The Basics

You must pass a math for medications quiz before starting clinicals. You also have to know the Conversion formulas. Two practice quizzes with answers are available to help you know what to expect on the math test-outs.

I highly recommend that you practice using these quizzes and tutorials prior to taking the clinical math quiz.

• Math Practice Quiz 1
• Math Practice Key 1
• Math Practice Quiz 2 Has the answers at the bottom of the quiz
• More Practice Quizzes - By popular request.
  • Nursing Math Page
  • Math Quiz page for Medical-Surgical Nursing I 
  • Matching and Multiple Choice Math Quizzes Just for Practice. Quizzes are self-grading. Thanks to Linda D. Puryear, RN, MSN Department of Nursing Education, San Antonio College.
  • Nursing Math Link Page  Has links to tutorials and more practice quizzes with answers. Thanks to  Marguerite Tamasy PhD, RN Associate Professor of Nursing, North Harris Montgomery C.C.

  • Another Math Tutorial

  • Pediatric Math Help

  • Purple Math.com - Has help for basic algebra and metrics, etc.
  • Basic Pharmacology Quiz - Has math and medication information included. 
  • http://equmath.net Has math tutorials for everything from fractions to calculus.
     

Dimensional Analysis Method (Also know as Factor Analysis Method)

Many of you have used this method in chemistry, so you can skip this section if you want. If you don't know how to use dimensional analysis, read through the steps below, then practice the sample problems in the two math practice quizzes using this method. It is much easier to learn one method which works for all medical math problems, than to try to figure out which formula you need to use, and which numbers go where. We have many problems on the quizzes than can not be solved using the old formulas, so I recommend that everyone use a method which can solve all types of problems.

Steps for Dimensional Analysis

1. Carefully read the problem. Determine the ORDERED or GIVEN QUANTITY (which is given to you in the problem).
2. Determine what unit the WANTED QUANTITY (answer) is supposed to be in (ml or mg or minutes, etc.)
3. Determine what CONVERSION FACTORS you will need to use. Some may be given to you in the problem (how many mg/ml) while others we expect you to know (how many cc in a teaspoon).
4. SET UP: Dimensional Analysis problems are set up like fractions, with a numerator (top number/s) and a denominator (bottom number/s). You need to set up the problem so that the unwanted units are canceled out. If you are given mg on top, and you really want the answer in ml, you would set up the problem using a ml to mg conversion (given in the problem) and place mg on the bottom, so the mg cancel out. (I KNOW THIS SOUNDS CONFUSING, BUT JUST STICK WITH ME, IT GETS EASIER AS YOU WORK THE PROBLEMS).
5. CROSS OUT the units which cancel out, leaving nothing but the WANTED QUANTITY.
6. DO THE BASIC MATH. Solve the problem by using basic math (no algebra required). Multiply the numbers across. Divide the top number by the bottom number. THAT's ALL THERE IS TO IT.

Sample Problems Using Dimensional Analysis

1. Ordered ceclor 500 mg. Have ceclor 400 mg in 5 ml. How many ml will you give?

• ORDERED QUANTITY 500 mg
• WANTED QUANTITY ____ ml
• CONVERSION FACTOR 400 mg / 5 ml (Given in the problem)
• SETUP
  500 mg x 5 ml
  _______________ = ______ml
                 400 mg 
• CROSS OUT the units which cancel out, leaving no units except the WANTED QUANTITY unit (In this case, you want the answer in ml).
  500 mg x 5 ml
  _______________ = ______ml
                 400 mg
• DO THE BASIC MATH
  Multiply the numbers across, then divide the number on top by the number on bottom. (500 x 5) divided by 400 = 6.25 ml.

