ck Out - hcmarketplace.com

About Drug Math

An Insider’s Guide to Success

• Drug preparation and administration

• Easy conversions

• Dosage calculations and equations

• Practice problems and test

. . . and much, much more

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Tackling drug dosage and calculation like you’ve never seen it before!Includes a math review, as well as advanced skills for measuring

and administrating medicines and intravenous solutions.

This book guides the student and clinician through:• A basic math review including working with decimals and fractions.• Setting up equations and finding your method to solve medication problems.• Measuring systems, conversions, and drug administration (IVs, liquids, tablets, suppositories, injectables,

and more!)• Solutions, dilutions, complex IV drug orders, and other advanced topics.

Let’s face it, lots of us struggle with drug math. Here you will find a friendly approach, use of examples thatwalk you through problems, and practice exercises to help you master drug math once and for all!

Helpful icons guide you and highlight all the important parts:

Filled with tips and expert advice to help protect you and your patients!

Take a look at the titles in the Stressed Out series:• Stressed Out About Nursing School• Stressed Out About Your First Year of Nursing• Stressed Out About the NCLEX-RN®

About Drug Math

|200 Hoods Lane | Marblehead, MA 01945www.hcmarketplace.com

SOADM2

Denise Tucker, RN, DSN, CCRN

TIP: A bit of “insideinformation,” a hint, or helpful advice.

EXERCISE: They saypractice makes perfect, sohere are some problems tohelp you hone your skills.

EXAMPLE:Highlights sampleproblems and theirstep-by-step solutions.

For more information visit us on the Web at

www.stressedoutnurses.com

StressedOut

SECOND EDITION

v© 2006 HCPro, Inc. v© 2006 HCPro, Inc.

Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iii

How to use this book . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ix

About the author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xi

Reviewers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xii

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xiii

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xv

Part One: We get down to the basics . . . . . . . . . . . . . . . . .1

Chapter 1: Basic math review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Decimal points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Those pesky fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6Adding and subtracting fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8Multiplying fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9Dividing fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10To summarize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

Chapter 2: Setting up a problem: Make it your way . . . . . . . . . . . . . .13Ratio and proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14Those means and ends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16The formula method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17The chemistry method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20To summarize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22

Contents

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Chapter 3: To convert or not to convert . . . That is the question . . . .23The household system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23The metric system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..24The apothecary system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26Simple conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27Complex conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30Conversion examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30To summarize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35

Part Two: The new recruit goes onward . . . . . . . . . . . . . .37

Chapter 4: Just what the doctor ordered . . . . . . . . . . . . . . . . . . . . . . .39Physician’s orders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39What to look for . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40Use your nursing knowledge and common sense . . . . . . . . . . . . . . . . . . . .41Those chicken scratches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42When in doubt, call . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42Don’t forget to read your rights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43To summarize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44

Chapter 5: Tablets, suppositories, and liquids—Oh my! . . . . . . . . . . .45How many tablets? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46Can I divide that tablet? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50To give a suppository . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52How much liquid? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55To summarize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58

Chapter 6: I’m on needles and pins . . . . . . . . . . . . . . . . . . . . . . . . . . .59How much injectable? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59What does “reconstitution” mean? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61Why reconstitute? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62Your choice or mine? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62Displacement factor? What’s that? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63One is the loneliest number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63No displacement factor? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65Which site? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66To summarize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68

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Chapter 7: And the solution is . . . Elementary, my dear Watson . . . .69The solution depends on its elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69Weight to weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70Weight to volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70Volume to volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70How strong can it be? (Expressions of strength) . . . . . . . . . . . . . . . . . . . . .71Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71Percentage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72Making conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72Ratio to fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72Percentage to fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73Ratio to percentage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74Dilution of a solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75Mixing percentages and ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76To summarize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78

Part Three: Are you ready? We’re almost there! . . . . . . .79

Chapter 8: Intravenously, my dear . . . . . . . . . . . . . . . . . . . . . . . . . . . .81Primary IV fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81Using an infusion pump: ml/hr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83Using gravity: gtt/min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83Drip chambers: Micro vs. macro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83IV drip rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84IV piggybacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .85Using gravity with IVPB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86Using an infusion pump with IVPB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87When push comes to shove . . . (IV Pushes) . . . . . . . . . . . . . . . . . . . . . . . . .87Diluent: How much? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88Do I have a choice? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88How fast? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90Is it compatible? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91To summarize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92

