct).

Only if any numeral following the minuend is smaller than the subtrahendFor example, "XCL" is not a valid representation of 140 (CXL is correct)

Modified from Final Answers 2000-2014, Grard P. Michon, Ph.D.http://www.numericana.com/answer/roman.htm#convert
http://www.numericana.com/answer/roman.htmhttp://www.numericana.com/answer/roman.htmhttp://www.numericana.com/answer/roman.htm


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Arabic Numbers and Roman Numerals (4)


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PracticeExercise 1.1 ArabicNumbers and Roman

Numerals

Companion Workbook/Clinical Calculations Ch. 1 and 2Source: Clinical Calculations Made Easy: Solving Problems UsingDimensional Analysis, Fifth Edition; LLW 2012- Pg. 2-46
https://drive.google.com/file/d/0B-tlCbPSHvfZUUhjbDA0b3pfODA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZUUhjbDA0b3pfODA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZUUhjbDA0b3pfODA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZUUhjbDA0b3pfODA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZUUhjbDA0b3pfODA/edit?usp=sharing


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Fractions

A common fraction is a comparison of two numbers.Fractionsusually are written , where ais called thenumeratorand bthe denominator.The denominator, or bottom number, tells how many total

partsit takes to make the wholeThe numerator, or top number, is the actual numberofparts of a whole being considered

QUOTES & NOTESFractionshave been used for more than 3,600 years.

They appear in an Egyptian handbook of mathematics

called the Rhind papyrus, written around the year 1650 B.C.
http://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrushttp://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrushttp://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus


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Fractions

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A fraction is a comparison of parts

(numerator) to a whole (denominator)

Source: Delmar/Cengage Learning

S f F i i H l h


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Summary of Fractions in HealthcareMedication dosages with fractions are occasionally ordered by the physician or used

by the pharmaceutical manufacturer on the drug label.

A fraction is a number that represents part of a whole number andcontains three parts:

1. Numeratorthe number on the top portion of the fractionthat represents the number of parts of the whole fraction

2. Dividing linethe line separating the top portion of thefraction from the bottom portion of the fraction

3. Denominatorthe number on the bottom portion of thefraction that represents the number of parts into which thewhole is divided


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Multiplying Fractions

The three steps for multiplying fractions are:1. Multiply the numerators2. Multiply the denominators

3. Reduce the product to the lowest possible fraction


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Multiplying Fractions(2) Examples


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PracticeExercise 1.2 Multiplying Fractions


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Dividing Fractions

The four steps for dividing fractions are:1. Invert (turn upside down) the divisor portion of theproblem (the second fraction in the problem)2. Multiply the two numerators.

3. Multiply the two denominators4. Reduce answer to lowest term (fraction or whole number)


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DividingFractions (2)

P ti


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PracticeExercise 1.3Dividing Fractions


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Simplifying Fractions to Lowest Terms Being able to simplify a fraction to the lowest equivalent fraction

(i.e., to the lowest terms) is extremely important

A most fundamental rule of fractions states that the numerator(the top number) and the denominator (the bottom number) canbe divided or multiplied by the same nonzero number without

changing the value of the fraction

Source: Modified from An Integrated Approach to Health Sciences 2e, Delmar Cengage Learning 2012: pg. 198


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Stop and Review

a. If 13 pills remain in a bottle originally containing 40 pills, what

fraction would apply?

b. If you gave a patient 20 mL of a 100-ml bolus (a concentratedamount of a drug) of Lidocaine, what fraction of the drug have yougiven to the patient?What fraction of the drug is left?

c. A bottle contains 300 mL of liquid. If 200 mL were given to apatient, what fraction does this represent? What fraction remains?

d. A bottle contains 800 tablets. The pharmacist asks that 350 tabletsbe sent to the nurses station. What fraction of the bottle was sent?

R l Lif

I d A li ti


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Source: Modified from An Integrated Approach to Health Sciences 2e, Delmar Cengage Learning 2012: pg. 207

Real Life Issues and ApplicationsHard Decisions with Fractions

Suppose for the sake of argument that you were chosen from the total population of theUnited States to dole out $100 billion for health care. This $100 billion would be the totalhealth care budget for our nation for 1 year. What fraction of this amount would you spend on new equipment for research or on new

equipment for diagnostics and treatment of disease? What fraction would you spend to find a cure for AIDS or a cure for cancer? What about prenatal care or the care of premature infants? How would you justify giving to one group and not to another? Would giving an equal amount to each group be a good idea, or would the resulting

lower amount of money given to each group prevent any one group from accomplishinganything?

Using what you have learned about fractions, devise a simple budget showing the actual amountof money to be given to each area of health care that you think is important. Then, explain thereasons for your decisions. If you have difficulty deciding to whom to give the money or even

how to divide up the money, you are not alone. State and federal governmental agencies have to

make these tough decisions on a regular basis.


