MATHEMATICS FOR MEDICAL PRACTITIONERS

DRUG CALCULATION

DR MUSA MARENA Drugs are prescribed by their generic (official) name or trade (brand) names and are

packaged in an average unit dosage

Tablets and capsules contain a solid concentration of drugs (paracetamol gr x) whereas solution contain a specific amount of drug (usually gram weight) dissolved in a specific

amount of solution (usually mLs or ccs) (promethazine 20mg per ml)

Parenteral medications (IM, SC, IV) are package in vials, ampoules, and pre-measured syringes. Dosages usually ranges from 1 to 3 ml

Medication orders refer to drug dosages, so calculation will be necessary if dosage prescribe is different from available dosage

Some drugs are measured in units (heparin, insulin, penicillin), and others are in solutions as mEq (grams per 1ml of solution). Some solutions need to be reconstituted from a`

powder form.

Infants and children cannot receive the same dose of medication as adult Basic Math skills are needed to calculate most dosage and solution problems encounter

today in clinical practice

Accurate dosage calculation are an essential component of total nursing role in safe administration of medication

NURSING STAFF HAVE a range of sophisticated electronic devices at their disposal for delivering essential drugs, fluids and nutritional therapy to patients in the healthcare

setting.

Accurate, low-flow-rate, small-volume infusions can be controlled by means of a syringe pump

Medium-to-high flow rates can be controlled by a volumetric infusion pump Basic fluid replacement can be delivered by the age old method of gravity

infusion more commonly known as the drip'.

Gravity infusion relies solely on the user setting up the infusion using a safe and sturdy drip stand, and then manually adjusting a plastic roller clamp, fitted to a disposable

administration set, to achieve the desired drip rate.

A controller electronically regulates drop rate by gravity An infusion pump consistently exerts pressure against the tubing or the fluid at

preselected rate. Syringe pump exert pressure through the tubing

Barriers to Calculation Success

Top ten reasons why healthcare professionals dont think they need to maintain competency in

calculations:

The computer does it The pharmacy does it The IV infusion pump does it We have charts and tables that do it The drug companies take care of it We use unit dose Its just a nursing school exercise We have a unit-based pharmacist

Math is just not one of my strengths Its not a good use of my time

Responsible professionals cannot afford to become complacent with drug calculations as

they are accountable for all drugs they administer

TYPES OF IV FLUIDS

IV fluids are packaged in sterile plastic bags or glass bottles. It is essential to choose the correct

IV fluid to avoid serious fluid and electrolyte imbalance that may occur from infusing the wrong

solution. Physicians and healthcare providers order IV fluids and the IV flow rate.

If you have any doubt about the correct IV solution, always double-check with another

healthcare professional.

COMMON ABBREVIATIONS FOR IV FLUIDS

ABBREVIATION DEFINITION

D Dextrose

W Water

NS Normal (or isotonic) saline

D5W 5% dextrose in water

0.9% NS 0.9% saline in water (sometimes termed normal saline)

0.45% NS 0.45% saline in water (sometimes termed 12 normal saline)

0.33% NS 0.33% saline in water (sometimes termed 13 normal saline)

LR Lactated Ringers solution (or Lactated Ringers)

D5NS 5% dextrose in normal saline

KINDS OF IV DRIP FACTORS IV fluids are administered through infusion sets. These consist of plastic tubing attached at one end to the

IV bag and at the other end to a needle or catheter inserted into a blood vessel. The top of the infusion set

contains a chamber. Sets with a small needle in the chamber are called microdrip because their drops are

small. To deliver 1 mL of fluid to the patient/client, 60 drops drip in the drip chamber (60 gtt 1 mL).

Commonest microdrip sets deliver 60gtt/mL. Others are 50gtt/ml and 40gtt/ml. Infusion sets without a

small needle in the chamber are called macrodrip (Fig. below).

Drops per milliliter differ according to the manufacturer. For example, Baxter-Travenol macrodrip sets

deliver 10gtt/mL, so10 drops drip in the drip chamber (10gtt 1 mL); Abbott sets deliver 15gtt/mL, so 15

drops drip in the drip chamber (15gtt 1mL). The package label states the drops per milliliter (gtt/mL).

Sometimes the drop factor is also stated on the top part of the chamber. To calculate IV drip rates, you

must know this information.

The tubing for these sets includes a roller clamp (Fig. below) that you can open or close to regulate the

drip rate;

Use a watch or a clock with a second hand to count the number of drops per minute in the chamber (Fig.

below).

The Dial-a-Flow device (sometimes referred to as Dial-a-Flo) is an extension IV tubing that

attaches to the primary IV tubing. It is calibrated in milliliters per hour; you dial the rate, and

the device regulates the flow. The roller clamp must be open all the way. Usually, these devices

are not used with an infusion pump. The rate is still an approximate amount, and changes in the

patient/client position can affect the flow rate.

INFUSION PUMPS Electric infusion pumps also deliver IV fluid. Some are easy to operate; others are more

elaborate. You must enter two pieces of information: the total number of milliliters to be infused

and the number of milliliters per hour. Pumps used in specialty units also allow you to input the

name of the medication, the concentration of the medication, the amount of fluid, and the

patient/clients weight. The infusion rate is set in milliliters per hour, and the pump automatically

calculates the dose in milligrams, micrograms etc. There are several manufacturers of IV pumps;

some pumps use regular IV tubing, while other pumps use tubing specific to that IV pump. All

IV pumps allow you to program the primary IV rate, volume to be infused, secondary IV rate,

and total volume that has infused over a period of time. The pump can also calculate the dosage

based on weight. The tubing factor for an IV infusion pump is 60gtt/mL; however, the rate is

stated and programmed as milliliters per hour.

A Buretrol is an IV delivery system with tubing and a chamber that can hold 150mL delivered as microdrip (1mL = 60drops).

(This device is sometimes referred to as a Volutrol.) The top of the Buretrol has a port so that a reservoir of fluid can be added.

The Buretrol is a volume control because no more than 150mL can be infused at one time

.LABELING IVS Every IV must be labeled so that any professional can check both the fluid that is infusing and

the drip rate. A typical order includes the following information:

Patient/client name, room, bed number, date, and time

Order: 500 mL D5W12NS. Rate: 50 mL/hr. Many factors can influence this drip rate in gravity infusion once it has been calculated and set.

These include positional problems, temperature and other external factors. However, this method

has no means of alerting staff to impending errors, or any other infusion-related problems.

Furthermore, it is reliant on using the force of gravity to deliver the fluid accurately to the

patient. Apart from fluid viscosity, type of cannula and clinical complications after set up, other

factors can affect the initial rate of infusion. These include static pressure, temperature, fluid

level, patient position and drip factor

Many factors may interfere with the drip rate. When you are not using an infusion pump, gravity

will cause the IV to vary from its starting rate; you will need to observe and assess the infusion

and IV site frequently. Youll need to monitor other conditions as well. As the amount of fluid

decreases in the IV bag, pressure changes occurand they, too, may affect the rate. The

patient/clients movements can kink the tube and shut off the flow; they can change the position

of the needle or catheter in the vein. The needle can become lodged against the side of the blood

vessel, thereby altering the flow, or it may be forced out of the vessel, allowing fluid to enter the

tissues (infiltration). (Signs of possible infiltration are swelling, pain, coolness, or pallor at the

insertion site. If you notice any of these signs, discontinue the IV and start a new one at another

insertion site.) Infusion pumps have an alarm system that beeps to alert you when the rate cannot

be maintained or when the infusion is nearly finished. Be sure to check the infusion pump

frequently, and know how to troubleshoot the various alarms.

STATIC PRESSURE: The pressure (in mmHg) exerted on the fluid varies according to the height difference between the patient access site and the fluid bag. An optimum

height of one meter above the patient should be sufficient to overcome initial venous

pressure. Should the bag be repositioned after set up, this height difference and

subsequent pressure difference will affect the drip rate.

TEMPERATURE: Increases in temperature can cause the plastic components in the roller clamp to lose tension and hence grip on the tubing as it tries to revert to its original

shape and this can adversely affect the drip rate.

FLUID LEVEL: As the fluid level falls in the bag, the static pressure decreases and results in a slowdown of the established infusion.

PATIENT POSITION: The set infusion rate (drip rate) is relative to the position of the patient and the fluid bag. Should the patient change position then the drip rate can also be

affected.

DRIP FACTOR: This is usually indicated on each manufacturers giving set package and is approximately the number of drops equivalent to 1ml water (H2O). Any change in

the type of giving set can affect the drip rate, and staff needs to be aware of the drip

factor for each giving set used in their area of work.

Each patients prescription is delivered from a fluid bag that can vary in size from 50ml to

2litres. An administration set, or giving set, is attached to the clean, sterile port of the fluid bag

and primed ready for the infusion. Once safely connected to the patients cannula, the roller

clamp is slowly opened to establish a flow rate (in drops per minute). This drip rate is calculated

before each infusion and set accordingly. Patients are then monitored throughout the infusion

(mostly every hour) to ensure that the delivery is as expected

To administer the right amount the nurse must have basic mathematical skills to be able calculate

the dosage of medication. This may involve using

Unit conversion Rates Proportions Ratio The nurse observes the three checks and six rights of medication administration.