  ---

  2. Lets try one which requires you to use more than one conversion.

• Ordered tylenol 10 grains. Have tylenol 160 mg in 1.6 ml. How many ml will you give?
• ORDERED QUANTITY 10 gr
• WANTED QUANTITY ____ ml
• CONVERSION FACTORS 60 mg in 1 gr (we expect you to know this) and 160 mg in 1.6 ml (Given in the problem)
• SETUP
  10gr x 60 mg x 1.6 ml
  __________________ = ______ml
             1 gr x 160 mg 
• CROSS OUT the units which cancel out, leaving nothing but the WANTED QUANTITY
  10 gr x 60 mg x 1.6 ml
  __________________ = ______ml
             1 gr x 160 mg
• DO THE BASIC MATH
  Multiply the numbers across, then divide the number on top by the number on bottom. (10 x 60 x 1.6) divided by (1 x 160) = 6 ml. 

  ---

  3. Now let's do an IV problem using the same method.

  You have an IV running at 21 gtts/min using macrodrip (15 gtt/ml) tubing. You are going to switch the infusion over to an Abbott pump. How many cc/hr will you set the pump at to keep the infusion running at the same rate?

• GIVEN QUANTITY 21 gtts/min
• WANTED QUANTITY ____ ml/hr (cc and ml are equivalent)
• CONVERSION FACTORS 60 min/ hr (you know this) and 15 gtt/ml (Given in the problem)
• SETUP
  21 gtts x 60 min x 1 ml
  __________________ = ______ml/hr
  1 min x 1 hr x 15 gtts 
• CROSS OUT the units which cancel out, leaving nothing but the WANTED QUANTITY
  21 gtts x 60 min x 1 ml
  __________________ = ______ml/hr
  1 min x 1 hr x 15 gtts
• DO THE BASIC MATH
  Multiply the numbers across, then divide the number on top by the number on bottom. (21 x 60 x 1) divided by ( 1 x 1 x 15) = 84 ml/hr. 

  ---

  4. Now let's do an IV piggyback (IVPB) problem.

  You are going to hang an IVPB. The medication is Mandol 500 mg. The volume is 75 ml. The pharmacy instructions state that the medication should be run in over 20 minutes. How many cc/hr should you set the IV pump at?

• ORDERED (GIVEN) QUANTITY 75 ml/ 20 min
• WANTED QUANTITY ____ cc/hr
• CONVERSION FACTORS 60 min/hr (you know this)
• SETUP
  75 ml x 60 min 
  _______________ = ______ml/hr
  20 min x 1 hr
• CROSS OUT the units which cancel out, leaving nothing but the WANTED QUANTITY
  75 ml x 60 min
  _______________ = ______ml/hr
  20 min x 1 hr
• DO THE BASIC MATH
  Multiply the numbers across, then divide the number on top by the number on bottom. (75 x 60) divided by ( 20 x 1) = 225 ml/hr. 

  ---

  Another type of problem you need to know how to do is a time problem.

  5. Order reads 90 ml of 10% Glucose to infuse at 50 gtt/min. Using 15 gtt/ml tubing, how many minutes will it take for the solution to infuse?

• ORDERED QUANTITY 90 ml
• WANTED QUANTITY ____ minutes
• CONVERSION FACTORS 50 gtt/ min and 15 gtt/ml (Given in the problem)
• SETUP
  90 ml x 15 gtt x 1 min
  __________________ = ______min
               1 ml x 50 gtt 
• CROSS OUT the units which cancel out, leaving nothing but the WANTED QUANTITY
  90 ml x 15 gtt x 1 min
  __________________ = ______min
               1 ml x 50 gtt
• DO THE BASIC MATH
  Multiply the numbers across, then divide the number on top by the number on bottom. (90 x 15 x 1) divided by ( 1 x 50) = 27 minutes. 

  ---

  As you can see, you can solve many different types of problems using the same basic steps over and over. However, some of our problems will require you to do a few more steps. For example, you need to know how to convert parts of hours to minutes, and to use military time.

