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Master math principles and see how they apply to patient care! Saunders Math Skills for Health Professionals, 2nd Edition reviews and simplifies the everyday math skills you need to succeed as a healthcare professional. Practical examples show how to solve problems step by step, and clarify fundamental math principles including fractions and percentages, ratios and proportions, basic algebra, and statistics. Written by expert educator Rebecca Hickey, this edition adds a chapter on solutions and IV calculations and even more practice problems with step-by-step solutions. No other textbook makes math so friendly and so accessible!

  • A workbook format lets you solve problems as you review the material.
  • UNIQUE! Full-color design highlights key information and fully illustrates examples such as how to set up problems, the different parts of equations, and how to move decimal points.
  • Learning objectives follow Bloom’s taxonomy, highlight the key topics in each chapter, and explain their importance in patient care.
  • Chapter Outlines and Chapter Overviews serve as a framework for each chapter and explain why it is important to understand the material presented.
  • EXPANDED! Example problems in each chapter use a step-by-step method for solving problems.
  • Master the Skill boxes provide quizzes that let you assess your knowledge of the information in each chapter.
  • Key terms that explain mathematical computations are bolded at first mention in the text and defined in the glossary.
  • Spiral binding with plenty of white space allows you to write out your answers and work through problems in the book.
  • NEW! Solutions and IV Calculations chapter includes topics seen in chemistry, such as calculations for IV solutions and drip rate conversions, duration and total volume of solutions, and discussions on solutes, solvents, logarithms, and pH conversions.
  • NEW! Additional content includes the translation of orders written with abbreviations, use of mercury thermometers, problems involving I&O, and reading and writing prescriptions.
  • NEW word problems include more Practice the Skill and more Building Confidence with the Skill exercises, helping you apply abstract mathematical concepts to real-world situations.
  • NEW! More focus on graph charting is provided throughout the book.
  • NEW! More Math in the Real World boxes take information that you use in your everyday life and demonstrate how the same concept can be applied in health care.

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Saunders Math Skills for
Health Professionals
SECOND EDITION
Rebecca Wallace Hickey, RN, MEd, AHI
Secondary Health Tech Instructor
Butler Technology and Career Development Schools
Hamilton, Ohio
Adjunct Professor, Allied Health
University of Cincinnati–Blue Ash Campus
Cincinnati, OhioTable of Contents
Cover image
Title page
Inside front cover
Mathematical Properties
Order of Operation
Positive and Negative Numbers for Multiplication
Copyright
Dedication
Contributors and Reviewers
Preface for Students
Preface for Instructors
Acknowledgments
Chapter 1 Basic Math Review
Review of Basic Mathematical Operations
Positive and Negative Numbers
Exponents
Parentheses
Order of Operations
Factoring
ConclusionChapter 2 Roman Numerals, Military Time, and Graphs
Review of Roman Numerals
Military Time
Rounding Numbers
Graphs
Circle and Bar Graphs
Measurement Graphs
Conclusion
Chapter 3 Fractions
Understanding Fractions
Addition and Subtraction of Fractions
Multiplication and Division of Fractions
Conclusion
Chapter 4 Word Problems, Percentages, and Decimals
Understanding Word Problems
How to Solve a Word Problem
Decimals
Percentages
Finding the Percentage of a Number
Conversion between Fractions, Percentages, and Decimals
Conclusion
Chapter 5 Ratios and Proportions
Ratio
Proportion
Conclusion
Chapter 6 General Accounting
Insurance
Cash Drawer, Day Sheets, Ledger Cards, and Petty CashComputing Wages
Purchase Order
Conclusion
Chapter 7 The Metric System
Prefixes and Base Units (Word Roots)
Conversion of Measurements in the Metric System
Conclusion
Chapter 8 US Customary Units and the Apothecary System
Apothecary System
US Customary System (Household Measurements) and Avoirdupois System
Conclusion
Chapter 9 Application of Measurement and Dose Conversion
Common Abbreviations Used in the Health Care Field
Interpretation of Physician's Orders
Conversion between Metric, Apothecary, and US Customary (Household
Measurements) Systems
Conversion between Fahrenheit and Celsius Temperatures
Conclusion
Chapter 10 Power of 10
Power of 10
Multiplication and Division by the Power of 10
Significant Figures
Standard Scientific Notation
Computations with Calculators
Conclusion
Chapter 11 Algebraic Equations and Introduction to Statistics
Like Terms
Solving EquationsSolve Literal Equations for One Variable
Arithmetic Average and Mean
Median
Mode
Data Types
Obtaining Samples
Probability
Basic Statistics
Conclusion
Chapter 12 Solutions and IV Calculations
Solutions
Concentrations
Tonicity
Measuring Concentration
Chemistry Concentrations
Changing Concentrations
Intravenous (IV) and Flow Rate
Intake and Output Graphs
Conclusion
Appendix Answers to Odd-Numbered Practice the Skill and Building Confidence
with the Skill Questions
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9Chapter 10
Chapter 11
Chapter 12
Glossary
Index
Inside Back CoverInside front cover
TEMPERATURE CONVERSION
= 1.8
Celsius = (F − 32) ÷ 1.8
Fahrenheit = (C × 1.8) + 32
Mathematical Properties
Associative Property of Addition: The sum stays the same when the grouping of
addends is changed.