THREE CHECKS WHEN PREPARING MEDICATIONS

Read the label: Check the drug label with the MAR (medication administration record) when removing

the container or unit-dose package.

Check the drug label again immediately before pouring or opening the medication, or preparing the unit-dose.

Check the drug label once more when replacing the container and/or before giving the unit-dose to the patient/client.

KNOWLEDGE BASE IN GIVING MEDICATIONS

Nurses should know the following before giving medications: generic and trade names of drugs to be administered class, category of drugs to be administered average adult or pediatric dose depending on the patient/client population routes of administration use side effects and adverse effects

contraindications nursing implications in administration signs of effectiveness possible drug interactions

The nurse should be aware of the patient/clients diagnosis and medical history, especially relative to drugs taken. Be especially alert to over the counter drugs (OTC) or herbal remedies

which patients/clients often do not consider important. Check for drug allergies.

Assess the patient/clients need for drug information. Be prepared to implement and evaluate a nursing care plan in drug therapy.

SIX RIGHTS BEFORE ADMINISTERING MEDICATIONS

Right medication Right patient/client Right dosage Right route Right time Right documentation.

MEDICATION ORDERS GUIDELINES

Only licensed physicians or health care providers can write orders/prescriptions. Nurse practitioners are licensed in all states to write orders, although some restrictions apply

and vary state to state.

Medical students may write orders on charts, but orders must be counter signed by a house physician before they are legal. Medical students are not licensed.

In states that allow nurses or paramedical personnel to prescribe drugs, these caregivers must follow hospital guidelines when carrying out orders.

Do not carry out an order that is not clear or is illegible. Check with the physician or healthcare provider who wrote the orderdo not assume anything.

Do not carry out an order if a conflict exists with nursing knowledge. For example, Demerol (meperidine) 500 mg IM is above the average dose. Check with the physician or

healthcare provider who wrote the order.

Nursing students should not accept oral or telephone orders. The student should refer the physician to the instructor or staff nurse.

Professional nurses may take oral or telephone orders in accord with institutional policy. The nurse must write these orders on the chart, and the physician or healthcare provider

must sign them within 24 hours. Verbal orders are discouraged, and the physician should

write the order if physically present in the nursing unit.

Physicians and nurse practitioners order medications using the six rights of medication

administration including the:

1. Right patient

2. Right drug

3. Right dosage

4. Right route

5. Right time

6. Right documentation

Right Patient

Many medication errors can be prevented by correctly identifying the right patient. Patients in

the hospital setting wear identification bands, whereas other facilities may use a photograph to

identify the right patient. Regardless of the identification method, the medication order must

correspond to the identification of the patient. Checking identification and asking patients to state

their names assists in reducing medication errors. It is also important to listen to the patient. If

the patient states, I dont take a blue pill, go back and check the medication order for

correctness.

Right Drug

Medications can be ordered using their trade name or generic name.

Examples:

1. Tagamet or cimetidine

2. Cipro or ciprofloxacin hydrochloride

It is the responsibility of the nurse to look up a medication before administration to ensure that

the right drug is being administered. It is the responsibility of the nurse to know the

classification of the drug being administered and that the drug corresponds with the patient

diagnosis. Many drugs have similar names.

Example:

1. Celebrex (an anti-inflammatory)

2. Celexa (an antidepressant)

It is also the responsibility of the nurse to know the side effects of the drug being administered.

The nurse must be aware of any patient allergies before medication administration to ensure

safety of the patient. Allergies should be clearly recorded on medication records or a patient

should wear an allergy bracelet. Because it is impossible to know all medications, the nurse can

use a nursing drug reference to look up medications to ensure accuracy and prevent medication

errors.

Right Dosage

Medications are available in different dosages. It is the responsibility of the nurse to ensure that

the right dosage is administered. The pharmacy may supply the exact dosage ordered or the

dosage may need to be converted using a common equivalent or calculated based on the weight

of the patient. If the medication must be reconstituted, the correct diluent must be used for

reconstitution. If a patient is to receive a tablet but has difficulty swallowing, the nurse must

obtain an order to have the medication changed to an elixir. Medication orders are to be

administered exactly in the dosage ordered. A nursing drug reference assists with preventing

medication errors by supplying information regarding the dosages of medications that can be

safely administered to a patient based on age and weight.

Right Route

Medications may be administered by different routes including oral (tablets, capsules, or liquid),

parenteral (intradermal, subcutaneous, intramuscular, or intravenous), or cutaneous (skin and

mucous membranes). Improper medication administration techniques (crushing an enteric-coated

tablet, opening a capsule, or giving an injection using the wrong route) are considered

medication errors. A nursing drug reference provides information regarding the routes that can

be safely used to administer medication and eliminate medication errors. It is the responsibility

of the nurse to use this information to safely administer the medication to the patient using the

right route.

Right Time

Medications are ordered and need to be administered at specific times to ensure the effective

absorption of the medication. Failure to administer a medication on time or failure to document

the administration of a medication is a medication error of omission. Some medications are

ordered before meals (ac), after meals (pc), or at bedtime. Other medications may be ordered

based on frequency of time (once a day [qd], twice a day [bid], three times a day [tid], or four

times a day [qid]). A nursing drug reference provides the nurse with the appropriate information

to ensure that the medication is effectively and safely administered to eliminate a medication

error based on adsorption.

Most facilities allow a window of administration that is usually 30 minutes before or 30 minutes

after the prescribed time. It is the responsibility of the nurse to use this information to safely

administer the medication to the patient at the right time.

Once you are able to interpret the important components of an order for medication, you can

perform accurate calculations for the correct drug dosage by using dimensional analysis.

Right Documentation

Documentation is the sixth right of medication administration and should be completed as

soon as possible after the administration of the medication. Documentation is an important right

that can prevent medication errors related to over- or under-medication. The general rule of

documentation is if you didnt chart it . . . you didnt do it therefore medication should never

be charted before administration of the medication. Documentation should follow medication

administration and include documentation regarding refusals, delays, and responses (including

adverse effects) of medication administration. Other rights that are important: the right drug preparation, right expiration date, right assessment, right

evaluation, the right to receive drug education, the right to refuse a drug.

Prerequisite of administrating any drug to a patient is for the nurse to read the label on the

package or bottle of the drug. In order to ensure that administration of medication is safe it is

imperative that the nurse remembers the 6 rights.

RIGHT PATIENT: check patients identity against the identification band and prescription chart.

RIGHT MEDICINE: check the prescription is legible, signed by an authorized prescriber and that it matches the label on the medication. Its important to ensure the

drug hasnt passed the expiratory date and to understand the reasons why the medication

is prescribed and that the patient doesnt have any allergies to the medication. Prescriber

should use the generic name rather than a trade name on the prescription.

RIGHT DOSE: check that correct dosage has been prescribed and carry out any calculation required to ensure the correct amount administered. Check that the maximum

daily dose has not been exceeded

RIGHT ROUTE: check prescribed route is appropriate for the patient and suitable preparation is available.

RIGHT TIME: check medication is given at the prescribe time and whether should be before or after meals.

RIGHT DOCUMENTATION: check the prescription chart is signed to state that the medication has been given. If not given reason must be documented. The effect observed

or side effect of the drug reported by patient must be documented

Intravenous fluid therapy involves the administration of

water nutrients (dextrose, protein, fats and vitamins) electrolytes (e.g. sodium, potassium, chloride)

blood products medications

A PHYSICIANS ORDER for intravenous fluid therapy must include the type/name of solution the dose

the unit of dose is expressed as a quantity to be given in unit time and it includes the following two:

quantity of solution in mililitres, litres, milligrams, grams, international units, or equivalent

unit time period/duration for administration in seconds, minutes or hours

the quantity of the solution to be administer or the total time duration of administering the dose

infusion rate in milliliters per second, minute or hour or drops per second, minute or hour) e.g. some institutions or areas (paediatrics)

THE NURSE is responsible for regulating infusion rate by: Calculating flow rate { milliliters per hour (ml/h)} Choosing a drop factor and Selecting the appropriate IV set with chosen drop

factor

Calculating the drip rate (gtt/min) that is needed to deliver the ml/h with the chosen drop factor.

Regulating the number of drops entering the drip chamber by using the roller clamp on the tubing to adjust the flow rate ( count number of drops for one

minute) or the infusion pump

Regularly checking whether the drip is flowing at the calculated rate i.e. hourly The flow rate is regulated either

manually by straight gravity via an electronic infusion pump or controller

A controller electronically regulates drop rate by gravity Whereas an infusion pump consistently exerts pressure against the tubing

or the fluid at preselected rate.

Intravenous set or intravenous tube has a drip chamber at one end of the IV tubing that connects the tubing to the IV solution (bag or bottle)

The IV solution must pass through this drip chamber which has an opening that regulates the drops/ml (gtts/ml) that enters the tubing.