Chapter 9: The longer the better . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93Heparin injections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93Those belly shots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .94Give it the old IV push try . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .94How to figure it out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95Heparin drips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95

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It all depends on how it’s mixed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96Once we know it’s units per hour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97Rounding down for infusion pumps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99To summarize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .100

Chapter 10: Sweets to the sweet . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101Basic insulin knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101Regular insulin vs. NPH insulin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102Sliding scales go up and down . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103How do you mix? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104To summarize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106

Part Four: It’s the home stretch! . . . . . . . . . . . . . . . . . . .107

Chapter 11: It’s the complexity that matters . . . . . . . . . . . . . . . . . . . .109Weight-based medications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109What do I do first? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110What’s next? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111Anything else? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111Complex intravenous orders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113IVs in mcg/min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113Find mcg/min when given ml/hr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118IVs in mg/min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120Find mg/min when given ml/hr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122Intravenous weight-based orders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126Using shortcuts to find the rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130To summarize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .133Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134

Chapter 12: You’ve made it! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .137Equivalency tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .139Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .143Comprehensive exam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .147Answers to exercise problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .151

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155

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It’s time to get down to the basics. Let’s review some basic math principlesfirst, to get your feet wet. Before that, let’s mention one thing. Are you handywith a calculator? Good. Calculators are wonderful tools and can help youwork smarter, not harder. But watch out: don’t trust them as if your lifedepended on it.

Calculators are only as good as the person who inputs the numbers—andpeople do make mistakes. Remember the old computer adage, “Garbage in,garbage out”? It’s important that you know how to set problems up anddouble-check the results. And—horror of horrors! —what if you don’t have aworking calculator handy when you need it? What if it doesn’t work becauseof a power outage or other disaster? What if the batteries are dead? You’dreally be stuck then! So let’s get to work on these problems now.

Division

Remember those multiplication tables? They really come in handy now.Most people are proficient in addition, subtraction, and multiplication.Division, however, is a trickier matter: Let’s talk about division first.

You always need two numbers to divide. First, let’s use two whole numbersto make it easy. “16 divided by 2” means the first number, 16, is divided bythe second number, 2. So you will write out the problem by putting 16 on

Chapter 1

Basicmath review

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top, drawing a line to separate the two numbers, and putting 2 on the bot-tom, thus

162

or 16 ÷ 2

This means “2” will go into “16” a number of times (we’ll call this “x”), thus

x = 162 = 8

Easy, wasn’t it? You found a whole number, 8, for your answer. But what if anumber doesn’t come out whole? For example, take 3 divided by 6. We setthis up the same way as the problem above:

x = 36 = 0.5

Therefore, x = 0.5 is our answer.

Wait! Something’s different. What happened?

You ended up with a decimal point! This is not a whole number, but a partof one.

Tip: Always put a “zero” before the decimal point if there is no numberthere (this means the number is less than one)—it helps you avoid con-fusion about where the decimals should be.

Decimal points

When you are working with decimal points, make sure that you account foreach decimal point. This is an easy place to make a mistake—and it can beone of the deadliest. So watch out!

Don’t forget: Don’t forget to account for those decimal places!

0.53.03.0

0

same as 6)



Chapter 1Basic math review

Example: 3.62 multiplied by (or “times,” also represented by 5) 6.5 willgive you three decimal points at the end, because you must account foreach decimal place in the problem (3.62 has two decimal places, and6.5 has one decimal place). Don’t forget to count those zeroes!

3.62 5 6.5 = 23.530, or 23.53

You don’t need to keep the zeroes if they are to the extreme right of thedecimal point, as in the example above.

When a decimal point went very wrong

A nurse in the intensive care unit of a busy hospital was taking care ofa man who had been admitted for a myocardial infarction (heartattack). The physician came in to admit the patient and to write admit-ting orders for him. When the nurse picked up the chart to review theorders, she saw that she was to give 1,000.0 units of heparin intra-venously to the patient right away. (Heparin is an anticoagulant andmakes the blood take longer than usual to clot.)

The nurse misread the order and moved the decimal point to the rightby mistake. She gave the patient 10,000.0 units of heparin instead—ten times the ordered dose.