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DecimalsMedication orders are often written using decimals, and

pharmaceutical manufacturers may use decimals when

labeling medications.

Therefore, you must understand the learning principles involving

decimals and be able to multiply and divide decimals.

N.B. A decimal point is preceded by a zero if notpreceded by a number to decrease the chance of an error

if the decimal point is missed


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Decimals(2)


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Rounding Decimals

Decimals may be rounded off If the number to the right of the decimal is greater than or

equal to 5, round up to the next number

If the number to the right of the decimal is less than 5, deletethe remaining numbers


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DECIMALS & PREVENTING MEDICATION ERRORS

Understanding the importance of a decimal point will assist in preventingmedication errors.

An improper placement of a decimal point can result in a serious

medication error

According to the Institute for Safe Medication Practices (ISMP):

Trailing zeros should not be used with whole numbersExample: Administer 1 mg of Xanax

WHY? If a decimal point and a zero are placed after the number (1.0 mg),the order could be misread as Administer 10 mg of Xanax

Leading zeros shouldalways

precede a decimal point when thedosage is not a whole numberExample: Administer 0.125 mg of Lanoxin

WHY? If a zero is not placed in front of the decimal point the order couldbe misread as Administer 125 mg of Lanoxin

Reference: Companion Workbook/Clinical Calculations Ch. 1 and 2
http://ismp.org/https://drive.google.com/file/d/0B-tlCbPSHvfZUUhjbDA0b3pfODA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZUUhjbDA0b3pfODA/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZUUhjbDA0b3pfODA/edit?usp=sharinghttp://ismp.org/http://ismp.org/http://ismp.org/


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PracticeExercise 1.4 Rounding Decimals


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Multiplying Decimals When multiplying with decimals, the principles of

multiplication still apply

The numbers are multiplied in columns, but the numberof decimal points are counted and placed in the

answer, counting places from right to left

The answer to the problem before adding decimalpoints is 345 but when decimal points are correctlyadded (two decimal points are added to theanswer, counting two places from the right to theleft) then 3.45 becomes the correct answer

Practice


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PracticeExercise 1.5 Multiplying Decimals


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Dividing Decimals

When dividing with decimals, the principles of division still apply,

except that the dividing number is changed to a whole numberby moving the decimal point to the right

The number being divided also changes by accepting the samenumber of decimal point moves

N.B. Division problems can be written as

"Dividend Divisor = Quotient" or

"Dividend / Divisor = Quotient." Because multiplication is the inverse of

division, you can turn the equationaround to read

"Quotient * Divisor = Dividend."

F f ll t lk th h
http://www.math.com/


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For full steps walk throughsee or your cloud

http://www.math.com/school/subject1/lessons/S1U1L6GL.html

Basic Math & Pre-Algebra for Dummies.pdf
http://www.math.com/http://www.math.com/https://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttp://www.math.com/school/subject1/lessons/S1U1L6GL.htmlhttp://www.math.com/school/subject1/lessons/S1U1L6GL.htmlhttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttp://www.math.com/school/subject1/lessons/S1U1L6GL.htmlhttp://www.math.com/https://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttp://www.math.com/school/subject1/lessons/S1U1L6GL.html


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Source: Basic Math & Pre-Algebra for Dummies.pdf
https://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharing


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Source: Basic Math & Pre-Algebra for Dummies.pdf

P i
https://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZSG53OWRXelgwckE/edit?usp=sharing


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PracticeExercise 1.6 Dividing Decimals


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Converting Fractions to Decimals

When problem solving with dimensional analysis, medicationdosage calculation problems may frequently contain both fractionsand decimals Some of you may have fraction phobia and prefer to convert

fractions to decimals when solving problems

RULES:

To convert a fraction to a decimal, divide the numerator portionof the fraction by the denominator portion of the fraction

When dividing fractions, remember to add a decimal point and azero if the numerator cannot be divided by the denominator

Converting Fractions to Decimals (2)


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Converting Fractions to Decimals (2)Example


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Understanding the importance of converting fractions to decimals

will assist in preventing medication errors

Many medication errors occur because of a simple arithmetic errorwith dividing

Every nurse should have a calculator to recheck answers foraccuracy. N.B. If a recheck results in a different answer, the next recheck

should include consulting with another nurse or pharmacist


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PracticeExercise 1.7 Converting Fractions to Decimals


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Basic Units ofMeasurement

Exponents, Scientific Notation, and the Metric System


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Upon completion of this lesson, you should be able to

Evaluate numbers having positive and negative exponentsRepresent numbers in scientific notation

Change units within the metric systemConvert units between systems of measurement

Objectives


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Key Terms

52

basecenti

deca (da)

deci (d)