IV SET/GIVING SET/INFUSION SET: A drop is abbreviated gtt, with gtts used for the

plural. These abbreviations come from gutta, the Latin for drop .The gtt/ml (drop factor), which

varies according to the manufacturer of the tubing will be displayed on the tubing package. The

eye of the dropper greatly influences the actual number of drops required to move 1 mL of fluid

into the drip chamber. Drop factor is the number of drops through the eye of dropper of a given

set that is required to move (infuse) 1ml of the fluid into the drip chamber (i.e. patient). The

label on the tubing box will indicate the dropper capacity of the specific tubing used*. The

calibration of IV tubing in gtt/ml is known as the drop factor. Common macrodrop factors are 10

gtts/mL, 15gtts/mL, 20gtts/mL and the common microdrop factor are 40gtts/ml, 50gtts/ml and

60gtts/mL. Determine drip capacity by choosing the microdrop chamber or macrodrip chamber.

If you are infusing UNDER 60 ML/HR., then choose a MICRO OR MINI DRIP SET which

delivers 40-60gtts/ml.

The SIZE OF CANNULA required will be determined by the type of fluid to be infused and

the size and condition of the patients veins. The smallest gauge capable of achieving the

required flow rate should be used (RCN 2010).

The administration sets are constructed so that the orifice in the drip chamber delivers a

predictable number of drops for each milliliter of fluid. The most common sets are called

macrodrip sets. These deliver 10-20drops per ml. These sets do vary, so consult the

manufacturers package for a correct figure. Remember that this figure is correct for regular,

water-type fluids; when very viscous fluids, such as those containing amino acids and fats, are

given, the drops per ml may be fewer. (The figure is usually supplied with the product). Most

manufacturers also supply microdrip sets. These sets deliver 40-60 drops per ml and can be

identified by the fine metal orifice in the drip chamber. Blood administration sets are

characterized by a larger lumen, which delivers fewer drops per ml, and a large built-in filter in

the drip chamber, which removes any clots or precipitates in the blood. Giving set is to replace

every 72hours for safety and prevent entry of microorganism. Blood or parenteral nutrition

giving sets should be change more frequently

*Check tubing package-may be 10, 15, 20 (macrodrip) or 40, 60(microdrip) gtt/ml. Microdrip is

selected if Flow Rate calculated or stated is less than 60 ml/hr.

Patients can receive a medication through a port in an existing IV line. This is called

INTRAVENOUS PIGGYBACK (IVPB): The medication is in a secondary bag. The secondary

bag is higher than the primary bag so that the pressure in the secondary line will be greater than

the pressure in the primary line. Therefore, the secondary medication infuses first. Once the

secondary infusion is completed, the primary line begins to flow. Be sure to keep both lines

open. If you close the primary line, when the secondary IVPB is completed the primary line will

not flow into the vein. A typical IVPB order might read: cimetidine 300 mg IVPB q6h in 50 mL

NS infuse over 30 min. This is an order for an IV piggyback infusion in which 300 mg of the

drug cimetidine diluted in 50 mL of a normal saline solution must infuse in 30 minutes. So, the

patient receives 300 mg of cimetidine in 30minutes via a secondary line, and this dose is

repeated every 6 hours.

A primary IV line (right) and an IVPB (or secondary) line (left). Fluid flows continuously through the primary line into the patient/clients vein. At timed intervals, medication placed in an IVPB is attached by tubing to the primary IV for delivery to the patient/client. The primary fluid is lowered and the IVPB fluid flows. After the IVPB has infused, the primary fluid begins infusing again. An IV infusion pump may also be used, where medication in the IVPB is infused through the pump.

Some IV medications are administered not continuously but only intermittently, such as every 4,

6, or 8 hours. This route is termed intravenous piggyback or (IVPB). The term admixture refers

to the premixed IVPB.

Most of these drugs are prepared in powder form. The manufacturer specifies the type and

amount of diluent needed to reconstitute the drug; later, you, the nurse, connect the IVPB

(containing the reconstituted drug) by IV tubing to the main IV line. Some IVPB medications

come premixed from the manufacturer.

For other medications, the institutional pharmacy may reconstitute and prepare IVPB solutions in

a sterile environment using a laminar flow hood. This procedure saves nursing time, because

when you are ready to administer the drugs, they have already been prepared, labeled, and

screened for incompatibilities.

Nevertheless, the nurse still bears considerable responsibility: You must check the diluent and

volume.

You must also check the dose and the expiration date of the reconstituted solution; note whether

the

IVPB should be refrigerated before use or whether it can remain at room temperature until hung.

Finally, you must calculate the drip rate and record this information on the IVPB label before

hanging the bag.

CHOOSING THE INFUSION SET Experience will enable you to judge which IV tubing to use. In clinical settings, the guidelines

below will help you make your choice. An electric infusion pump poses no problem, because it

will deliver the amount programmed. Specialized pumps in neonatal and intensive care units can

deliver 1 mL/hour and even less. Specialized syringe pumps also can deliver less than 1

mL/hour.

When an IV pump is not available, consider these guidelines:

Use microdrip when

The IV is to be administered over a long period

A small amount of fluid is to be infused

The macrodrops per minute are too few (Without an infusion pump, IV fluids flow by gravity.

Blood flowing in the vein exerts a pressure. If the IV is too slow, the pressure of the blood in the

vein may back up into the tubing, where it may clot and cause the IV to stop infusing.)

Use macrodrip when

The order specifies a large amount of fluid over a short time

The microdrips per minute are too many, and counting the drip rate becomes too difficult

INFUSION RATE CALCULATION Generally there are at least three methods employed in medication calculation. These are

dimensional analysis, proportion and formula method. No one method is best for solving every

type of problem. Several good approaches are available, however one of the best is dimensional

analysis as the name implies, in dimensional analysis we use the units (dimensions) that are a

part of measurements to help solve (analyze) the problem.

Rule #1 in drug calculations - STICK TO ONE METHOD!

1: DIMENSIONAL ANALYSIS/DEDUCTION METHOD Is a process of manipulating units, which are actually descriptions of numbers, to solve mathematical

equations. This method of mathematic problem solving is used in chemistry with great success. The

goal of this approach to drug calculation problem solving is to:

CANCEL OUT UNWANTED UNITS LEAVING ONLY THOSE UNITS YOU WANT

YOUR ANSWER TO BE EXPRESSED AS! Think of Unit Equivalence as a link that will help you get the desired units you are solving for.

It involves calculating the unknown variable using its units to deduce a formula.

(Also known as factor analysis, factor-label method, or unit-factor method, chemistry math).

This method involves the logical sequencing and placement of a series of ratios (termed factors)

into an equation. The ratios are prepared from the given data as well as from selected conversion

factors and contain both arithmetic quantities and their units of measurement. Some terms are

inverted (to their reciprocals) to permit the cancellation of like units in the numerator(s) and

denominator(s) and leave only the desired terms of the answer. One advantage of using

dimensional analysis is the consolidation of several arithmetic steps into a single equation.

The Mathematical Foundation for Dimensional Analysis Dimensional Analysis relies on two simple mathematical concepts.

Concept 1: When a nonzero quantity is divided by the same amount, the result is 1.

For example: Because you can also write a division problem in fractional form, you get

Since

is a fraction equal to 1, and the word unit means one, the fraction

is called a unit

fraction.

In the preceding unit fraction, you may cancel the 7s on the top and bottom. That is, you can

divide both numerator and denominator by 7.

Units of measurement are the labels, such as inches, feet, minutes, and hours, which are

sometimes written after a number. They are also referred to as dimensions, or simply units. For example,

in the quantity 7 days, days is the unit of measurement.

The equivalent quantities you divide may contain units of measurement.

For example:

Or in fractional form:

In the preceding unit fraction, you may cancel the number 7 and the unit of measurement days on

the top and bottom and obtain the following:

Going one step further, now consider this equivalence: Because 7 days is the same quantity of time as 1 week, when you divide these quantities, you

must get 1.

So, both and

Or in unit fractional form:

and

Other unit fractions can be obtained from the equivalences.

Equivalents for some common units of measurement

12 inches (in) = 1 foot (ft)

2 pints (pt) = 1 quart (qt)

16 ounces (oz) = 1 pound (lb)

60 seconds (sec) = 1 minute (min)

60 minutes (min) = 1 hour (h or hr)

24 hours (h or hr) = 1 day (d)

12 months (mon) = 1 year (yr)

Concept 2 When a quantity is multiplied by 1, the quantity is unchanged.

In the following examples, the quantity 2 weeks will be multiplied by the number 1 and also by

the unit fractions

and

Consider the previous line again. This time you cancel the week(s)!

( )

uivalents for Some Common Units of Measurement So,

This shows how to convert a quantity measured in weeks (2 weeks) to an equivalent quantity measured in

days (14 days). With the Dimensional Analysis method, you will be multiplying quantities by unit

fractions in order to convert the units of measure. This procedure demonstrates the basic technique of

Dimensional Analysis.

Many of the problems in dosage calculation require changing a quantity with a single unit of measurement

into an equivalent quantity with a different single unit of measurement; for example, changing 2 weeks to

14 days as was done above. Other problems may involve changing rates of flow to equivalent rates of

flow.