What happened to the patient? He developed bleeding into his brainand had a massive stroke. He died several days later, never regainingconsciousness. The nurse was devastated. How could she have prevent-ed herself from making this mistake in the first place?

Two things come to mind. First, if she were unsure of the physician’sorder, she should have asked the physician to clarify the order. Second,she should have double-checked the order and the dose with a sec-ond nurse before administering the medication. Heparin is a drug, likeinsulin, that must always be double-checked with another nurse—forsafety’s sake.

3.626.5

18102172

23.530

5

three decimal places




Those pesky fractions

Many students quake at the sight of a fraction. Oh, no! We like to work withwhole numbers the best—and whole numbers with decimal points secondbest. Anything to avoid working with the enemy, fractions. So, many peopledecide to convert fractions into decimal points to make it easier for them towork with the numbers. It’s more calculator friendly, too. But…

Watch out: By converting one or more fractions into decimals, you areadding one or more steps to your problem. Any time you add steps to aproblem, you have increased the possibility of making a mistake. Use thefewest number of steps possible—don’t make work for yourself.

You can use fractions to help you through some really rough times. Do youremember how to work with fractions? Let’s review.

Just what is a fraction, anyway?

Think of a fraction as part of a number. All fractions have two parts: a topnumber and a bottom number. You can leave the fraction as is, if you wishto work with the fraction (try it out before you decide against it), or you canconvert the fraction into a number with decimal places.

Let’s jog your memory. You will be dividing the top number by the bottomnumber. For example

36 = 3 divided by 6 = 12 or 0.5. That’s one half!

We need to do another problem. Try this one:

__26 = 2 divided by 6 = 0.33 same as

Notice the “3” keeps repeating itself, on and on.

Tip: Many people prefer to “cut off” a number at the hundredths place,or two decimal points.

0.336)20

182018

2




What is this? You have a number with a decimal point! Notice, however, thatyour answer has a line drawn above the numbers to the right of the decimalpoint. Just what do these lines over the “33” mean?

__ _ Actually, 0.33 can also be written as 0.3, by rounding down. Whenever yousee a line over a number or a group of numbers, it means that number orgroup of numbers repeats itself indefinitely. Since we can’t write out thenumber “3” indefinitely—we would run out of space—we use that as a kindof shortcut to mean that they repeat.

But is this number an exact number? No!

_This brings up an important point. “0.3” is an approximation of “one third.”Even if you are using a calculator that has just calculated one third for youby figuring “one divided by three” for you to use in the problem, and thenumbers to the right of the decimal point go on and on, you will not beusing the exact number, and you may get an answer that is a little differentfrom working the calculation with the fraction. Hopefully this won’t be toodifferent, but the possibility does exist.

___ ___What if you have 0.666? Some people, instead of writing 0.666, prefer toround up (because the “6” is larger than “5”) and write the number as 0.67.Once again, these only approximate the real meaning of two thirds.

Tip: When do you need to “round up” or “round down” a number? Lookat the number immediately to the right of the decimal place where yourlast number will be when you are finished. If you have four decimalplaces and you want to round to the hundredths, look at the third num-ber. If the third number is five or greater, you make the second numberlarger by one. If the third number is four or less, you keep the secondnumber the same. Then, you will drop the numbers to the right of thesecond number.

Example: You come up with “45.6832”as an answer to your calculation. Youdecide to “cut off” the number at thehundredths place. The third number tothe right of the decimal place is “3”.Since it is less than “4”, you will notchange the number “8”; you just dropthe “3” and “2” from your answer,which leaves you with “45.68.”




Example: You come up with “54.3883” as an answer to your calculation.You decide to “cut off” the number at the hundredths place. The thirdnumber to the right of the decimal place is “8”. Since it is greater than“5,” you will change the number “8” to “9”; you then drop the “8” and“3” from your answer, which leaves you with “54.39.”

What if you come up with “54.3983” as an answer to your calculation?You decide to “cut off” the number at the hundredths place. “8” is thethird number to the right of the decimal place. Since it is greater than“5”, you need to change the “9” to a higher number. “10” is higher than“9”, so you make the “9” a “0” and add “1” to the “3”, immediately toits right, making the “3” a “4”. You then drop the “8” and “3” from youranswer, which leaves you with “54.40.”