English system ofmeasurement

exponent

factor-label method

giga (G)

gram (g)

hecto (h)

kilo (k)

liter (L)

mega (M)

meter (m)

metric system of measurement

micro (mc)milli (m)

nano (n)

pico (p)

scientific notationunits


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Introduction

53

In health care we deal with very large numbers, such as thenumber of cells in your body, or very small numbers, such as themicroscopic size of the cell

Also, health care professionals regularly use the metric system ofmeasurement in their clinical practice

Therefore, this unit focuses on scientific notation and the metric

system of measurement,both of which are based on the powerof 10, and therefore can be related to the decimal system,discussed earlier and to follow


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Introduction(2)

54

Working with scientific notation and the metric system

requires a basic understanding of the powers of 10 and of

where to move the decimal point

This is especially true for conversions within the metric system

Also discussed in this unit are conversions between the Englishsystem of measurement, which is used predominately in UnitedStates, and the metric system of measurement, which is used

worldwide and in the health professions


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Exponents and Base

55

The health professions often require use of both extremely largenumbers and extremely small numbers

For example, there are about 25,000,000,000 blood cells

circulating in an average adults body, and many organismsfound in the body are microscopic in size

Thus, it convenient to write these numbers in an abbreviated

form known asscientific notation

Doing this requires an understanding of certain terminology


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Scientific notation terminology

Exponents and Base

56

Consider the expression bn, where bis called the baseand nthe exponent The nrepresents the number of times that bis

multiplied by itself: bn is read the nth power of b. Exponents of 2 and 3 are read squared and cubed

That is,32

is read 3 squared

, while43

is read 4 cubed

Examples:

34= 3 3 3 3 = 81

5

3

= 5 5 5 = 125


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Stop and Review

57

Evaluate each of the following

a. 32b. 43

c. 25d. 103e. 105

Note: When the exponent is positive, the resultingnumber is relatively large


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SN for small numbers less than 1

58

Small numbers less than 1 canalso be represented in scientificnotation In these cases, negative

exponents are used A negative exponent

can be thought of as afraction

To do this, you simply put binthe denominator and thepositive version of nin thenumerator


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Stop and Review

59

Write each of the following using a positive

exponent, and then change each to a fractional form

a. 4 3

b. 3 4c. 10 1d. 10 2

e. 104


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The Power of 10Base 10

60

Of special interest are the powers of 10, or base 10

When b is 10, the number of zeros in the answer

equals the exponent

Example:102= 10 10 = 100103= 10 10 10 = 1,000104= 10 10 10 10 = 10,000105= 10 10 10 10 10 = 100,000

Evaluate each of the followinga. 106b. 107


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Scientific Notation(SN)

61

To write a number in scientific notation, write it as a product of anumber greater than or equal to 1 and less than 10, with acorresponding power of 10 In other words, only one number should be to the left of the

decimal point

As an example, consider those 25,000,000,000 blood cellsin your body We can shorten this number to 2.5 1010

The exponent is 10 because in order to ensure that only one

number is to the left of the decimal point, we need to movethe decimal point 10 placesfrom the end of the number tobetween the 2 and 5


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The process of scientific notation illustrated

62


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Scientific Notation Summary

63

So, in scientific notation, the decimal point is moved so that onlyone nonzero digit is to the left of the decimal; the number ofplaces that the decimal is moved is the exponent

Further, as is illustrated in the preceding example and slide , if the decimal point is moved to the left, the exponent is

positive; if the decimal point is moved to the right, the exponent

is negative Notice also that

the exponent is positive if the number is large and negative if the number is small (less than 1)


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Systems of Measurement:Basic Definitions

64

Several systems are used for measuring.

The one we commonly use in the United States is theEnglish system

In the English system, distanceis measured in inches, feet, yards, and miles; weightis measured in ounces, pounds, and tons; and volumeis measured in pints, quarts, and gallons

English system is not the system of choice usedthroughout the world and within the health professions


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International System of Units

65

Most scientific and medical measurements utilize what is commonlyreferred to as the metric systemThe system accepted as the metric system is the InternationalSystem of Units

The metric system uses only three basic units of measure:1. the meter(m) for length,2. the liter(L) for volume, and3. the gram(g) for weight

The metric system has only one basic unit of measure for each typeof measurement.Compare this to the English system, which has many units of measurefor distance, volume, and weight


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Source: Modified from An Integrated Approach to Health Sciences 2e , Delmar

Cengage Learning 2012: FIGURE 1-14, pg. 197

In the metric system, the prefixes are used to indicate the differentlengths, volumes, and weights The conversion is the same for each type of measurement.