It is important to understand the following four terms that provide the basis for dimensional

analysis.

Given quantity: the beginning point of the problem commonly the doctors order. Wanted quantity: the answer to the problem Unit path: the series of conversions necessary to achieve the answer to the problem Conversion factors: equivalents necessary to convert between systems of measurement

and to allow unwanted units to be canceled from the problem.

Each conversion factor is a ratio of units that equals 1. UNIT - a dimension that is given to a number.

For Example - If you are to give 50, you would ask, 50 what? This could be mg, mL, tablets,

teaspoons, etc. (mg, mL, tablets, tsp. are the units)

UNIT EQUIVALENCIES - the value of equivalencies between two units.

For Example: 1 kg = 2.2lbs, 5mL = 1tsp, 30mL = 1ounce,

1gram = 1000mg, 60minutes = 1hour, 15gtt = 1mL, 1grain = 60mg, 1IU=1000mIU

CONVERSION FACTOR - it is a unit equivalency written as a fraction.

or

(The above is simply stating that 60 mg is equal to 1 grain or 1 grain is equal to 60mg.both

mean the same thing regardless of how they are set up).

Conversion factors are derived from information provided in the dosage problem.

Dimensional analysis is a method of calculation in which a series of ratios or factors, organized

in the form of fractions, are multiplied.

Factors are two quantities that are related, such as 30 mg in 2 ml.

In dimensional analysis, factors are expressed as fractions.

30 mg in 2 mL may be expressed as:

o

or

One unit of measurement is converted to another unit of measurement by means of conversion

factors or unit equivalence. A conversion factor is a unit equivalence expressed as fraction such

as 2.2lb = 1 kg or 1,000 mcg = 1 mg. ie

or

Conversion factors link units of measurement of what is desired with units of measurement of what is available.

Conversion factors are arranged in the form of a fraction. o 1,000 mcg = 1 mg may be expressed as:

o

or

For example:

Covert 50 lb to kg

The Unit Equivalence (link) is: 2.2 lb = 1 kg

Note:

is another way of saying that 2.2 lb = 1 kg

The desired units we are seeking are kg in this example.

Using Dimensional Analysis in the above example, we set the problem up in the following format:

Problem: Covert 50 lb to kg

50 lb X

= 22.7 kg (lb cancel one another out and we are left with kg, the units we want)

Another way of stating this problem is: How many kg are there in 50 lb? or 50 lb is equal to how

many kg?

In this example, the units of lbs cancel each other out, leaving behind kg (the units we want our

answer to be in). We have eliminated the units we dont want and are left with the units we do want.

Note: In Dimensional Analysis we simply multiply straight across first (on both sides of the

horizontal line if applicable) and then divide. There is no cross multiplication or algebra involved in

this method of problem solving.

Note: This approach to drug calculations can be used with every type of problem. This is not true

of other methods.

Remember, drug calculation problems are simply story problems. You have to develop a

mathematical problem from the information that is provided.

Using the Dimensional Analysis approach, this can be accomplished in a few simple steps:

Determine what it is that is being asked

Determine what units your answer must be represented in (desired units)

Determine what the unwanted units are

Determine what the link (unit equivalence) is (there may be more than one link per problem, and these conversions may have to be made before the final problem can be set up)

Set up your problem so that you can eliminate unwanted units to end up with desired units

Apply this method to the problem above: Covert 50 lb to kg

Determine what it is that is being asked - How many kg are there in 50 lb? or 50 lb is equal to how many kg?

Determine what units your answer must be represented in (desired units) - kg is what we are solving for

Determine what the unwanted units are - We want to eliminate lb

Determine what the link is - 2.2 lb = 1 kg

Set up your problem so that you can eliminate unwanted units to end up with desired units

Problem: Covert 50 lb to kg

50 lb X

= 22.7 kg

lb cancel each other out and you are left with kg (the units we want)

Dimensional analysis also uses the same terms as fractions: numerators and denominators.

Numerator = the top portion of the problem Denominator = the bottom portion of the problem

Some problems will have a given quantity and a wanted quantity that contain only numerators.

Other problems will have a given quantity and a wanted quantity that contain both a numerator

and a denominator.

The problem-solving method of dimensional analysis uses the following five steps.

1. Identify the given quantity in the problem.

2. Identify the wanted quantity in the problem.

3. Establish the unit path from the given quantity to the wanted quantity using equivalents as

conversion factors.

4. Set up the conversion factors to permit cancellation of unwanted units. Carefully choose each

conversion factor and ensure that it is correctly placed in the numerator or denominator portion

of the problem to allow the unwanted units to be canceled from the problem.

5. Multiply the numerators, multiply the denominators, and divide the product of the numerators

by the product of the denominators to provide the numerical value of the wanted quantity.

In solving problems by dimensional analysis, the student unfamiliar with the process should

consider the following steps:

Step 1. Identify the given quantity and its unit of measurement.

Step 2. Identify the unit of wanted quantity (the unit of the required answer).

Step 3. Establish the unit path (to go from the given quantity and its unit to the arithmetic answer

in the wanted unit), and identify the conversion factors needed. This might include:

(a) A conversion factor for the given quantity and unit, and/or (b) A conversion factor to arrive at the wanted unit of the answer.

Step 4. Set up the ratios in the unit path such that cancellation of units of measurement in the

numerators and denominators will retain only the desired unit of the answer.

Step 5. Perform the computation by multiplying the numerators, multiplying the denominators

and dividing the product of the numerators by the product of the denominators.

To create an equation using dimensional analysis:

Collect all data (variables) for the questions. Step 1: draw a long straight line (magic line) and place an equals to sign at the right end

of the line.

Figure out what are you solving for (ask yourself what am I solving for?) and write its unit on the right side of the equals to sign. With space between the equals to sign and the

unit so that the value of unknown variable (what you are looking for) can be written in

the space provided after solving the equation

Step 2: Identify the first variable to be written on the left side. It can either be: The doctors order (given quantity)

or It is determined by the numerator unit of the unknown variable. The numerator

unit of the first variable should be the same as the numerator unit of what we are

solving for.

The variables are written such that the numerators and their units are on top of the magic line. The denominator and its unit are below the magic line.

If the similar unit of the selected variable is the Numerator unit then the variable is written directly. If the similar unit of the selected variable is the denominator unit then

the variable is written as an inverse so as to position the similar unit as the numerator.

Step 3: Each subsequent variable is written as a product of the previous variable and the subsequent variable is determine by

o The denominator unit of the previous variable. A variable with one of its units similar to the denominator unit of the previous variable is selected as the next

variable. The numerator unit of this selected subsequent variable should be

similar (SI unit) to the denominator unit of the previous variable. If the similar

unit is the numerator unit of the subsequent variable then the subsequent variable

written directly as a multiple. If similar unit is also a denominator in the

subsequent variable then the variable should be written as an inverse so that the

similar unit can be the numerator.

o Conversion factor for the previous variable to be able to cancel out the unwanted units

Step 4: More variables are added until all the unwanted units on the left side cancelled out except the wanted units (one as numerator and other as denominator) similar to those

units of the unknown variable (units of what you are looking for)

Note check whether each variable needs conversion and convert it (by multiplying it with a conversion factor) before writing the subsequent variable.

Note if a variable has two units first one is the numerator and the second the denominator.

Multiplying by variable as an inverse is equal to dividing by the variable. A/B= 1B/A so if the

desire unit is in a position opposite to its required position then we inverse the variable.

If drops is the numerator unit of the unknown variable or the denominator unit of the previous

variable, then we need to identify a variable with one of its units as drop to be selected as the

first variable after the equals to sign or as the subsequent variable respectively. Secondly if drops

is the numerator unit of the selected variable then the selected variable be written directly for

the first variable on the left side of the equals to sign but if its the denominator units of the

selected variable then the subsequent variable will be written as an inverse.

The variables are written as a product of one another (multiplication). The next variable to be

multiple is determined by the denominator unit of the previous variable.

USING SEQUENTIAL METHOD (OTHER WAY) Start with the unit of measurement that is to be calculated:

o For example, to convert mcg to mg, mg are desired, so start with: mg =

Find the quantity with the same unit of measurement or the conversion factor with the same unit

of measurement as what is desired (1 mg = 1,000 mcg) and place this (mg) in the numerator.

Remember, fractions are set up as the numerator over the denominator:

o

The fractions are arranged so that unwanted units cancel out and desired units remain.

A single quantity not associated with a related quantity is expressed as a fraction by placing it in the numerator and placing 1 in the denominator.

o

If mcg are available and mg are desired, arrange the conversion factor such that mcg may be

cancelled out to leave mg remaining:

Mg=

Cross out the identical units that are across and diagonal:

Mg=

In dimensional analysis, fractions are multiplied. To multiply fractions, first multiply across the

numerator, and then multiply across the denominator. Finally, divide the numerator by the

denominator.

Equations involving multiple factors are arranged so that the unit of measurement in the

denominator of one factor is placed in the numerator of the following factor and so on.

Unwanted units are then cancelled.