If you use a calculator, you will probably want to convert all your fractionsinto decimal points. Just keep this in mind: Sometimes it is better to workwith fractions in the beginning and then convert the answer to a number witha decimal point. By reducing the number of steps in a problem (or by notadding any additional steps), you reduce your chances of making a mistake.

Adding and subtracting fractions

What if you want to add (or subtract) two fractions? This shouldn’t be hardat all.

The trick to adding or subtracting fractions? Make sure the bottom half of bothfractions are the same number. Then all you have to do is add (or subtract) thetwo top numbers together. The same thing goes if you want to add three ormore fractions together—just make sure the bottom numbers are all thesame. How do you do that? Just multiply the bottom numbers together tofind your “common denominator.”

Example:

The common denominator for 12 and 13 is 2 x 3 = 6.

But wait! We’re not through yet. Don’t we have to do something to the topnumbers, too? We can’t add any old numbers to our problem just becausewe want too.

And you’re right. As long as you multiply the bottom of one number byanother, you’ll need to multiply the top of that number by that same num-ber. Essentially, we’re just multiplying the number by “1.” And that’s okay.




So the first number, 12, will be multiplied by 33, giving us our answer of 36 .

The second number, 13 , will be multiplied by 2

2 , giving us our answer of 26 .

Now all we have to do is add 3 + 2 = 5 (for the top numbers) and keep 6 on

the bottom, leaving us 56 . That’s our answer!

Don’t forget: Whatever you do to the top number, you must do to the bottom.The proportion remains the same.

You do the same thing for subtracting fractions. Let’s borrow the num-bers we just used and subtract them instead! We find our commondenominator in exactly the same way.

12 – 13 = 3

6 – 26 = 1

6 .

Easy, huh?

Only add or subtract the top number (numerator). The bottom number(denominator) stays the same.

Multiplying fractions

Multiplication is easier. When you want to multiply fractions, you will multiply the top numbers together and then multiply the bottom numbers together.

Let’s try a problem first.

__16150 multiplied by 43 = 16 5 4 = 64

450 = 0.14223 5 150

=

=

+


10 © 2006 HCPro, Inc.


Here’s another group of “repeaters.” We can also round down to 0.142.(And don’t forget to put your “zero” before the decimal point—it helps toavoid confusion!)

Dividing fractions

Division is a little trickier than multiplication, but there is one trick toremember: when you divide fractions, turn it into a multiplication problem.And most people do find it much easier to multiply than to divide.

The trick? Multiply the top number by the inverse (turn the fraction upsidedown) of the bottom number. Let’s do an example.

13 divided by 16 = 13 multiplied by 61 (this is the inverse of 16

)

now it’s a multiplication problem: 13 5 61 = 63 = 2.

That wasn’t so bad, was it? Let’s try more complicated numbers to see if itworks the same way.

11,000 divided by 110,000 is equal to 11,000 multiplied by 10,000

1 or

1 5 10,000 =

10,000 =

10 = 10.

1,000 5 1 1,000 1

Tip: Remember cancellation? You can cancel numbers out when you aredividing to simplify the problem. In the above problem, there are fourzeroes on top and three zeroes on the bottom. Remember, whatever youdo to the top number you must do to the bottom. Therefore, you cancancel out three zeroes (cross them out) on both the top and bottom.That leaves us with the “10

1 ”, or “10”.

10,000 =

10 = 1

1,000 1

That was a difficult problem. If you got it, pat yourself on the back. If youdidn’t, you might want to review this section and try some more examples atthe end of the chapter.




To summarize

Work with your fractions, not against them. Try to set up problems so youuse the fewest number of steps you need to solve the problem. Remember,the more steps you add to a problem, the more of a chance you have ofmaking a mistake! It’s only logical—you’ve got more room for error. Andpractice, practice, practice!


Exercises

As you know, practice makes perfect. Let’s do a few problems and seewhat the answers are.

1. 34 + 6

9 =

2. 12 + 3

5 =

3. 79 – 1

2 =

4. 23 – 1

6 =

5. 411 ÷ 1

5 =

6. 110 ÷ 2

3 =

7. 16 5

65 =

8. 1320 5

13 =

9. 3.87 5 15.3 =

10. 10.99 5 62.4442 =

12 © 2006 HCPro, Inc.



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