  6. If you start a 250 cc IV at 2100 hours going 30 cc/hour, what time will the infusion be complete?

• GIVEN QUANTITY 250 cc and 2100 hours
• WANTED QUANTITY ____ time (hours and minutes)
• CONVERSION FACTORS 30 cc/hr (Given in the problem)
• SETUP
  250 cc x 1 hr
  _______________ = ______hr
                 30 cc 
• CROSS OUT the units which cancel out, leaving nothing but the WANTED QUANTITY
  250 cc x 1 hr
  _______________ = ______hr
                 30 cc
• DO THE BASIC MATH
  (250 x 1) divided by 30 = 8.33 hours

  PAY ATTENTION HERE 8.33 hours is NOT 8 hours and 33 minutes. It is 8 hours and 0.33

  hours.

  You need to change the 0.33 hours into minutes, so use dimensional analysis again.

  • GIVEN QUANTITY 0.33 hr
  • WANTED QUANTITY ____ minutes
  • CONVERSION FACTORS 60 min/ 1 hr
  • SETUP
    0.33 hr x 60 min
    _______________ = ______min
                 1 hr
  • DO THE BASIC MATH
    (0.33 x 60) divided by 1 = 20 minutes 
    So 8.33 hours is the same as 8 hours 20 minutes.
  • Now add 8 hours and 20 minutes to the time you started.
    ...2100 
    + 0820
    ...2920 

    However, there are only 2400 hours in a military day, so you need to subtract 2400 from any answer you get over that amount. 

    ...2920 
    - 2400
    ...0520 (5:20 am the next day) 

    ---

  What about problems involving mcg/min or mg/kg/min?

  You use the same steps for these more complicated types of problems. They can involve more conversion factors, etc. but the basic steps remain the same. See the examples below.

  Your patient is to receive 10mcg/min of a medication, the available concentration

  is 100mcg/ml, how many ml/hr should the patient receive?

  Steps for Dimensional Analysis

  1. Carefully read the problem. Determine the ORDERED or GIVEN QUANTITY (which is given to you in the problem).   à 10/mcg/min
  2. Determine what unit or Units the WANTED QUANTITY (answer) is supposed to be in  à ML/hr
  3. Determine what CONVERSION FACTORS you will need to use. Some may be given to you in the problem (how many mg/ml) while others we expect you to know. For this problem, the conversion factors you need are  à  how many mcg/ml, which is given to you in the problem (100mcg/ml).  You will also need to know how many minutes in an hour (60). Given this information, you should be able to solve the problem.
  4. SET UP: Dimensional Analysis problems are set up like fractions, with a numerator (top number/s) and a denominator (bottom number/s). You need to set up the problem so that the unwanted units are canceled out. If you are given mg on top, and you really want the answer in ml, you would set up the problem using a ml to mg conversion (given in the problem) and place mg on the bottom, so the mg cancel out. (I KNOW THIS SOUNDS CONFUSING, BUT JUST STICK WITH ME, IT GETS EASIER AS YOU WORK THE PROBLEMS).

  ORDERED QUANTITY 10/mcg/min

  WANTED QUANTITY   ml/hr

  CONVERSION FACTORS 100mcg/ml (Given in the problem) and 60 minutes per hour.

  SETUP
  
  10 mcg         60 min            1 ml  
  _______  X   ______  X     _____ =       _ ml
       min           1 hr              100 mcg        hr

  CROSS OUT the units which cancel out, leaving nothing but the WANTED QUANTITY
  10 mcg         60 min            1 ml  
  _______  X   ______  X     _____ =           ml   
       min           1 hr              100 mcg         hr

  5. DO THE BASIC MATH
     Multiply the numbers across, then divide the number on top by the number on bottom. (10 x 60 x 1) divided by (1 x 100) = 6 ml/hr.  THAT's ALL THERE IS TO IT.

  2. the medication drip in question above has been titrated to 15ml/hr, how many mcg/min

  is the patient to receiving?