Remember: o A single quantity not associated with a related quantity is expressed as a fraction

by placing it in the numerator and placing 1 in the denominator.

o Factors are two quantities that are related. Related quantities are arranged as fractions.

Process of calculating dosage using dimensional analysis:

MEDICATIONS:

STEP 1: What is to be calculated?

What is the unit of measurement that is to be calculated?

STEP 2: What quantities are needed? Needed = desired

The quantity needed may be the prescribed dosage.

STEP 3: What quantities are available? Available = have

STEP 4: Are conversion factors needed to find the units that are to be calculated?

Conversion factors link units of measurement of what is available with units of

measurement of what is to be calculated.

STEP 5: Set up an equation of factors using needed and available quantities and the

conversion factors.

STEP 6: Multiply the numerator.

Multiply the denominator.

Divide the numerator by the denominator.

STEP 7: Reassess to determine if the amount makes sense.

IV Flow Rates

To determine mL/hr when administering fluid via an IV pump, the process is the same as the ratio and proportion/desired over have methods.

When calculating gtt/min, follow these steps: o STEP 1: What is to be calculated?

What is the unit of measurement that is to be calculated? gtt/min

o STEP 2: What quantities are needed? Needed = desired The quantity needed may be the prescribed dosage. Volume (mL)/infusion time (min or hr)

o STEP 3: What quantities are available? Available = have Drop factor (gtt/mL)

o STEP 4: Are conversion factors needed to find what is desired? 60 min = 1 hr

o STEP 5: Set up an equation of factors using needed and available quantities and the conversion factors.

If minutes are available, the process is the same as the ratio and proportion/desired over have methods.

If hours are available:

IV flow rate(gtt/min) gtt/min=

( )

( )

Cancel out identical units:

IV flow rate(gtt/min) gtt/min=

( )

( )

o STEP 6: Multiply the numerator. Multiply the denominator.

Divide the numerator by the denominator.

o STEP 7: Reassess to determine if the amount makes sense.

EXAMPLE

Calculate the drip rate of 3000mls of 5% dextrose over 24hrs using an IV set with drop factor of

20drops/ml?

Collect data: Drip rate (DR) =? Volume (V) = 3000ml Concentration ( C )= 5% dextrose = 5g dextrose in 100ml of 5% dextrose solution = 5g/100ml Time (T) = 24hrs Drop factor (DF) = 20drops/ml

METHOD 1(SEQUENTIAL METHOD)

STEP1: Identify the wanted variable (unknown variable/ what you are looking for) and its unit.

Drip rate drops/min Step2: Identify the given quantity (doctors order) and its units.

3000ml in 24hrs Step 3: Identify known equivalent or conversion factors.

5% dextrose =5g/100mL, 20drops/min, 60min/hr

Step 4: Draw the magic line

---------------------------------- STEP 4a: Write the given quantity with its units at the beginning of the line making sure the

numerator is above the line and denominator is below the line.

STEP4b: Write an equal to sign at the end of the magic line.

STEP4c: Write the units of the wanted variable after the equals-to sign making sure you leave

some space between the equals to sign and the unit of the wanted quantity.

Step5: Place the equivalent or conversion factors so that the unwanted units cancel out until the

wanted units similar to units of wanted quantities are left.

STEP6: Multiply all the numerators.

Multiply all the denominators

Divide the two values and record it in the space provided

METHOD 2 (RANDOM METHOD) Step 1: Unknown variable (what are you looking for- wanted quantity) is drip rate (DR)

and its unit is drops/min.

= drops/min Step 2: Write the given quantity with its units at the beginning of the line making sure the

numerator is above the line and denominator is below the line.

Step 3a:insert all the conversion factors without order making sure all unnecessary units are cancelled out ie 1hr=60mins, 20drops=1ml

Step 3b: need conversion factor to covert hours to minutes and relationship of hours to minutes is 1hr=60min, i.e. 1hr/60min. DR (drops/min) = 20drops/min x 3000ml x 1/24hrs

x 1hr/60min= 41.67drops/min=41drops/min

Our equation has now same units on both sides of the equation if we cancels like ones out hence we can now solve the equation.

Step 4; compute your answers by multiplying all the numerator and multiplying all the denominators then dividing the two results

Question 19 below:

A:

Data collection: Concentration ( C ) = 1.5%=1.5g of glycine in 100ml of 1.5% glycine solution=1.5g/100ml Flow rate (FR) = 80ml/min (doctors order) Gram (M) = ? Time (T)=3hrs

METHOD 3(SEQUENTIAL-ANOTHER WAY) STEP1: Identify the wanted variable (unknown variable/ what you are looking for) and its unit.

mass grams g Step2: Identify known variable with numerator unit as the wanted quantity.

1.5g/100ml Step 3: Identify known equivalent or conversion factors.

1.5% glycine= 1.5g of glycine in 100ml of 1.5% glycine solution= 1.5g/100ml Time 3hours 60min=1hr

Step 4: Draw the magic line

---------------------------------- STEP 4a: Write the known variable with numerator the same as the wanted quantity at the

beginning of the line making sure the numerator is above the line and denominator is below the

line.

STEP4b: Write an equal to sign at the end of the magic line.

STEP4c: Write the units of the wanted variable after the equals-to sign making sure you leave

some space between the equals to sign and the unit of the wanted quantity.

Step5: Place the equivalent or conversion factors so that the unwanted units cancel out until the

wanted units similar to units of wanted quantities are left.

STEP6: Multiply all the numerators.

Multiply all the denominators

Divide the two values and record it in the space provided

QUESTION:

An IV of 1000ml of 5% D/0.9% NaCl is started at 8pm. The flow rate is 38drops per minute, and

the drop factor is 10drops per milliliter. At what time will this infusion finish?

ANSWER:

SEQUENTIAL METHOD

Given quantity: 1000ml (volume to be infuse)

Known equivalences (conversion factors): 10gtt/ml (drop factor)

38gtt/min (flow rate)

1hr=60min

Wanted quantity: hr? (Time)

=4hrs 23min

Time of finish will be 8pm + 4hr 23min= 12:23am

EXAMPLE

The prescriber writes an order for 1000ml of 5% D/W with 10units of Pitocin (oxytocin). Your

patient must receive 3mU of this drug per minute. Calculate the flow rate in microdrops per

minute.

ANSWER

SQUENTIAL METHOD

Given quantity: 3mU/min (dosage rate)

Known equivalences: 10units/1000ml (strength)

60gtt/ml (standard microdrop drop factor)

1unit=1000mU

Wanted quantity:?mcgtt/min (flow rate)

EXAMPLE

Gynaecologist performing hysteroscopy uses 1.5% Glycine as distending medium. If the flow

rate is 80ml/min, how many grams of glycine will the infusion into the uterus if the operation

lasted for 3hrs? If the flow rate is change to 100ml/min what is the dose of glycine infusion? If

the drop factor of the IV set is 10drops/ml what is the new drip rate? The assistant changes the

giving set to give 10drops/sec in order to be able to give 150mg/min. what is the new flow rate in

ml/min. what is the drop factor of the new IV set?

SEQUENTIAL METHOD

Given quantity =80ml/min (doctors order)

Wanted quantity (what am looking for) amount grams g

Unit equivalencies: 1.5% glycine i.e. 1.5g/100ml

Time 3hrs

60min=1hr

Hence

Unit path way

SEQUENTIAL METHOD (OTHER WAY)

Data collection: Concentration (C) = 1.5%=1.5g of glycine in 100ml of 1.5% glycine solution =1.5g/100ml

Flow rate (FR) = 100ml/min (doctors order)

Dose (D) =?

Dose (g/min) =

SEQUENTIAL METHOD

C:

Data collection: Flow rate (FR) = 100ml/min

Drop factor (DF) = 10drops/ml

Drip rate (DR) =?

Drip rate (drops/min)

SEQUENTIAL METHOD

Wanted quantity drip rate drops/min

Given quantity 100ml/min

Unit equivalent drop factor 10drops =ml

Unit path

E:

RANDOM METHOD

Data collection: Concentration (C) = 1.5g of glycine in 100ml of 1.5% glycine solution =1.5g/100ml

Dose (D) = 150mg/min

Drip rate (DR) = 10drops/sec

Flow rate (FR) =?

Flow rate (ml/min)

Note because variable available is 1.5g/100ml and variable need should have ml as numerator

hence the variable is inversed. Also changing gram to mg and to cancel both g and mg variable

need is 1g/1000mg, i.e. 1g=1000mg

:

RANDOM METHOD

Data collection:

Concentration (C) = 1.5%=1.5g of glycine in 100ml of 1.5% glycine solution =1.5g/100ml

Dose (D) = 150mg/min

Drip rate (DR) = 10drops/sec

Drop factor (DF) =?

Drop factor (drops/ml)

=

SQUENTIAL METHOD

Given quantity dose=10drops/sec

Wanted quantity drop factor drops/min

Unit equivalent drip rate 150mg/min

1.5mg/100ml

1min=60sec

1g=1000mg

The physician has ordered 500mL D5W with 10units oxytocin intravenously. Begin at 1mU/min

and then increase by 1mU/min every 30minutes until active labor is achieved. Maximum dose is

28mU/min.