Associative Property of Multiplication: The product stays the same when the
grouping of factors is changed.
Commutative Property of Addition: The sum stays the same when the order of the
addends is changed.
Commutative Property of Multiplication: The product stays the same when the
order of the factors is changed.
Distributive Property: When one of the factors of a product is written as a sum,
multiplying each addend before adding does not change the product.
Order of Operation
PLEASE EXCUSE MY DEAR AUNT SALLY
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction
Kings Have Dragons Because Dragons Melt Marshmallows
Kilo, Heclto, Deka, Base, Deci, Centi, Milli, Micro
Positive and Negative Numbers for Multiplication
Positive number × Positive number = Positive numberNegative number × Negative number = Positive number
Positive number × Negative number = Negative number
APOTHECARY-TO-METRIC CONVERSION
Apothecary Metric Metric
grain 30 mg
1 grain 60 mg
15 grains 1,000 mg 1 gram (G)
2.2 pounds 1,000 G 1 kilogram
METRIC EQUIVALENTS FREQUENTLY USED IN HEALTH CARE
Metric Apothecary U.S. Customary (Household Measurements)
1 minim* 1 gtt
1 ml† 15 minims 15 gtt
5 ml 1 tsp
15 ml 3 tsp
1 Tbsp
oz
30 ml 6 tsp
2 Tbsp
1 oz
240 ml 8 oz 8 oz
500 ml 16 oz 16 oz
1 pt
1,000 ml 32 oz 32 oz
1 liter 2 pt
1 qt
4 liters 128 oz 1 gallon
4 qt
2.5 cm 1 inch 1 inch
1 decimeter 4 inches
1 meter 39 inches
1 km 0.6 mile
1 mg grainM30e tmrigc Apo gthraeicn ary U.S. Customary (Household Measurements)
60 mg 1 grain
1 gram 15 grains tsp
4 grams 60 grains 1 tsp
15 grams 1 Tbsp
30 grams 2 Tbsp
1 oz
1 kg 2.2 pounds
*Minims and grains are not commonly used in pharmaceutical preparations.
†Cubic centimeter (cc) and milliliter (ml) are equal measurements; ml is the common
measurement in health care practice.
Data from Mulholland JM: The nurse, the math, the meds: Drug calculations using
dimentional analysis, St. Louis, 2007, Mosby, and Fulcher RM. Fulcher EM: Math
calculations for pharmacy technicians: A worktext, St. Louis, 2007, Saunders.
ABBREVIATIONS COMMONLY USED BY LABORATORY AND NURSING HEALTH
CARE WORKERS
Abbreviation Meaning
BM Bowel movement
CBC Complete blood count
CMP Comprehensive metabolic panel
FBS Fasting blood sugar
Hct Hematocrit
Hgb Hemoglobin
H/H Hemoglobin and hematocrit
Plat. Platelets
WBC White blood countCOMPARISON OF ROMAN AND ARABIC NUMERALS
Roman Numeral Arabic Numeral
I 1
V 5
X 10
L 50
C 100
D 500
M 1,000
Data from Mulholland JM: The nurse, the math, the meds: Drug calculations using
dimentional analysis, St. Louis, 2007, Mosby, and Fulcher RM. Fulcher EM: Math
calculations for pharmacy technicians: A worktext, St. Louis, 2007, Saunders.