1. 1,000 meters in a kilometer,2. 1,000 grams in a kilogram, and

3. 1,000 liters in a kiloliter.For now, just be aware that a milliliter (mL) is a unit of volume, acentimeter (cm) a unit of length, and a kilogram (kg) a unit ofweight


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Systems of Measurement (3 systems)Metric System, Apothecaries System and Household System

67

1. The Metric System The metric system is a decimal

system of weights and measures

based on units of ten in whichgram,meter, and liter are the basic unitsof measurement

However, gram and liter are

the only measurements from themetric system that are used inmedication administration

The most frequently usedmetric units of weight and theirequivalents are summarized:

1 kilogram (kg)1 gram (g)1 milligram (mg)---------------------

1 microgram (mcg)1 kg= 1000 g1 g= 1000 mg1 mg= 1000 mcg

M t i t it f i ht d


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Metric system units of weight andequivalents

Source: Clinical Calculations Made Easy: SolvingProblems Using Dimensional Analysis, Fifth Ed:32

Metric System Units of Volume &


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Metric System Units of Volume &equivalents

1 liter (L)1 milliliter (mL)

1 L 1000 mLSource: Clinical Calculations MadeEasy: Solving Problems UsingDimensional Analysis, Fifth Ed:32

2 Th A th i S t


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2. The Apothecaries System

The apothecariessystem is a system ofmeasuring and

weighing drugs andsolutions in whichfractions are used to

identify parts of the

unit of measure

The basic units ofmeasurement in theapothecaries system

include weights andliquid volume

The Apothecaries System (2)


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e po eca es Sys e ( )

Apothecaries System Units of

Volume and Equivalents1 gallon (gal)1 quart (qt)1 pint (pt)1 fluid ounce (fl oz)

1 fluid dram (fl dr)1 minim (M)1 gal= 4 qt

1 qt =2 pt

1 pt =16 fl oz1 fl oz = 8 fl dr

1 fl dr = 60 M

1 fl oz =1 oz

1 fl dr = 1 dr

Apothecaries System Units of

Weight and Equivalents

1 pound (lb)1 ounce (oz)1 dram (dr)1 grain (gr)

1 lb =16 oz1 oz =8 dr

1 dr =60 gr

Apothecaries system of equivalents for weight and


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Apothecaries system of equivalents for weight andvolume Illustrated

Source: Clinical Calculations Made Easy: SolvingProblems Using Dimensional Analysis, Fifth Ed:35

Avoirdupois
http://en.wikipedia.org/wiki/Avoirdupoishttp://en.wikipedia.org/wiki/Avoirdupois


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3. The Household System

The use of household measurements is consideredinaccurate because of the varying sizes of cups, glasses,and eating utensils, and this system generally has beenreplaced with the metric system.

However, as patient care moves away from hospitals,which use the metric system, and into the community, it isonce again necessary for the nurseto have an

understanding of the household measurement system tobe able to use and teach it to clients and families.

H h ld t t d


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Household measurement system andequivalents for volume Illustrated

Source: Clinical Calculations Made Easy: Solving ProblemsUsing Dimensional Analysis, Fifth Ed:32

Drugs and Dosage


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Drugs and DosageFormulas and Conversions

Volume60 minims = 1 dram = 5cc = 1tsp4 drams = 0.5 ounces = 1tbsp8 drams = 1 ounce16 ounces = 1pt.32 ounces = 1qt.

Drugs and Dosage


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Weight60 grains = 1dram1/60 grain=1mg8 drams = 1 ounce15 grains=1g12 ounces = 1 lb. (Troy weight/ Apothecaries )

2.2 lbs.=1kg

Drugs and DosageFormulas and Conversions (2)

NIST General Tables of Units of Measurement

Troy weight is a system of units of mass customarily used for precious metalsand gemstones. There are 12 troy ounces per troy pound rather than the 16ounces per pound found in the more common avoirdupois system.

D d D
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Household pothecary1tsp = 1 dram1tsp = 60 gtts (drops)

3tsp = 0.5 ounce1tbsp = 0.5 ounce


D d D


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Household Apothecary Metric

1 tsp=5cc 1fl.dram=4cc 5cc=1tsp

3 tsp=1tbsp 4 drams=0.5oz 15cc=1tbsp1tbsp=0.5oz or15cc 8 drams=2tbsp (1oz) 30cc=2tbsp(1oz)2tbsp=1oz or 30cc 16 minims=1cc 1cc=16 minims

1pt.=16oz or 480cc 500cc=0.5L or 1pt.1qt=32oz or 960cc 1000cc=1L or 1qt.


http://www.nurse-center.com/studentnurse/nur11.html

T C i M h d
http://www.nurse-center.com/studentnurse/nur11.htmlhttp://www.nurse-center.com/studentnurse/nur11.htmlhttp://www.nurse-center.com/studentnurse/nur11.htmlhttp://www.nurse-center.com/studentnurse/nur11.htmlhttp://www.nurse-center.com/studentnurse/nur11.html


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Temperature Conversion Method

To convert from Fahrenheit to Celsius:

C (F 32) 1.8To convert from Celsius to Fahrenheit:

F C 1.8 + 32

C temperature in degrees CelsiusF temperature in degrees Fahrenheit

ABBREVIATIONS USED IN CLINICAL CALCULATIONS


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Factor-Label Method of Units Conversion

81

The factor-label method works for all conversions of units, even

outside of the metric system

To use this method, simply write the original quantity as a fraction,and then treat the units as is done in the multiplication of fractions In other words, cancel the units

---------------------In Nursing Clinical Calculations this is called:Dimensional Analysis or the Conversion Factor Method


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Factor-Label Method of Units Conversion (2)

82

For example, to change from hours to seconds, first write hours as afraction over 1You may not know how many seconds are in one hour, but you do knowhow many minutes are in one hour

so you first convert to minutes by making a fraction that

represents this Since we are solving for seconds, we need to determinehow many

seconds are in a minute by making a representative fraction The next step is to cancel the like units that divide out

The final conversion should look like this:

Factor-Label Method


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Factor Label Methodof Units ConversionExamples


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Dimensional Analysis Terms and Steps

84

TERMS USED IN DIMENSIONAL ANALYSIS Given quantitythe beginning point of the problem Wanted quantitythe answer to the problem Unit paththe series of conversions necessary to achieve the answer to the problem. Conversion factorsequivalents necessary to convert between systems of measurement andallow unwanted units to be canceled from the problem

THE FIVE STEPS OF DIMENSIONAL ANALYSIS

1. Identify the given quantity in the problem2. Identify the wanted quantity in the problem3. Establish the unit path from the given quantity to the wanted quantity using equivalents asconversion factors

4. Set up the conversion factors to allow for cancellation of unwanted units5. Multiply the numerators, multiply the denominators, and divide the product of the numeratorsby the product of the denominators to provide the numerical value of the wanted quantity

Source: Clinical Calculations Made Easy: Solving Problems Using Dimensional Analysis,

Fifth Edition; LLW 2012- Pg. 48-59

DIMENSIONAL


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DIMENSIONALANALYSIS

Source: Clinical Calculations Made

Easy: Solving Problems Using

Dimensional Analysis, Fifth Edition;

LLW 2012- Pg. 48-59

DIMENSIONAL


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DIMENSIONALANALYSIS

Source: Clinical Calculations Made Easy:

Solving Problems Using DimensionalAnalysis, Fifth Edition; LLW 2012- Pg.48-59

Practice Dimensional Analysis


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Practice Dimensional AnalysisSource: Clinical Calculations Made Easy: Solving Problems Using Dimensional Analysis,

Fifth Edition; LLW 2012- Pg. 48-59

Learn and Practice moreSolving Problems Using DimensionalAnalysis-Ch. 3-Clinical Calculations.pdf

E l
https://drive.google.com/file/d/0B-tlCbPSHvfZZXNlYnFGX0ZQNk0/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZZXNlYnFGX0ZQNk0/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZZXNlYnFGX0ZQNk0/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZZXNlYnFGX0ZQNk0/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZZXNlYnFGX0ZQNk0/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZZXNlYnFGX0ZQNk0/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZZXNlYnFGX0ZQNk0/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZZXNlYnFGX0ZQNk0/edit?usp=sharing


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Example

88


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Decimals, Percents,and Ratios

89

Decimals, Percents, and Ratios


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Decimals, Percents, and Ratios

Objectives

Upon completion of this chapter, you should be able toWrite decimals in word formEstimate values for operations involving decimals and use acalculator to find the results

Write equivalent numbers as percents, fractions, and decimalsRepresent fractions as ratios in simplest formDifferentiate the terms solute, solvent, and solutionDifferentiate between W/V solutions and V/V solutions andexpress each as percent solutions and ratio solutionsCalculate unit price and rate of flow

Reading:

Colbert BJ et. Al. Chapter 15 DECIMALS, PERCENTS, AND RATIOS , An Integrated

Approach to Health Sciences 2e, Delmar Cengage Learning 2012: 209-19

Key Terms
https://drive.google.com/file/d/0B-tlCbPSHvfZWHdSaTE4eG9Rcm8/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZWHdSaTE4eG9Rcm8/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZWHdSaTE4eG9Rcm8/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZWHdSaTE4eG9Rcm8/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZWHdSaTE4eG9Rcm8/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZWHdSaTE4eG9Rcm8/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZWHdSaTE4eG9Rcm8/edit?usp=sharing


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Key Terms

decimals

intake and output (I&O)percents

percent solution

ratios

solute

solution

solvent

unit priceV/V solution

W/V solution

Decimals Ratios and Percents


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Decimals, Ratios, and Percents In the previous lesson, we learned about fractions

There are, however, other ways to represent parts of awhole These include decimals, ratios, and percents.