A: Calculate the IV rate (ml/hr) for the beginning infusion

B: Calculate the IV drip rate for the beginning infusion.

C: What is the maximum IV rate(ml/hr) the Pitocin infusion may be set for?

D: What is the maximum IV drip rate the Pitocin infusion may be set for?

A: data

Given quantity; dose = 1mu/min

Wanted quantity; flow rate = ml/hr

Unit equivalents; 500ml=10unit, 1000mU=1unit, 60min=1hr

Unit path:

D: data

Given quantity; dose =28mU/min

Wanted quantity; drip rate = drops/min

Unit Equivalent; 60gtt=ml, 10unit=500ml, 1000mU=1unit,

Unit Path;

Ratio: is the numerical relationship between two dimensions (units). It means part per part it can

be express as

A: B

A/B

Ratio can be converted into fraction which can be converted to decimals which can also be

converted to percentages. Eg

1:2=1/2=0.5=50%

Ratio 1:2 means 1part per 2parts e.g. 20mg/ml means 20mg of solute per ml of solution.

2: RATIO & PROPORTION A ratio is the same as a fraction: it indicates division. A ratio is used to express a relationship

between one unit

or part of the whole. A slash (/) or colon (:) is used to indicate division, and both are read as is

to or per.

The numerator (N) of the fraction is always to the left of the colon or slash, and the denominator

(D) of the fraction

is always to the right of the colon or slash. With medications, a ratio usually refers to the weight

of a drug (e.g., grams) in a solution (e.g., mL). Therefore, 50 mg/mL = 50 mg of a drug (solute) in 1 mL of a liquid (solution). For the ratio of 1 part to a total of 2 parts, you can write 1:2 or 1/2.

A proportion is two ratios that are equal. A proportion can be written in the fraction or colon

format. In the fraction format, the numerator and the denominator of one fraction have the same

relationship as the numerator and denominator of another fraction (they are equivalent). The

equals symbol (=) is read as as or equals. In the colon format, the ratio to the left of the double colon is equal to the ratio to the right of the

double colon. The double colon (::) is read as as. You can also use an equals symbol (=). The first and fourth terms are called extremes and the second and third terms are called the means.

Is the relationship between two ratios. It equates two ratios.

There are two ways of expressing proportions. It use variables with one common unit and based

on their units it relates them through proportion to find the unknown variable. It uses the

common unit between the variable to find the unknown. It is commonly used to calculate drugs

doses and injections. It may sometimes needs multiple steps before the final answer

PROPOTIONS EXPRESSED AS TWO RATIOS: This uses the relation of the various variables as proportion to one another. Its works on lot of logic deduction base on how

one variable is related to the next base on their common unit. It is easier for use by those

with poor mathematical skills. It does need the nurse to memorize any formula hence best

for most nurse and health care worker. Example if drop factor 15drops/ml of drop rate is

45drops/min. flow rate in ml/min will be: the common unit between the two known

variables is drops and the unit of the unknown variable is ml/min.

Hence: 15drops :1ml=45drops : x

PROPORTION EXPRESSED AS TWO FRACTIONS: It is similar to proportion but put the units into fractions rather than proportion. 15drops/1ml = 45drops/x

In proportion expressed as 15drops:1ml=45drops:3ml. The two inner values are called the

means and the outer values are called the extremes. The product of the means is equal to the

product of the extremes. I.e. 1ml45drops=15drops3ml.

A proportion consists of two ratios of equal value. The ratios are connected by a double colon

(::), which symbolizes the word as. 2 : 3 :: 4 : 6

Read the above proportion: Two is to three as four is to six.

The first and fourth terms of the proportion are the extremes. The second and third terms are the

means. 2 : 3 :: 4 : 6

2 and 6 are the extremes

3 and 4 are the means

A helpful way to remember the correct location of the extremes and means is

E = The end of the problem

M = The middle of the problem

In a proportion the product of the means equals the product of the extremes because the ratios are

of equal value. This principle may be used to verify your answer in a proportion problem.

3 4 = 12, product of the means 2 6 = 12, product of the extremes If three terms in the proportions are known and one term is unknown, an x is inserted in the

space for the unknown term. 2 : 3 :: 4 : x

RATIO AND PROPORTIONS

Ratio is same as fraction Use to express a relationship between two units or quantities A slash (/) or colon (:) is use to indicate division and both are read as is to or per With medication usually refers to weight of drug (i.e. gram) in a quantity of the

solution ( i.e. ccs)

50mg/cc= 50mg of a drug (solute) in 1cc of a liquid (solution) A proportion states that two ratios are equal

In fraction form where two fractions are equal1/3=3/9 Colon form e.g. 1:3 :: 3:9

Frequently in dose calculation problems one quantity is known ( i.e. 100mg per mL = 100mg/1mL) and it is necessary to find an unknown quantity because the physician has

ordered something different from what is available ( i.e. 75mg)

In proportion problem the unknown quantity (? mL) to give 75mg is identify as x

SOLVING A SIMPLE PROPORTION PROBLEM 1. Multiply the extremes.

2. Multiply the means.

3. Place the product that includes the x on the left of the equal sign and the product of the known

terms on the right of the equal sign.

4. Divide the product of the known terms by the number next to x. The quotient will be the value

of x.

COLLECT ALL THE DATA FOR THE QUESTION

Step 1: Identify the unknown variable

Step 2: Identify a variable that has one of its unit similar to one of the unit of the unknown

variable.

Step 3: Identify a second known variable that has its numerator unit similar to the other unit of

the selected variable.

Step 4: Relate the two selected variables as a ratio or as a fraction inn order to help in finding the

second unit of the unknown variable.

Step 5: solve for the unknown.

Pitocin (oxytocin) 10 units/1,000 mL RL, start at 0.5mIU/min increases by 1 mIU/min q20

minutes. What is the rate of flow in mL/h for the initial dose of Pitocin? The drop factor is

60mcgtt/ml. Calculate the flow rate in mcgtt/min.

Data collection:

Concentration (C) = 10units/1000ml

Dose (D) = 0.5mIU/min at 1mIU/min

Time (T) =20mins

Flow rate (FR) =?

Drop factor (DF) = 60mcgtt/ml

Drip rate (DR) =?

Step 1: unknown variable is flow rate (FR) and its unit is ml/min

Step 2: variable 10unit/1000ml has one of its unit similar to the unknown variable flow rate.

Step 3: variable 0.5mIU/min has one of its units similar to the identified variable 10IU/1000ml.

Step 4: relate the two variables:

10000mIU: 1000ml :: 0.5mIU: x or 10000mIU 1000ml= 0.5mIU x

Step 5: x=

= 0.05ml

Hence 0.05ml is given in one minute i.e. flow rate is 0.05ml/min.

b. 60gtt:1ml::Xgtt:0.05ml

60gtt0.05ml=1mlXgtt

Xgtt =

=3gtt

Drip rate =3gtt/min

3: FORMULA METHOD This uses various formulas in the medication calculation. These formulas need memorization. It

is faster and less tedious if the formula is remembered. In certain instances the nurse (health care

worker) may forget the formula or even memorize the wrong one. This may lead to giving wrong

amount of medication to the patient with detrimental effects

First step is to calculate the flow rate, this value would then give you a crude idea as to whether

to choose microdrop or macrodrop as your drop factor then second step is drip rate can be

calculated by using the product of flow rate and the drop factor. Hence

STEP ONE: The flow rate is calculated either by dividing the total volume (in millilitres) prescribed for the patient by the

number of hours required for the delivery. This gives the flow rate in milliliters

per hour (ml/hr).

( ) ( ))

( )

or by dividing the dose of the medication by the final concentration into which the drug/ medication is prepared.

Flow RATE (FR)= ( )

( )

Dose is amount per unit time. It is calculated by dividing amount of drug over by the time to give the drug.

( ) ( )

( )

Concentration is the amount of drug per unit volume of the solution. It is amount of drug divided by the total volume of the solution.

( ) ( )

( )

STEP TWO: The flow rate (ml/hr) is then multiplied by the drip factor of the selected, chosen or identified giving set(nominal number of drops per ml) to give the drip rate i.e.

the total number of drops required per hour(Dougherty and Lister 2004): note if flow rate

is less than 60ml/hr. a microdrip is chosen.

To obtain the number of drops required per minute, divide the number of drops per hour by 60 (number of minutes in 1 hour):

To calculate (flow rate) milliliters per hour you need two pieces of information The total volume to be infuse in milliliters The total time for infusion in hours

Use this standard formula ( )

( ) (

Example: from question 1 of the problem below we are to give 1000ml D5/RL in 8hrs hence

To calculate the time of infusion you need Total volume of infusion (milliliters) Rate of infusion (milliliters/minute or hours)

Use the formula

( )

( ) ( )

Example If Doctor ordered that patient should be giving 2L of NS at a rate of 100ml/hr.

To calculate drops per minute (drip rate), you need two pieces of information

Flow rate Drop factor Use the formula

( ) ( ) ( ) Note: variables should be converted to similar units before inserting into the formula.

