Basic Math Rules

A good web site for theory and practice is http://www.accd.edu/sac/nursing/math/default.html

Fractions & Ratios

Fractions and ratios are reduced to their lowest terms. Improper fractions are changed to mixed numbers. Answers are never left as improper fractions

A good website for explanations and practice on fractions is http://www.math.com/homeworkhelp/HotSubjects_fractions.html

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Calculation of Decimal

During calculation of decimals:

• If the number is greater than one (as a whole number), carry out the answer to hundredths (two spaces beyond the decimal).  For example, 5.3333333 would be written as 5.33.
  
• If the number is less than one (as a whole number), carry out the answer to  thousandths ( three spaces beyond the  decimal).  For example, 0.3333333 would be written as 0.333.
  
• Do not round off decimals while solving a problem.
  
• If the final answer (the one that goes on the answer sheet) is greater than one, it  should be rounded to tenths (one space beyond the decimal).
  
• If the final answer (the one that goes on the answer sheet ) is less than one, it should be rounded to hundredths (two spaces beyond the decimal).

A good website for explanations and practice on decimals is http://www.math.com/homeworkhelp/HotSubjects_decimals.html

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The Apothecary System

Answers in the apothecary system are expressed in lower case Roman numerals for quantities of twenty (20 ) or less.

 For quantities greater than twenty, answers are expressed in Arabic numbers and fractions.

Decimals are never used .

For quantities of less than twenty (20) that have  half (1/2) as part of the answer, use the symbol  "ss" for 1/2.  If any other fraction is part of the quantity, the entire answer is written in Arabic numbers and fractions. Roman numerals are never combined with fractions except the fraction  expressed as "ss"

Minims (m) are always rounded to the nearest whole number.

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The Household System

Answers in the household system are expressed in Arabic numbers and fractions. Decimals are never used.

Drops  (gtt) are rounded to the nearest whole number. Never use a decimal or a fraction.

Remember a drop is very tiny.

Can we have part of a drop?  No!

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Time

Time is expressed in hours and minutes. It is necessary  to convert part of an hour to minutes. Minutes are rounded to the nearest whole minute before the end of the problem. Time is expressed in standard time or military time. For standard time, the hours and minutes are expressed as we read them on the clock separated by a column followed by AM or PM.

To convert standard time to military time, add 12 to any PM hour. The minutes stay the same. Do not add AM or PM to military time. Military time is written in 4 digits (22:10 or 05:00)

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Metric System  

The kilogram is the largest, the microgram is the smallest. When going from largest to smallest, multiply by 1000 or move the decimal three spaces to the right .

When going from smaller to larger, divide by 1000 or move the decimal three spaces to the left.

The same rule applies when converting Liter to milliliter or cc.

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Factor Labeling/Ratio & Proportion

This method can be used to solve any problem

The physician orders 25 mg of medication .The label reads 50 mg per tablet. How many tablets would you give?

We know that we want our answer in tablets (x tab). We know that there are 50 mg to 1 tab or 50 mg/1 tab. However, we do not know how many tabs in 25 mg or 25 mg/x tab.

x tab = 25 mg/1 x  1 tab/50 mg

The answer is 1/2 tab.

Steps to solve any problem using factor labeling:

1. Find the question.
   In the above problem, we need to find how many tablets equal the 25 mg ordered.
   We may express this as (x tab); 25 mg /x tab.
   

2. Make sure that we have two  items of the same unit; if not, check to see if there is any relationship between any set of two items. In other words, see if there is a conversion factor between two items.
   
   For example: 
   1G/1000 mg
   1 kg/2 lbs
   gr xv /1G.
   
   If after using the conversion factor,  we still have single, unmatched items, the single item should  be eliminated. 
   

3. Pull x, the unknown, and write x tab =
   
4. When we pull out x from the set of proportions  x becomes one (1) and is always placed at the denominator of the first  proportion.
   Then, the next set of fractions or proportions will be set according to the this first one making sure the unit item from the first numerator matches with the denominator of the second fraction or proportion.
   The unit item should match crossways, first numerator to second denominator, second numerator to third denominator and so on.
   
5. Multiply all numerators then all denominators to obtain the final result. See above example.           

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Daily Dosage

Tablets are considered to be scored in halves and are given in whole and 1/2 tablets. Never write 0.5 tablet for 1/2 tab.