   Step one - Determine the ORDERED or GIVEN QUANTITY (which is given to you in the problem).   à 15ml/hr

  Step two - Determine what unit the WANTED QUANTITY (answer) is supposed to be in (ml or mg or minutes, etc.)  à mcg/min

  Step three - Determine what CONVERSION FACTORS you will need to use. For this problem the conversion factors are    à  how many mcg/ml, which is given to you in the problem (100mcg/ml).  You will also need to know how many minutes in an hour (60). Given this information, you should be able to solve the problem.

  SETUP
  
  15 ml              1 hr             100 mcg                       
  _______  X   ______  X     _____          = _ mcg
       hr             60 min              1ml                min

  CROSS OUT the units which cancel out, leaving nothing but the WANTED QUANTITY
   

  15 ml              1 hr             100 mcg                       
  _______  X   ______  X     _____          = _ mcg
       hr             60 min              1ml                min

   

  6. DO THE BASIC MATH
     Multiply the numbers across, then divide the number on top by the number on bottom. (15 x 1 x 100) divided by (60 x 1) = 25 mcgl/min. 

  As you can see, the steps are the same for both problems, you just have to apply this same method to all of your nursing math problems.

  Lets try one with a lot of conversions   

  3. In report you l earn that your patient is on a Dopamine drip, which is running at 15ml/hr. The  patient weights 150lbs,  and the concentration of Dopamine is 1600mcg/ml. How many mcg/kg/min is the patient receiving?

   Step one - Determine the ORDERED or GIVEN QUANTITY (which is given to you in the problem).   à 15ml/hr AND Patient weight (150 lbs)

  Step two - Determine what unit the WANTED QUANTITY (answer) is supposed to be in (ml or mg or minutes, etc.)  à mcg/kg/min

  Step Three - Determine what CONVERSION FACTORS you will need to use. For this particular problem, we need several conversion factors.  à  how many mcg/ml, which is given to you in the problem (1600mcg per ml).  You will also need to know how many lbs in a kg (2.2 lbs per kg),  and minutes in an hour (60 minutes per hour). Given this information, you should be able to solve the problem.  

  SETUP
  
                   2.2 lbs      15ml               1 hr            1600 mcg              
                X   _______  X   ______  X    _____  X     _______     X      = _ mcg/kg/min
  150 lbs        1 kg         1hr               60 min          1 ml               

   So if you have it set up right, all the units you don’t want cancel out and leave just the three units you want (mg/kg/min).

  
                    2.2 lbs       15ml             1 hr            1600 mcg               
                X   _______  X   ______  X    _____  X     _______     X         = _ mcg/kg/min
  150 lbs          1 kg        1hr             60 min          1 ml              

  DO THE BASIC MATH
  Multiply the numbers across, then divide the number on top by the number on bottom. (2.2 x 15x 1600) divided by (150 x 60) = 5.86 mcg/kg/min

  Of course, you could have canceled out the 1600 and 60, leaving 160 on the top and 60 on the bottom, if you wanted to. Some people are more familiar with this technique of reducing the numerators and denominators, while other just plug all the numbers into their calculators. It is up to you. How you end up working out this type of problem is up to you, but I have shown you one method that pretty  much works for just about any math problem which requires converting one thing into another (which is most of the math we do for meds).

  By using the Dimensional Analysis method, you should be able to solve all math for medication problems which require conversions.

  • You can get more practice using Dimensional Analysis from the following book: Clinical Calculations Using Dimensional Analysis - by Gloria Craig
  • Another good resource is Dimensional Analysis for Meds-Textbook and CD-ROM are available in the LRC
  • If you want to practice math questions using a computer format, check out Dosage Calculation by Bille Wilson and Margaret Shannon. It has a study disk with practice questions.
  • See Peg Myers in the learning lab to Check any of these Resources.
    You will also be asked to calculate Intake and Output from a case study, which involves a synthesis of critical thinking and basic math skills. A sample Intake and Output question is included in the practice quiz. Good Luck on your Clinical Math Test Outs!

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Last Modified 06/06/07