FOR FLUID INFUSION

( ) ( )

( ) ( )

Other formula includes

Desired Over Have Times Vehicle Drug Formula - This formula is useful when

solving problems that involve oral and injectable drugs. One must have the

following information in the story problem in order to use this formula:

Dose Required = Desired = D Dose on Hand = Have = H Vehicle = How Drug is Supplied = V Give = What We Will Actually Give To Our Patient = G

( ) ( )

( ) ( )

From the information that is provided in the problem to be solved, certain words or

phrases can provide the reader with clues as to how to set up the problem. For

example:

The Desire or Need (what is ordered) in the problem is generally written

as follows:

- You have an order to give

- The doctors order reads, give

- The order reads

- You have an order for

- You are to give

- Your patient has an order for

- Amoxicillin 500 mg is ordered

- Gentamycin 50mg/kg is ordered (must figure this calculation out

to determine what the need or desire is)

- The recommended dose of drug A is 200-400mg/kg/day (must

figure out the range of the recommended dose)

The Have (what you physically have in your hand) in the problem is

generally written as follows:

- On hand is

- Available is

- The medication is supplied as

- The vial reads

- Amoxicillin is available in

- Your patient is receiving

- You have available

- The bottle reads

- Drug A comes in

The Vehicle (form the medication is supplied in) in the problem is

generally written as follows:

- tablets, capsules, mL, etc.

The Give is what you will actually give to the patient

Remember, many drug calculations require a multi-step approach to solving. You

may have to perform several conversions before you can actually set up the final

problem to obtain the answer you are seeking.

PERCENT Percentage is Always a division of 100 It means the hundredth part Has a symbol of % In solution (combination of solute and solvent) the % means proportion of solute per

portion of the solution. It is can be expressed as weight of solute per hundredth portion of

the solution (weight/volume)or volume of solute per hundredth volume of solution

(volume/volume)

grams of solute per 100ml or 100cc of solution for (w/v) solutions Millilitres of solute per 100ml or 100cc of solution for v/v solutions

A 5% solution means 5grams of drug (solute) per 100cc (100ml) of solution. Another way of putting it is every 100ml of the 5% contains 5g od the solute

0.9% means 0.9g of solute per 100cc of the solution e.g. normal saline (100cc(100ml) of solution contains 0.9g of NaCl)

10% means 10g of solute per 100cc (100ml)of solution e.g. 10% glucose means every 100ml of 10% glucose contains 10g of glucose

20% means 20g of solute per 100cc (100ml) of solution e.g. 20% mannitol contains 20g of mannitol for every 100ml of the solution

50% means 50g of solute per 100cc (100ml) e.g. 50% MgSO4 means every 100ml 0f the 50% MgSO4 contains 50g of MgSO4.

For example question 7 of problem below;

The label on the vial of magnesium sulphate is 50% w/v means every 100ml of the 50% MgSO4

contains 50g of MgSO4.In other words 50g of MgSO4 are contain in100mls of the solution from

the vial.

RATIO STRENGTH The concentrations of weak solutions are frequently expressed in terms of ratio strength. Because

all percentages are a ratio of parts per hundred, ratio strength is merely another way of

expressing the percentage strength of solutions or liquid preparations (and, less frequently, of

mixtures of solids). For example, 5% means 5 parts per 100 or 5:100. Although 5 parts per 100

designates a ratio strength, it is customary to translate this designation into a ratio, the first figure

of which is 1; thus, 5:100 = 1:20.

When a ratio strength, for example, 1:1000, is used to designate a concentration, it is to be

interpreted as follows:

For solids in liquids=1 g of solute or constituent in 1000 mL of solution or liquid preparation.

For liquids in liquids = 1 mL of constituent in 1000 mL of solution or liquid preparation.

For solids in solids = 1 g of constituent in 1000 g of mixture.

The ratio and percentage strengths of any solution or mixture of solids are proportional, and

either is easily converted to the other by the use of proportion.

Some medications like epinephrine are written as 1 in1000, 1in 10000, 1 in 100000 or as 1:1000,

1:10000, 1:100000.

This means 1g of solute in 1000ml of solution, 1g in 10000ml, 1in 100000ml, 1g in 1000000ml

or 1g:1000ml

TITRATING MEDICATIONS The process of adjusting the dosage of a medication based on patient response is called titration.

Titration is adjustment of the dose, either increasing or decreasing, to attain the desired patient

response. Weaning is a gradual decrease of the dose when the medication is being discontinued.

Orders for titrated medications are often prescribed for critical-care patients. Such orders require

that therapeutic effects, such as pain reduction, be monitored. The dose of the medication must

be adjusted accordingly until the desired effect is achieved. An order for a titrated medication

generally includes a purpose for titrating and a maximum dose. If either the initial dose or

directions for subsequent adjustments of the initial dose are not included in the order, the

medication cannot be given, and you must contact the prescriber. Dosage errors with titrated medications

can quickly result in catastrophic consequences. Therefore, a thorough knowledge of the

particular medication and its proper dosage adjustments is crucial. Dosage increment choices are

medication-specific, and depend on many factors that go beyond the scope of this document.

Suppose an order indicates that a certain drug must be administered with an initial dosage rate

of 10mcg/min, and that the rate should be increased by 5mcg/min every 35min for chest pain

until response, up to a maximum rate of 30mcg/min. The IV bag has a strength of 50mg/250 ml.

To administer the drug, first determine the IV rate in mL/h for the initial dose rate of 10mcg/min

Sometimes medications must be titrated. That is, the dose of the medication must be adjusted

until the desired therapeutic effect (e.g. blood pressure maintenance, normal blood sugar, normal

heart rate, adequate uterine contractions, pain control etc.) is achieved.

The order is:

Pitocin (oxytocin) start at 1 mU/min IV may increase by 1mU/min q30min until adequate uterine

contractions are achieve to a max of 10mU/min. The IV strength is10 mU/mL.

(a)Calculate the initial pump setting in mL/h.

(b)Construct a titration table for this order

Example doctor orders that a patient in labour with inadequate contractions should be augmented

with oxytocin 5miu/min and increasing the dose by 5miu every 30mins until contractions are 3-5

in 10mins lasting 40-60 seconds and maintain the dose attain to achieve 3-5contractions in

10mins. What will be the flow rate? What will be the drips rate and the increase drip rate at each

30mins?

To titrate an I.V. drug that is up and running, you can simplify the main equation by using a

single unit of ordered medication. That allows you to determine the infusion rate for a single unit

of medicationwhether its 1 mcg, 0.1 mcg, or 0.01 mcg.

Using the original order for nitroprusside 0.5mcg/kg/minute for a patient who weighs 75kg,

heres the equation youd use to identify the infusion rate for a single unit (0.1mcg) of

medication:

0.1 X 75 X 60

= 2.25 ml/hour

200

Calculate the initial I.V. pump infusion rate by multiplying the infusion rate for a single unit of

medication with the ordered amount of drug. The original order was for 0.5mcg/kg/minute; that

equals 5units of ordered medication. Thus:

5 X 2.25 = 11.25 ml/hour.

Titrate the medication by multiplying the infusion rate for a single unit of medication by the

newly desired drug dose, increasing or decreasing the infusion rate as appropriate. For example:

3 X 2.25 = 6.75 ml/hour (0.3mcg/kg/minute)

4 X 2.25 = 9 ml/hour (0.4mcg/kg/minute)

6 X 2.25 = 13.5 ml/hour (0.6mcg/kg/minute)

8 X 2.25 = 18 ml/hour (0.8mcg/kg/minute)

...and so on.

First, calculate the flow rate for a single unit of ordered medication. Then, determine the infusion

pump rate by multiplying that rate by the desired amount of drug that you want to deliver.

Intropin (dopamine) 2mcg/kg/min IVPB, titrate to maintain SBP above 90, increase by 5

mcg/kg/min q 1030 minutes. Maximum dose 20 mcg/kg/min. Monitor BP and HR q 25 minutes

during titration. The label on the 500 mL medication bag states 800mcg/ml and the patient

weighs 175 pounds.

(a) How many mcg/min of Intropin should the patient receive initially?

(b) Calculate the initial pump setting in mL/h.

Pregnancy Category The U.S. Food and Drug Administration (FDA) has established the following categories for pregnant

women:

A: No risk to the fetus in any trimester

B: No adverse effect demonstrated in animals; no human studies available

C: Studies with animals have shown adverse reactions; no human studies are available; given only after

risks to the fetus have been considered

D: Definite fetal risk exists; may be given despite risk to the fetus if needed for a life-threatening

condition

X: Absolute fetal abnormality; not to be used anytime during pregnancy

FLUID THERAPY In fluid therapy maintenance is calculated using 4, 2, 1 formula (Holliday-Segars Formula):

This was standard looking at maintenance daily fluid requirement of health children

4ml/kg/hr. for first 10kg,

2ml/kg/hr. for next 10kg

1ml/kg/hr. for remaining kilogram weight.