Sometimes you will be asked to determine the total amount of medicine (active ingredient)  a client is receiving in a day or over several days.

Example: Order for 1 Tbsp of medicine q 6 h. Label reads 1 mg per 1 cc.
How much medicine should be administered in one (1) day?                                                                                                                                                                                                                                  q 6 h. means every six hours which is 4 times a day.
The order is for 1 Tbsp each dose and 4 doses each day

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Powdered medications

Example: 

A vial (dry powder) is labeled:

For IM use, dilute this 250 mg with 2.7 ml sterile water. The resultant solution will have a concentration of 250 mg per 3 ml.

The  physician has ordered 125 mg IM.

After reconstituting the medication, how much should the nurse administer to the client ?   

Calculation:  
 

The amount of liquid added to the vial is not part of the problem. Although 2.7 ml was added, the resultant solution has 3 ml. This is because the powder added volume to the solution.

There are several steps to consider when mixing powdered medications:
We need to determine if the medication is to be administered SC or IM.
If SC, the nurse needs to mix the medication so that 1 ml or less is drawn up in the syringe after the powder is reconstituted.
If IM, the dosage desired should be contained in as close to 2 ml as possible.
To do this, we need to determine what amount of fluid would be drawn up for each of the possible directions. Then, we can make our choice.

Adult and Pediatric Dosages

The most common way of determining adult and pediatric dosages is based on the weight of the child as compared to a safe dosage based on weight as found in the literature. There is a minimum and maximum dose for each unit of weight.

Example:
Your client weighs 87 lbs.
The literature says a safe dose is 0.3 mg - 0.5 mg /kg/day given in four divided doses.
What is one maximum safe dose for your client.

To solve this problem, you must realize that the literature gave the safe dose for the entire day, in other words, the total amount of medication or doses that are administered for a whole day.
Therefore, you must realize that there are four doses in one day (in this problem).

When setting up your problem, be sure to write "kg/day" and we need to add "4 doses/day" as a ratio

As a rule, if the problem gives you "mg/kg /day" and you need to calculate "per dose" or if the problem gives you "per dose" and you need to calculate "per day", you need to add the ratio "# doses/day".
However, if the problem gives you "per day" and you need to calculate "per day" or the problem gives you "per dose" and you need to calculate "per dose", you do not need to use the ratio "# doses/day"

Calculations:

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IV Discussion

All IVs are infused over time or x cc/minute/hour.

Flow rate means number of drops per minute (gtt /minute)

Drop factor means how many drops per one cc that the particular tubing set delivers.
It is set by the manufacturer.
The tubing set may deliver 60 gtt /cc ( microdrop ) or 10,15 gtt per cc (macrodrop)

Example 1: 

An IV of 800 cc Ns is running at 30 gtt/min. The drop factor is 10. How many cc/min is your client receiving?

Example 2 :

The physician has ordered 1800 cc of an IV fluid to be infused over the next day. The tubing set delivers microdrops. How many cc/hr is the client receiving?

Note that the ratio with the drop factor is not used; there is only one item with gtt which is unmatched.

Example 3 :

Your client has an IV with 600 cc D5w running at 25 gtt /min. The drop factor on the IV is 20. How many cc/hr is your client receiving?

x cc /1 hr   25 gtt /1 min   20 gtt /1 cc   60 min/hr x cc = 1 hr/1  x  60 min/1 hr  x  25 gtt /1 min  x  1 cc/20 gtt  =  75 cc/ hr

Example 4 : 

You determine that an IV will run for 7 hours and 52 minutes. The IV started at 10:49 PM. What time will it all be infused?

Example 5 :

The physician orders Ampicillin 500 mg IV q h for 3 days. The medicine comes up to the floor labeled Ampicillin 500 mg in 100 ml D5W. The instructions read that the IV should be infused over 45 min., the drop factor is 20.

Calculate the flow rate. 

Remember the rules of factor labeling; we need two of each item that should match.  

We notice that there are three ratios with minutes and 500 mg twice; we need to make a choice.
We are looking for gtt /min, and the IV is in ml running over 45 min.
So we can choose 100ml /45 min .

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