MILITARY TIME CONVERSION
a.m. Military Time p.m. Military Time
12:00 a.m. 2400/0000 12:00 p.m. 1200
1:00 a.m. 0100 1:00 p.m. 1300
2:00 a.m. 0200 2:00 p.m. 1400
3:00 a.m. 0300 3:00 p.m. 1500
4:00 a.m. 0400 4:00 p.m. 1600
5:00 a.m. 0500 5:00 p.m. 1700
6:00 a.m. 0600 6:00 p.m. 1800
7:00 a.m. 0700 7:00 p.m. 1900
8:00 a.m. 0800 8:00 p.m. 2000
9:00 a.m. 0900 9:00 p.m. 2100
10:00 a.m. 1000 10:00 p.m. 2200
11:00 a.m. 1100 11:00 p.m. 2300Copyright
3251 Riverport Lane
St. Louis, Missouri 63043
SAUNDERS MATH SKILLS FOR HEALTH PROFESSIONALS, EDITION 2 ISBN:
9780-323-32248-5
Copyright © 2016, 2010 by Saunders, an imprint of Elsevier Inc.
All rights reserved. No part of this publication may be reproduced or transmitted in
any form or by any means, electronic or mechanical, including photocopying,
recording, or any information storage and retrieval system, without permission in
writing from the publisher. Details on how to seek permission, further information
about the Publisher's permissions policies and our arrangements with organizations
such as the Copyright Center and the Copyright Licensing Agency, can be found at
our website: www.elsevier.com/permissions.
This book and the individual contributions contained in it are protected under
copyright by the Publisher (other than as may be noted herein).
Notices
Knowledge and best practice in this field are constantly changing. As new research
and experience broaden our understanding, changes in research methods,
professional practices, or medical treatment may become necessary.
Practitioners and researchers must always rely on their own experience and
knowledge in evaluating and using any information, methods, compounds, or
experiments described herein. In using such information or methods they should
be mindful of their own safety and the safety of others, including parties for whom
they have a professional responsibility.
With respect to any drug or pharmaceutical products identified, readers are advised
to check the most current information provided (i) on procedures featured or (ii) by
the manufacturer of each product to be administered, to verify the recommended
dose or formula, the method and duration of administration, and contraindications.
It is the responsibility of practitioners, relying on their own experience and
knowledge of their patients, to make diagnoses, to determine dosages and the best
treatment for each individual patient, and to take all appropriate safety
precautions.
To the fullest extent of the law, neither the Publisher nor the authors, contributors,
or editors, assume any liability for any injury and/or damage to persons or property
as a matter of products liability, negligence or otherwise, or from any use or
operation of any methods, products, instructions, or ideas contained in the materialherein.
The Publisher
Previous edition copyrighted 2010
International Standard Book Number: 978-0-323-32248-5
Executive Content Strategist: Kellie White
Content Development Manager: Billie Sharp
Content Development Specialist: Elizabeth McCormac
Publishing Services Manager: Julie Eddy
Project Manager: Jan Waters
Design Direction: Renee Duenow
Printed in China.
Last digit is the print number:987654321D e d i c a t i o n
“Families are the compass that guides us. They are the inspiration to reach great heights,
and our comfort when we occasionally falter.”
Brad Henry
To the men in my life: Gerry, Ryan, Shawn, Kevin and Ben Thank you for your
constant love, support, and humor throughout this process.
“Creativity is especially expressed in the ability to make connections, to make associations, to
turn things around and express them in a new way.”
Tim Hansen
To my parents, Fred and Barbara: Thank you for all your encouragement, especially
when I didn't want to be a square peg forced to fit into a round hole.Contributors and Reviewers
Contributors
Benjamin Cory Beaman BS
Science Instructor
Butlertech Career Development Schools
Hamilton, Ohio
Nicole R. Cassidy BS, MSED
Instructor, Mathematics
D. Russel Lee-Butler Technology and Career Development Schools
Hamilton, Ohio
Reviewers
Kathy Burlingame MSN, CRN
Instructor
Galen College of Nursing
Louisville, Kentucky
Ashley Pitlyk PhD
Lead Scientist
Booz Allen Hamilton
St. Louis, Missouri
Deborah Ravestein BS
ABLE Instructor, Medical Math Instructor, Developmental Education Instructor
Miami Valley Career Technology Center
Dayton, OhioPreface for Students
We use math every day. Most people do not realize how often math concepts creep
into our daily lives. A s this textbook was being developed, I strived to take the math
concepts we use every day and illustrate that these are the same concepts that are
used in health care math. I n addition, I tried to provide a broad scope to include a
variety of problems that people in a l l health careers will encounter.
For those of you who do not like math, reflect on what it is about math that you do
not like. What are your strengths? What are your weaknesses? Many students say that
they do not like math because they do not feel confident in their knowledge level or
because they never succeeded at math in the past. “Practice the S kill” exercises are
provided for you to assess your level of knowledge. Once you recognize your
strengths and weaknesses, you will be able to focus on those areas.