This can be simplified by using formula

Maintenance fluid requirement (ml/hr) = {60+ (Weight kg-20)} ml/hr for weight 20kg

Example: 65kg women who is nil per Os will require

Fluid required= 60+ (65-20)

60+45

105ml/hr of intravenous infusion

Similarly 70kg who had fasted over (night) 8hrs for elective surgery will have deficit of

Fluid deficit = 60 + (70-20)

=60 + 50ml

=110ml/hr

Hence total fluid deficit is 110ml/hr 8hr=880ml

BODY SURFACE AREA CALCULATION

Most accurate method commonly used in oncology department

Mostellers rule

( ) ( )

( ) ( )

SAFE DOSE Medications have an upper and a lower safe dosage range used to indicate a safe, total daily

dose. This is very important and emphasis in paediatric. You can find this information on the

drug package insert, a drug reference, or an institutional protocol. You need this information

before you calculate any dose to give to a child.

PAEDIATRIC DOSAGE CALCULATION Posology ( Greek pso(s) how much + -logy)

the branch of medicine concerned with the determination of appropriate doses of drugs or agents

[ from French posologie, from Greek posos how much]

1. Proportion to age Youngs formula

( )

The above formula is used for calculating the doses for children less than 12years of age

(1-12years)

Dillings formula

( )

The above formula is used for calculating the doses of a child in between 4-20years of

age

Frieds formula

The above formula is applicable only for infants(less than 1year)

2. Calculation base on body surface area Catzel rule:

The average body surface area for an adult=1.73m2

Hence

http://www.thefreedictionary.com/-logy

3. Calculation base on body weight: Clarks rule

( )

( )

The rule is applicable only when child dose is less than 150lb or 70kg

SOLUTIONS MAKING PARALLEL DILUTION.

A dilution consists of adding additional solvent (usually) to a solution to reduce its concentration.

1/10 means 1part of solute is combines with 9 parts of solvent to give 10 parts off solution. I.e. 1part of solute are in 10parts of the solution.

/ means total volume of solution

: means ratio of combination therefore 1:9 means 1part of solute combines with 9 parts of solvent

1/10 is not equal to 1:9

Parts can be any in unit. A 1ml added to 2ml produces same dilution as 1oz added to 2oz.

Serial dilution is produce by diluting a dilution rather than going back to the stock solution each time. They are made because

A number of dilutions of same dilution factor are desired Final concentration is so small that original volume needed to make it cant be

accurately measured e.g. 1ml of 1mM solution from stock of 10M.

Making a 1/10 dilution will bring you closer to the final concentration so that large

amounts can be measure. 1/10 dilution is 1part solute to 9parts water. Label your five bottles 10M (stock), 1M, 0.1M, 0.01M and 0.001M

Add ml of stock to first tube Put 900ul of water into the remaining 4 tubes Dilution1: 100ul stock combine with 900ul water gives 1M solution Dilution2:100ul dilution1 combines with 900ul water gives 0.1M solution Dilution3:100ul dilution2 combines with 900ul water gives 0.01M solution Dilution4:100ul dilution 3 combines with 900ul water gives 0.001M solution.

TEMPERATURE Measure either Fahrenheit or centigrade

The relationship of centigrade and Fahrenheit (F) degrees is

( ) ( ) Where

0C is the number of degree centigrade

0F is the number of degree Fahrenheit

Medication orders often use Centigrade temperature. To convert from Fahrenheit to Centigrade, use this

formula:

C = (F 32) 1.8

To convert from Centigrade to Fahrenheit, use this formula:

F = (C 1.8) 32

UNIT EQUIVALENT (CONVERSION) In medicine three common measurement systems are usually use. These are

Metrics system

Apothecary system

Household system. Unit is a dimension that is given to a number.

Unit equivalent is the value of EQUIVALENCE between two units. If expressed as a fraction it

is call unit conversion factor. Conversion between these units uses their unit equivalency.

Pico10-12 Nano 10-9 Micro 10-6 means dividing into million parts Milli 10-3 into thousand Centi 10-2 into hundred Deci 10-1 into ten Deka102 multiply by ten Kilo 103 Mega106 multiply by million Giga 109 Tera 1012 1cc=1ml 1000ml=1L 1000g=1kg 1000mg=1g 1000microgram=1mg 1kg=2.2ib 1000miu=1iu 1teaspoon(tsp.)=5ml 1tablespoon(tbsp.)=15ml 2.2Ib=1kg 1 oz (or fl oz) = 30 mL 1 pt = 500 mL 1 qt = 1 L or 1000 mL 2.2 lb = 1 kg 1 inch = 2.4 or 2.5 cm (centimeters)

1 minim 1 gtt

1 dr 4 mL

8 dr 1 oz or fl oz

MATH TIP Try this to remember the order of six of the metric unitskilo-, hecto-, deca-, (BASE), deci-, centi-, and milli-: King Henry Died from a Disease Called Mumps. gram liter

meter kilo hecto deca BASE deci centi milli K H D D C M

King Henry Died from a Disease Called Mumps. Relationship and value of metric units, with comparison of common metric units used in health care Prefix kilo hecto deka base deci centi mili micro

Weight kilogram gram miligram microgram Volume liter mililiter Length meter deciliter centimeter milimeter 0.000001 Value to base

1000 100 10 1 0.1 0.01 0.001 0.0001 0.00001

measurement Metric system Household system Apothecary system

volume 1gtt 1M

1ml 15gtt 15M

5ml 1tsp(60gtt) 1dr(60M)

15 1tbsp(3tsp) 1/20z(4dr)

30ml 2tbsp 1oz(dr)

180ml 1teacup 6oz

240ml 1glass 8oz

500ml 1pt(16floz)

1L(1000ml) 1qt(2pt)

4000ml 1gal(4pt)

weight 60mg 1gr

1g(1000mg) 15gr

1kg(1000g) 2.2lb

length 2.5cm 1inch

NOTE TO ALL NURSING STUDENTS

You are all very intelligent individuals, and you can be successful at

dosage calculations. Try to relax, critically think about the question, and

then set up the problem using one of the methods that you have been

shown here.

YOU CAN DO THIS!

PROBLEM

A woman is admitted to the labor room with a diagnosis of preterm labor. She

states that she has not seen a physician because this is her third baby and she

knows what to do while she is pregnant. Her initial workup indicates a

gestational age of 32 weeks, and she tests positive for Chlamydia and Strep-B. Her

vital signs are: T 100 F; P 98; R 18; B/P 140/88mmHg; and the fetal heart rate is

140150. The orders include the following:

NPO

IV fluids: D5/RL 1,000 mL q8h

Electronic fetal monitoring

Vital signs q4h

Dexamethasone 6 mg IM q12h for 2 doses

Brethine (terbutaline sulfate) 0.25 mg subcutaneous q30 minutes for 2h

Rocephin (ceftriaxone sodium) 250 mg IM stat

Penicillin G 5 million units IVPB stat; then 2.5 million units q4h

Zithromax (azithromycin) 500 mg IVPB stat and daily for 2 days

1. Calculate the rate of flow for the D5/RL in mL/h.

2. The label on the dexamethasone reads 8 mg/mL. How many milliliters will you

administer?

3. The label on the terbutaline reads 1 mg/ml. How many milliliters will you

administer?

4. The label on the ceftriaxone states to reconstitute the 1 g vial with 2.1 mL of

sterile water for injection, which results in a strength of 350 mg/mL. How many

milliliters will you administer?

5. The instructions state to reconstitute the penicillin G (use the minimum amount

of diluent), add to 100 mL D5W, and infuse in one hour. The drop factor is

10drops/ml. What is the rate of flow in gtts/min? The label on Penicillin G reads

pfizerpen (penicillin G Potassium) for injection 5million units. Additional

information 18.2ml diluent added gives 250 000units/ml, 8.2ml diluent added gives

500 000units/ml and 3.2ml diluent added gives 1 000 000units/ml of solution.

6. The instructions for the azithromycin state to reconstitute the 500 mg vial with

4.8 mL until dissolved, and add to 250 mL of D5W and administer over at least 60

minutes. What rate will you set the infusion pump if you choose to administer the

medication over 90 minutes? If drop factor is 15drops/ml, what is the drip rate?

7. The patient continues to have uterine contractions, and a new order has been

written:

Magnesium sulfate 4g IV bolus over 20 minutes, then 1g/h.

The label on the vial of magnesium sulphate is 50% w/v and IV bag states

magnesium sulfate 40 g in 1,000 mL.

(a) What is the rate of flow in mL/h for the bolus dose? If the drop factor is

20gtt/mL, determine the drip rate?

(b) What is the rate of flow in mL/h for the maintenance dose? If the drop factor is

60gtt/min, determine the flow rate in gtt/min?

What volume of magnesium sulphate was withdrawn for the bolus and how

many mililitres of magnesium sulphate was place in the IV bag?

The patient continues to have contractions and her membranes rupture. The

following orders are written:

Discontinue the magnesium sulfate.

Pitocin (oxytocin) 10 units/1,000 mL RL, start at 0.5mIU/min increases by 1

mU/min q20 minutes.

Stadol (butorphanol tartrate) 1mg IVP stat.

8. What is the rate of flow in mL/h for the initial dose of