In the health field, these representations tendto be used more often than fractions are used.

Blood Tests and Decimals


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Blood Tests and Decimals For example, blood tests reveal information about a patients

health Tests are performed in laboratories by medical laboratory technicians and

results are analyzed by clinicians

Many of the levels are reported in decimal form. The presence of abnormal values can often be of diagnostic significance

for specific disease states An analysis of red blood cells, (carry oxygen to the tissues),

would shows a value within the range of 4.5 to 6.3 million cellsper milliliter If the number of red blood cells is too low, the patient may have a

condition called anemiawhere the bodys tissues may not get enoughoxygen.

This can be the result of a deficiency in iron or certain vitamins

Blood Tests and Decimals(2)
https://drive.google.com/file/d/0B-tlCbPSHvfZYzRWLTRmb2ZDRWc/edit?usp=sharinghttps://drive.google.com/file/d/0B-tlCbPSHvfZYzRWLTRmb2ZDRWc/edit?usp=sharing


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Blood Tests and Decimals(2)Another type of cell found in the blood is the white blood cell

This type of cell is important for the body to fight infections. A normalwhite blood cell (WBC) count is between 4.5 and 11.0

thousand cells per milliliter (thou/mL) A level that is too high might indicate diseases such as a

bacterial infection or leukemia a level that is too low might indicate bone marrow disease.

So you can see why a thorough understanding of decimals is important


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Writing Decimals in Word Form

Given the widespread use of calculators, a complete understandingof decimals has never been more important. Using a calculator, itcan easily be seen that , which equals 3 4, can be written as0.75The decimal 0.75 is read seventy-five hundredths, which can bewritten as the fraction This, of course, simplifies to

W i i D i l i W d F (2)


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Writing Decimals in Word Form (2)

In math, the symbol {} means and so forth.Any fraction having a denominator of {10, 100,1,000, 10,000 } can easily be written as a decimal

The decimal system (showingdi l l )


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corresponding place values) In each of the preceding examples, notice that the

number of zeros in the denominator of the fraction isthe same as the number of places to the right of thedecimal point, which, in turn, corresponds to the way

the fraction is read

Decimal point read as the word and


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Another important use of the decimal point is to separatethe whole number from the portion that is less than 1 The decimal point is read as the word and

For example, 10.23 is read ten andtwenty-threehundredths

Another Example:

0.104 is read one hundred four thousandths100.004 is read one hundred andfour thousandths

Stop and Review

Write each of the following decimalsin words.a. 0.23b. 1.003c. 104.2

Decimal Operations and Estimation


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p

Because you will likely use a

calculator to perform problemsinvolving decimals, no need to spendmuch time discussing mathematicaloperations involving decimals

You should learn enough, however, todetermine whether answers obtainedvia use of a calculator arereasonable Will help you catch errors that

result from hitting wrong calculator

keys

For example, if you use acalculator to add 2.1 + 5.06and the result is 52.7, you shouldbe able to draw the conclusionthat an error has occurred You do this through

estimation

Given that 2.1 is approximately2 and 5.06 is approximately5,the sum of these two numbersshould be approximately 7 Estimation, thus, gives you

an idea of reasonableness

of an answer

Estimation


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examples(rounding off)

Stop and Review


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Stop and Reviewa. Estimate the value of each of the following, and then use a

calculator to determine the exact value.

2.01 + 3.66 + 15.1

4.02 16.03

b. Over an 8-hour period, a pediatric patients fluid intakeand urinary output (intake and output, or I&O) weremeasured. The child ingested 200.2 mL, 150.0 mL, and 25.1

mL of fluid; the childs urine output was 130.5 mLand 170.5 mLWhat was the childs fluid balance (the difference between

the I&O) for that 8-hour period?

Percents


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Percents are used frequently in the health fieldFor instance, drug concentrations often are represented as

percents (e.g., 2% [two percent] solutions), and percentages areoften used with burn patientsto describe how much of thepatients body has been burned (e.g., 5% of body surface)

nondepolarizing neuromuscular blocking agent

Changing Percents to Fractions


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In physiology we learned the importance of oxygen; if there were no

oxygen, we would not exist

But do you know how much of our atmosphere is composed of oxygen? The answer is approximately 21%, or 21 parts out of 100 parts

Carbon dioxide makes up 0.03% of our atmosphere, or 0.03 partsout of 100 parts

The most abundant gas is nitrogen, which composes approximately79% of our atmosphere, or 79 parts out of 100 parts

the symbol % represents the word percent, which means out of 100

-----------------------

A percent is a simple means of writing any

fraction having a denominator of 100

Changing Percents to Fractions (2)


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For example, 50% means or

50 (parts) out of 100 (parts)