A fter you have completed each chapter in this text, ask yourself the following
questions to help measure your success: Which exercise was your strongest skill and
why? Which exercise was your weakest skill and why? I f you feel you need additional
practice, here are a few suggestions:
• Talk to your instructor regarding which concepts are the hardest.
• Form a study group.
• Create your own practice problems and have someone check them for you.
• Contact your school counselor or advisor to arrange tutoring services.
Remember, new math strategies are being developed on a regular basis. For
example, students have taught me mnemonics to remember conversions and a
different way to set up and work proportion problems. Confidence in your abilities
will increase your accuracy with mathematical computations. I hope that you find this
text challenging and it provides you with approaches for applying your knowledge in
the health career of your choice.
Please note that the examples and practice problems in this book are meant to
teach specific concepts and they may not necessarily reflect actual medical or
insurance fees or wages.Preface for Instructors
Saunders Math Skills for H ealth Professional sbegan with my idea of creating a textbook
that could be used in all health career disciplines as a stand-alone text or review
manual for students who are weak in math. Math—just the word brings groans and
negative feedback from many students, as well as a few health care instructors.
D uring the development of this book, I included strategies that I use in the classroom
to present the material in a positive, realistic manner, with a splash of humor. I want
students to see that math can be fun!
Each chapter includes the following helpful features:
• Chapter Outline: Brief outline that helps to highlight the key topics in the chapter.
• Learning Objectives: Measurable objectives that emphasize the expected
learning outcomes. Throughout the text, an Objective icon is placed next to
sections that discuss the objective indicated by the number next to the icon.
• Key Terms: Key terms are listed at the beginning of the chapter. Definitions can be
found throughout the chapter and in the glossary.
• Chapter Overview: Introduction to the chapter content and why it is important to
understand the material.
• Practice the Skill: Exercises for students to assess their knowledge about the topic at
hand. (Answers to the odd-numbered questions can be found at the end of the book.
In addition, all answers are provided on the Evolve website that accompanies the
textbook.)
• Building Confidence with the Skill: Exercises that appear after several topics have
been discussed in the chapter and include all topics discussed so far in the chapter.
(Answers to the odd-numbered questions can be found at the end of the book. In
addition, all answers are provided on the Evolve website that accompanies the
textbook.)
• Master the Skill: Exercises that are found at the end of each chapter, designed to test
the student's knowledge of the information presented throughout the chapter.
(Answers are provided on the Evolve website that accompanies the textbook.)
In addition, special boxes appear throughout the text that include the following:
• Strategy: Provide a systematic process for solving the featured math concept.
• Math Trivia: Include useful and fun tips on when and how math is applied.
• Math Quick Tips: Remind students of math rules.
• Human Error: Remind students to check their work and ask themselves such
questions as, “What are the common errors? Did I perform the proper computation?
Did I write down the problem correctly?”
• Math in the Real World: Take information that the students use in their everyday
lives and demonstrate how the same concept can be applied in health care.“Example” problems are included throughout each chapter to help illustrate the
topic at hand. Because there is more than one way to solve a math problem, I tried to
focus not on the result but on the process of finding the result. Many examples will
have more than one explanation of how to solve the problem. I n my mind, either way
is correct as long as the students can explain how they obtained the answer and used
proper mathematical concepts.
Like students, many instructors either enjoy math or become frustrated with it.
I nstructors who teach in health care programs frequently say, “I know how to work
the problem; I just don't know how to explain it.” I have tried to make the instructor's
resources that accompany this text user-friendly to allow the instructor to be
successful in delivering the material and the student to be successful in learning it.
For an instructor, nothing is more frustrating than appearing to be unprepared for
class. I hope these resources help instructors to feel confident in their math abilities
and prepared when students challenge their methodology for solving a problem.
I nstructor's resources available on the Evolve website that accompanies this book
include the following:
• Lesson plans
• PowerPoint presentations
• Test bank
• Complete set of answers to “Practice the Skill” boxes, “Building Confidence with the
Skill” boxes, and “Master the Skill” boxesA c k n o w l e d g m e n t s
Behind every author stands a great support system—the unsung heroes. I would like
to take this opportunity to thank my unsung heroes:
My students, who over the years have supplied me with different strategies for
teaching medical math. Even though they may not all enjoy math, they have learned
how to appreciate it.
Ben Beaman and N icole Cassidy, for their contributions to this textbook. I have
greatly enjoyed the different activities we have developed together. Thank you for
working with me on this endeavor.