To change a percent to afraction, simply write the percentas a fraction having a

denominator of 100; rememberto simplify the fraction

Stop and ReviewWrite each of the following percents

as fractions in the simplest forma. 40%b. 200%c. 75%

Changing Percents to Decimals


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C g g e ce o ec

To change a percent to a decimal, move the

decimal point two places to the left Remember, a whole number is considered to

have a decimal point to the right of it

Example:25% = 0.25 Stop and Review

Change each of the following

percents to decimals

a. 15%b. 300%c. 37.5%

Changing Decimals to Percents


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To change a decimal to a percent, move the

decimal point two places to the right, for example, 0.35= 35%

Note that it may be necessary to add zeros

for example, 0.6 = 60%

Change each of the following decimals to a percent

a. 0.15b. 0.2c. 1.25

Changing Fractions to Percents


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To change a fraction to a percent, first

change the fraction to a decimal, and thenchange the decimal to a percent Use a calculator when appropriate

QUOTES & NOTES

Practical Application Did you ever

wonder if there is an easy way to

figure out a 15% tip at a restaurant?Just move the decimal point on the bill

one place to the left to find 10%

Then take half of that 10% to arriveat the remaining 5%

Add those two numbers, and youve

got 15%!

Changing Mixed-Number


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Percents to Simple Fractions

Sometimes percents are written using mixed numbers(i.e., whole numbers along with fractions), such as

To change a mixed-number percent to a simple fraction, firstchange the mixed number to an improper fraction

Next, divide by 100 and simplify. (Remember, percentmeans out of 100)

Thus, is the same as the fraction


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One of the most common therapies is oxygen therapy

As you breathe, you are breathing room air which contains 21%oxygen

Certain disease states and environmental conditions maynecessitate increasing the amount of oxygen delivered to your

body tissues For example, at sea level the atmospheric pressure (PB ) is 760 mm Hg(millimeters of mercury)

We can find the available oxygen by multiplying the atmospheric pressureby the oxygen percent

To perform the calculation, you must convert the percentage into the decimal

formTherefore, the answer becomes:

760 mm Hg .21 (decimal form of 21% oxygen) =159.6 mm Hg of oxygen


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If we want to increase the amount of available oxygen, we can

place the patient on a higher-percentage device such as anoxygen mask set at 50%

This patient would now have more oxygen available as follows:760 mm Hg .50 = 380 mm Hg of oxygen

An environmental example is mountain climbing

As you climb above sea level, the atmospheric pressure becomesless

Lets assume you have reached a height where it has dropped to

600 mm Hg The oxygen now available is: 600 mm Hg .21 = 126 mm Hg

of oxygen

Ratios


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Ratios Another way to show the relationship between numbers is to

use ratios A ratio is simply a comparison between two numbers

For example, the fraction can be written as the ratio 1:2

Thus, the fraction is the same as the ratio 1:2, the decimal 0.50,and the percent 50% All of these are different ways of expressing the same value

As is the case with fractions, ratios can be simplified As with fractions, simply divide both numbers in the ratio by

the largest number that divides evenly into both

Equivalent expressions for fractions,

ratios, decimals, and percentages


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Ratios (2)

Example:For the ratio of 50:2, the largest number that will divideevenly into both 2 and 50 is 2Dividing both numbers in the original ratio by 2 yields a

simplified ratio of 25:1------------------Simplify each of the following ratios

a. 50:5b. 30:15c. 100:1

Ratios (3)


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Another use of ratios is to find the individual cost or unit price of anitem-that is, the price of one item

To find the unit price, set up a fraction,

Example:

A bottle of 100 aspirins sells for$7.50, while a bottle of 150aspirins of the same brand sells for$12.00. Which is the better buy?

Since each aspirin in the 100-tabletbottle costs less, it is the better buy

Stop and Review

a. An IV dispenses fluid at a rateof 750 mL in 5 hours. How much

liquid is dispensed in 1 hour?How much in 3 hours?

b. Which can of coffee is the

better buy, a 42-ounce can for$13.00 or a 12-ounce can for$4.00?


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Ratios in Medicine

114

Real Life Issues and Applications With normal breathing, it takes twice as long to exhale as it does

to inhale This can be expressed by the ratio 1:2

Certain disease states of the lungs can alter this ratio. Patient A has a 2-second inspiratory (I) time and a 4-second

expiratory (E) time

Patient B has a 2-second I time and a 1-second E time

What are their respective I:E ratios?

Which patient has a normal ratio?

CALCULATING ADULT DOSAGE

Mathematics and Dosage Calculations


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When a physician orders a medication and the dosageordered is not the same as what is available, you mayuse two additional methods to determine the correct

dosage. First is the proportional method, which may be used to

solve almost any type of dosage problem, and second isthe formula method.

Both of these methods are described in the following slides

CALCULATING ADULT DOSAGE(Alternatives to dimensional analysis)

Reference: Rice J. Unit 5 Calculating Adult Dosages: Oral and Parenteral Forms.