The wonderful staff at Elsevier—Billie S harp, Betsy McCormac, Kellie White, and all
the behind-the-scenes staff. This has been a journey of peaks and valleys. Thank you
for your knowledge, support, and reality checks.
My coworkers and the many reviewers who helped me take this book from a dream
to reality.
Rebecca Wallace Hickey RN, MEd, AHI
“Education is not an affair of ‘telling’ and being told, but an active and constructive process.”
John DeweyC H A P T E R 1
Basic Math Review
CHA P T E R OUT LINE
Review of Basic Mathematical Operations
Addition
Subtraction and Borrowing
Multiplication
Division
Positive and Negative Numbers
Exponents
Positive and Negative Exponents
Scientific Notation
Multiplication and Division of Exponents
Parentheses
Order of Operations
Factoring
Greatest Common Factor
Least Common Multiple
Conclusion
Learning Objectives
Upon completion of this chapter, the learner will be able to:
1. Define the key terms that relate to basic mathematical computations.
2. Perform calculations using basic addition, subtraction, multiplication, and division.
3. Perform calculations with both positive and negative integers.
4. Demonstrate when exponents can be used.
5. Perform calculations involving parenthesis, and multiplication/division with exponents.
6. Solve mathematical computations using the “order of operation” theory.
7. Identify greatest common factors, least common multiple, and prime numbers.
K E Y T E RM S
Addend
Addition
Arithmetic
Associative Property of Addition
Associative Property of Multiplication
Base of an Exponent
Borrow
Carry
Common Multiple
Commutative Property of Addition
Commutative Property of Multiplication
Computation
Compute
Difference
Digit
Directed Number
Distributive PropertyDivide
Dividend
Divisible
Division
Divisor
Equation
Evaluate
Exponent
Factor
Greatest Common Factor (GCF)
Identity Property of Addition
Identity Property of Multiplication
Least Common Multiple (LCM)
Mental Math
Minuend
Multiple
Multiplicand
Multiplication
Multiplier
Negative Numbers
Number Sentence
Operations
Order of Operations
Place Value
Positive Numbers
Power
Power of 10
Prime Number
Product
Quotient
Reciprocal
Remainder
Subtraction
Subtrahend
Sum
Symbol
Whole Number
Zero Pair
Zero Property
Math, just the term, initates one of two responses: “I love math” or “I never was very good at math.” Why do
people avoid using math? The answer depends on the person's level of confidence in recognizing mathematical
computations and how to solve the equation. Most people perform some type of mathematical computation every
day. Examples include:
• Leaving a tip
• Balancing a checkbook
• Figuring out discounts
• Adding up the total cost of a purchase
• Figuring out how much it will cost to fill up the gas tank
Yet, when I point this out during class, a student usually responds, “Yeah, but that's not medical math.” True,
but the principles and formulas are the same. What is medical math? When is math used in health care? Here are
a few examples:
• Figuring out medication dosages
• Measuring intake and output
• Measuring laboratory values
• Collecting deductibles or copayments at the time of service
• Performing an inventory of office equipment
• Ordering nonreusable equipment
• Preparing the office staff payroll
• Billing an insurance company for payment of services rendered
• Creating a budget for a company or for personal useThis chapter is a review intended for students to renew their mathematical knowledge and build confidence in
their abilities. Maybe you have been out of the educational arena for a while, or possibly math was never your
strongest subject in school or you have forgo= en some basic mathematical rules. This chapter will help you
strengthen your math skills. S ome of your classmates may use mental math to solve some problems, but pencil
and paper will be needed to figure out many problems. I n this age of technology, you may be tempted to use a
computer. However, even with calculators, the user must be able to properly input the calculations into the
device. Avoid the temptation. Refresh your knowledge of mathematical rules and order of operations, and then
use the calculator to check your answers in this section. A machine is only as accurate as the person
programming the information.
Review of Basic Mathematical Operations
I n this section we will be using whole numbers and the different operations in which we manipulate them. A s a
reminder, the order of the numbers represents the different place values of each digit (Figure 1-1). Many students
prefer to rewrite math problems in a vertical format so that the number place values match up.
M a th Q u ic k T ips 1 -1
The answer to an addition problem is the sum.
The answer to a subtraction problem is the difference.
The answer to a multiplication problem is the product.
The answer to a division problem is the quotient.
FIGURE 1-1 Review the place value using the following number: 9,876,543,210.
Addition
M a th T rivia 1 -1
Do you remember addition terminology?75 > Addend
+ > Symbol (in this case addition)
> Addend
100 > Sum
Have you ever added a column of numbers by regrouping in ascending order? Or have you changed the problem
by adding some of the smaller numbers together to form a larger number (so that you had fewer numbers to add
together)? D id you come out with the correct answer? The answer is yes because of the following mathematical
properties:
Associative Property of Addition: The sum stays the same when the grouping of addends is changed.
Example:
Commutative Property of Addition: The sum stays the same when the order of the addends is changed.
Example:
Remember, there can be more than one way to solve a math problem. The goal is to come up with the same
solution.
P ra c tic e th e S kill 1 -1
Compute the following addition problems without the use of a calculator.
1.
2.
3.
4.
5.
6.
7.
8.
9. 10.
11.
12.
13.
Identify the proper place value for the bolded, red number in each problem.
14. 7,896,013 _________________________________________________________
15. 892,456,032_______________________________________________________________
16. 8,945_____________________________________________________________________
17. 5,437,890,002_____________________________________________________________
18. 765,420,301_______________________________________________________________
19. 45,678____________________________________________________________________
20. 356,781,010_______________________________________________________________
H u m a n E rror 1 -1
When adding, did you remember to carry your extra digit over one place value?
Subtraction and Borrowing
What is the opposite operation of addition? Subtraction! S ubtraction is used when you want to separate
quantities. A s with addition, it may be easier to compute the answer if the subtraction problems are rewri= en in
a vertical fashion. One step of subtraction commonly forgo= en is borrowing. I f you have a number that cannot be
subtracted without resulting in a negative number, you will need to borrow.
S tra te gy 1 -1
1. We cannot subtract 9 from 8 as a positive number.
2. We must borrow 10 from the tens column.
3. This changes the 8 to 18 and the 7 to 6.
4. Now we can perform the subtraction problem.
Example:
Let's try a few practice problems without the use of a calculator.
1.
2.
3.
4.
5.
6. Excellent! Did you remember to borrow? Now let's move on to a series of numbers.
H u m a n E rror 1 -2
When se ing up your problem, make sure you have lined your numbers up according to their place value. You should
start solving your problem by subtracting from the one’s column and working to the left.
Incorrect Example:
Correct Example:
I t is easy to add a series of numbers together. When you're faced with a series of numbers you need to subtract,
however, it is easier to subtract in groups of two unless you are using a calculator.
Example:
First, let's subtract: 453 − 221 = 232
Next: 232 − 47 = 185
Next: 185 − 2 = 183
Your final difference is 183.
M a th T rivia 1 -2
Do you remember subtraction terminology?
75 > Minuend
− > Symbol (in this case subtraction)
> Subtrahend
50 > Difference
P ra c tic e th e S kill 1 -2
Compute the following subtraction problems without the use of a calculator.
1.
2.
3.
4.
5.
6. 7.
8.
9.
10.
Multiplication
I f you had the choice, when working with a series of the same number, would you rather add or multiply to
obtain your answer? Look at the following example. Which method do you think is easier?
Example:
4 > The digit
> The number of times we are adding 4
20 > The answer
A s with addition, there are mathematical properties that allow us to manipulate the factors within the
computation and still arrive at the same answer.
Commutative Property of Multiplication: The product stays the same when the order of the factors is changed.
Example:
D istributive Property: When one of the factors of a product is wri= en as a sum, multiplying each addend
before adding does not change the product.
Example:
H u m a n E rror 1 -3
Remember when multiplying two or more digits, it is helpful to add a 0 to hold the place value.
Hint: Add a 0 to hold the place value.
M a th T rivia 1 -3
Do you remember multiplication terminology?
75 > Multiplicand
× > Symbol (in this case multiplication)
> Multiplier
1,875 > ProductP ra c tic e th e S kill 1 -3
Compute the following multiplication problems without the use of a calculator.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Division
A s subtraction is the opposite of addition, division is the opposite of multiplication. With division, the goal is to
divide the information into smaller portions. I f a number does not divide evenly, what is left is called a
remainder.
Example:
12 divided by 5 is 2 with a remainder of 2 (12 − 10 = 2).
Bring down your 5 to make a new number of 25.
25 divided by 5 is 5.
Answer is 25.
Example:
2 divided by 2 = 1
Bring down the 7.
7 divided by 2 = 3 with a remainder of 1.
Answer is 13 with remainder of 1.
Can you check the answer? Yes, by doing a reverse operation. To check division problems, multiply your
quotient by the divisor and add the remainder. The resulting product should be equal to the dividend.