In Principles of Pharmacology for Medical Assisting; Cengage Learning; 5 ed. 2010:51-8

Calculating Adult Dosages Using theMathematics and Dosage Calculations
http://www.amazon.com/Principles-Pharmacology-Medical-Assisting/dp/1111131821http://www.amazon.com/Principles-Pharmacology-Medical-Assisting/dp/1111131821http://www.amazon.com/Principles-Pharmacology-Medical-Assisting/dp/1111131821http://www.amazon.com/Principles-Pharmacology-Medical-Assisting/dp/1111131821


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Proportional Method

The physician orders 0.2 g of meprobamate tabs. The dose onhand is 400 mg tabs

Step 1. Determine whether the medication ordered and themedication on hand are available in the same unit of measure

Step 2. If the medication ordered and the medication on hand arenot in the same unit of measure, convert so that both measures areexpressed using the same unit of measure

Conversion: To change 0.2 g to mg

1000 mg : 1 g =x mg : 0.2 gX=200 mg

ormultiply 0.2 x1000 =200

Proportional Method cont



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Step 3. Now use the following proportion to calculate the dosage.

Remember, you converted 0.2 g to 200 mg

Proportional Method cont.

Step 4. Prove your answer. Remember to place your answer in theoriginal formula in thex position

Calculating Adult Dosages Using the



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g g gFormula Method

The physician orders 0.2 g of meprobamate tabs. The dose onhand is 400 mg tabs

Step 1. Determine whether the medication ordered and themedication on hand are available in the same unit of measure

Step 2. If the medication ordered and the medication on hand arenot in the same unit of measure, convert so that both measures areexpressed using the same unit of measure

Conversion: To change 0.2 g to mg1000 mg : 1 g =x mg : 0.2 g

X=200 mgor

multiply 0.2 x1000 =200

Formula Method cont



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Formula Method cont.

Step 3. Now use the following formula to calculate the dosage

The physician ordered 0.2 g of meprobamate tabs (0.2 gconverts to 200 mg). The dose on hand is 400 mg tabs.

MEDICATIONS MEASURED IN UNITS



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MEDICATIONS MEASURED IN UNITS

Medications such as insulin, heparin, some antibiotics,hormones, vitamins, and vaccines are measured in units

These medications are standardized in units based on

their strengths

The strength varies from one medicine to another,

depending upon their sources, their conditions, and themethods by which they are obtained

When calculating medications that are ordered in units you may useHOW TO CALCULATE UNIT DOSAGES



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When calculating medications that are ordered in units, you may useeither the proportional or the formula method

The Proportional MethodThe physician ordered 4000 United States Pharmacopria (USP) unitsof heparin to be administered deep subcutaneously. On hand isheparin, 5000 USP units per milliliterStep 1. Use the following proportion to calculate the dosage

You may use a tuberculin syringe to draw up 0.8 mL

HOW TO CALCULATE UNIT DOSAGES (2)

http://en.wikipedia.org/wiki/United_States_Pharmacopeiahttp://en.wikipedia.org/wiki/United_States_Pharmacopeiahttp://en.wikipedia.org/wiki/United_States_Pharmacopeiahttp://en.wikipedia.org/wiki/United_States_Pharmacopeiahttp://en.wikipedia.org/wiki/United_States_Pharmacopeia


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The Formula Method

The physician ordered 450,000 units of Bicillin for deep IMinjection. Available is Bicillin, 600,000 units per milliliter

Step 1. Use the following formula to calculate the dosage

Mathematics and Dosage Calculations Group Oral Exam 04-2014
http://localhost/var/www/apps/conversion/tmp/scratch_7/BEPPA-Integrated%20Health%20Sciences%20Mathematics%20and%20Dosage%20Calculations%20Group%20Oral%20Exam%2004-2014.pdfhttp://localhost/var/www/apps/conversion/tmp/scratch_7/BEPPA-Integrated%20Health%20Sciences%20Mathematics%20and%20Dosage%20Calculations%20Group%20Oral%20Exam%2004-2014.pdfhttp://localhost/var/www/apps/conversion/tmp/scratch_7/BEPPA-Integrated%20Health%20Sciences%20Mathematics%20and%20Dosage%20Calculations%20Group%20Oral%20Exam%2004-2014.pdfhttp://localhost/var/www/apps/conversion/tmp/scratch_7/BEPPA-Integrated%20Health%20Sciences%20Mathematics%20and%20Dosage%20Calculations%20Group%20Oral%20Exam%2004-2014.pdf


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THE END BEPAA IHS AbridgedMath Review Guide

Thank You for your attention and participation ,

Dr. Cray

BEPAA-Integrated Health Sciences (IHS) Curriculum, Fundamentals of Mathematics | Student Version

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