H u m a n E rror 1 -4
Remember when dividing, that if the divisor cannot be divided into the dividend, then a zero should be placed in the
answer and moved to the next place value.M a th T rivia 1 -4
Do you remember the terminology for division?
75 > Dividend
÷ > Symbol (in this case division)
> Divisor
3 > Quotient
H u m a n E rror 1 -5
Most incorrect answers come from inaccurately performing addition, subtraction, multiplication, and division, not
because the person did not know what he or she was doing. Take your time—the key to math is accuracy.
P ra c tic e th e S kill 1 -4
Compute the following division problems without the use of a calculator.
1. 125 ÷ 15 = ___________________
2. 72 ÷ 9 = _____________________
3. 450 ÷ 9 = ____________________
4. 574 ÷ 22 = ___________________
5. 124 ÷ 12 = ___________________
6. 500 ÷ 75 = ___________________
7. 43,791 ÷ 8 = _________________
8. 565 ÷ 5 = ____________________
9. 34,791 ÷ 44 = ________________
10. 8,762 ÷ 445 = ________________
11. 81 ÷ 9 = _____________________
12. 6,432 ÷ 8 = __________________
Positive and Negative Numbers
One common use of negative numbers (Figure 1-2) in everyday life is to describe temperature during the winter
months. I n many of the northern states, for example, it is not uncommon for the temperature to range from 10
degrees above zero to −20 degrees below zero on the Fahrenheit scale in J anuary and February. When it gets
down to −10° F, life can be miserable.
FIGURE 1-2 Negative and positive numbers on the same number line.
What do negative numbers have to do with medical math? Negative numbers are used to determine:
• Temperature
• Weight loss
• Body fat
• Cell count
• Cash flow
• Profit or loss margins
A s a reminder, positive numbers are greater than 0 and are usually symbolized with a plus (+) sign when used
in a number sentence that has negative numbers. I f all integers are positive, the + sign is not used, and it is
assumed that all numbers are positive. N egative numbers are less than 0 and are preceded by a minus (−)
symbol.
You can remember this by always placing the positive numbers first.
Example:
Add 14 and −8.
Because 14 is the larger number, the equation becomes: 14 + (−8) = 14 − 8 = 6.Example:
Add −20 and −8.
Because both integers are negative, we should add the two numbers together and assign the negative sign.
Example:
What is the difference of −6 and 4 degrees?
We can determine the answer by adding 6 + 4 = 10.
This could also be accomplished with mental math: −6 is 6 degrees below 0; add that to the 4 degrees above 0
and the difference is 10 degrees (6 + 4). The difference would be 4 − (−6), which would be the same as 4 + 6.
When trying to compute a list of positive and negative numbers, place the positive numbers first followed by
the negative numbers. The order of the numbers within the two groups does not matter. Next, add all the positive
numbers together and determine a sum. Then determine the sum of the negative numbers. Last, take the two
sums and perform the required operation.
Example:
Example:
Add the following numbers: 12, 10, 5, −12, −5, 15
List the positive numbers first and find the sum: 12 + 10 + 5 + 15 = 42
List the negative numbers and find the sum: (−12) − 5 = −17
Perform the proper computation. 42 − 17 = 25
Remember, as with the temperature, the larger the negative number, the farther away from 0 the number is.
When you are multiplying or dividing, if the numbers in the computation are both positive or both negative,
the answer will be a positive number. I f the numbers in the computation are a combination of positive and
negative, the answer will be a negative number (Figure 1-3).
M a th Q u ic k T ips 1 -2
Like symbols = POSITIVE answer
+ multiplied by + = Positive
− multiplied by − = Positive
Unlike symbols = NEGATIVE answer
+ multiplied by − = Negative
− multiplied by + = Negative
FIGURE 1-3 Symbols play a major role in addition of positive and negative numbers.
Example:
+ times + = Positive
− times − = Positive
+ times − = Negative
These are important rules to remember as we discuss order of operations later in this chapter.
P ra c tic e th e S kill 1 -5Compute the following problems without the use of a calculator.
1. (−6) + 14 = ___________________
2. (−81) + (−8) = ________________
3. (−456) + 67 = ________________
4. (−435) + 76 = ________________
5. 457,621 + (−334,211) = ________
6. (−3) + (−34) = ________________
7. (−557) + (−892) = _____________
8. 80 + (−36) = _________________
9. (−45) + 65 = _________________
10. 334 + (−433) = _______________
11. (−6) − 2 = ___________________
12. (−14) − (−4) = ________________
13. (−81) − 57 = _________________
14. 21 − 3 + (−7) = ______________
15. (−54) + (−22) − 6 = __________
16. (−6) × (−56) = _______________
17. 345 × (−22) = _______________
18. (−67) × 3 = _________________
19. 897 × (−2) = _________________
20. 5,423 × (−43) = ______________
21. 56 ÷ (−9) = _________________
22. 459 ÷ (−3) = _________________
23. 5,674 ÷ (−22) = ______________
24. (−4577) ÷ 7 = ________________
25. 89,243 ÷ (−3) = ______________
B u ildin g C on fide n c e w ith th e S kill 1 -1
Complete the following math computations without the use of a calculator.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. 13.
14.
15.
16. (−24) + 43 = ______________________________________________________
17. (−21) + 5 = _______________________________________________________
18. (−53) − (−35) = ____________________________________________________
19. (−112) − 21 = _____________________________________________________
20. 547 − (−443) = ____________________________________________________
Identify the digit that corresponds with the place value: 8,721,045,683
21. Hundred __________________________________________________________
22. Hundred thousand _________________________________________________
23. Million ___________________________________________________________
24. Ten_______________________________________________________________________
25. Thousand _________________________________________________________
M a th T rivia 1 -5
Zero Pair occurs when a positive and negative number are either added or subtracted, result in a zero as the
answer.
Example:
−1 + 1 = 0 or 1 − 1 = 0
Exponents
Many of us had to memorize multiplication tables in grade school. We were drilled on multiplication tables—
remember 50 problems in 2 minutes? Building on that concept, if you think about it, exponents are simplified
multiplication problems. D etermine how many times the same base number appears in the problem. Write the
base number, and the exponent becomes the number of times it is repeated in the problem.
Many of us remember exponents with terms like base, power, squared, and cubed. The base is the number that
will be multiplied to itself, and the exponent is the number of times by which it is to be multiplied. The square
root of a number is a number when multiplied by itself, gives you the original number.
Example 1:
65 × 5 × 5 × 5 × 5 × 5 = 5 or 5 to the 6th power
Example 2:
M a th T rivia 1 -6
Do you remember what term is used instead of 2nd power?
Do you remember what term is used instead of 3rd power?
P ra c tic e th e S kill 1 -6
Express the following problems with exponents.
1. 2 × 2 × 2 × 3 × 3 = ________________________________________________2. 4 × 4 × 6 × 6 × 7 × 7 = _____________________________________________
3. 5 × 5 × 5 × 5 × 5 = ________________________________________________
4. 3 × 3 × 2 × 2 × 7 × 7 × 7 = _________________________________________
5. 2 × 3 × 4 × 4 × 3 × 2 × 2 = _________________________________________
6. 7 × 7 × 7 × 8 × 8 × 8 × 8 = _________________________________________
7. 10 × 10 × 10 × 12 × 12 × 12 = ______________________________________
8. 25 × 25 × 25 × 30 × 30 × 30 = ______________________________________
9. 60 × 60 × 30 × 30 × 30 × 10 × 10 = __________________________________
10. 6 × 6 × 6 × 14 × 14 × 2 × 2 = _______________________________________
Positive and Negative Exponents
Exponents can be either positive or negative numbers. A s a reminder, any number that does not have an
exponent is to the 1st power.
What happens when we have a negative exponent? I t becomes the reciprocal of the indicated power of the
number. Using the following example, we will go through a strategy for working with negative exponents.
Example:
S tra te gy 1 -2
Disregard the negative symbol and find the answer to the exponent.
Now we need to address the negative symbol.
When we are working with a negative exponent, we must determine the reciprocal.
The reciprocal of 3,125 is .
In Chapter 3, we will be discussing fractions in detail. A s a reminder, fractions are part of a whole number.
Negative exponents will be moving the fraction closer to zero.
Scientific Notation
Exponents are most commonly used when dealing with scientific notation.
S cientific notation is often used in the laboratory or in research when working with either a very large or a very
small number. The use of an exponent decreases the chances of error. S cientific notation will be discussed in
Chapter 10, but the following is an example of how exponents and scientific notation work.
Our number system and scientific notation are based on powers of 10. I n scientific notation, we can change
large numbers into numbers with exponents. Using exponents decreases the chance of computation errors or
errors in the answer.
Examples:
100 = 1 103 = 1,000
101 = 10 106 = 1,000,000
102 = 100 109 = 1,000,000,000
Examples:
Examples of writing scientific notation: