Roman Numerals

ss ½I 1V 5X 10L 50C 100D 500M 1000_

V 5000

Rules for Roman Numerals

1. Write larger on left and decrease as you go to the right. The Arabic equivalent is the sum of the symbols.2. Do not use a symbol >3 times.3. If you need 4 symbols (4 or 9), then you must use subtraction; place smaller value symbol to the left of a larger value.4. You are limited in subtraction by which symbols are allowed. Only a symbol 1/100 or less is allowed.5. Use the largest symbol.

Fractions and Decimals

___ ____ ___ ____ . ___ ____ ___ ____ 1000s 100s 10s 1s 10ths | 1000ths | 100ths 10000ths

6.1 = “six and one tenth”208.31 = “two hundred eight and thirty-one hundredths”.215 = incorrect form – leading zero required0.215 = Correct form: “two hundred fifteen thousandths”

Decimals Addition

Line up the decimals and add.

Decimals Subtraction

Line up the decimals and subtract (include zeros to the right of the decimal for

whole numbers).

Decimals Multiplication

Do not need to line up decimals.Multiply values out.Count total places behind the decimal.Move from right to left that number of places

Decimals Division

a ÷ b a/b a divided by bMove the decimal to the right as many times as needed to make the denominator a whole number. Move the decimal an equal number of times to the right for the numerator.

Fractions

Changing mixed to Improper and Vice Versa:ex: 2 1/3 = 7/3 (2*3) + 1 = 6 + 1 = 7 3 3 3

Changing Improper (“Dolly Partons” => top-heavy) to Mixed:ex 13/7 = 1 6/7 = 1.86ex 22/3 = 7 1/3 = 7.33333333

FractionsAddition & Subtraction

(Algebra Way)

1. Write both in fractional form (a/b form).2. Rah Rah Kick (cross multiply top and multiply bottom):a + c = ad + bcb d bd

FractionsAddition & SubtractionOld School

1. Find the common denominator.2. Write equivalent fractions.3. Add or subtract.

Ex: 2 ¼ = 2 5/20 3 2/5 + 3 8/20 5 13/20

Fractions Multiplication

1. Write all in a/b form: 2 3/5 = 13/5; 6 = 6/12. Simplify. Reduce any numerator with any denominator if there is a common factor.3. Multiply straight across.4. Simplify.

FractionsDivision

Change to multiplication by using “flip” of the the fraction to the right of the division sign (denominator). [Flip = reciprocal]

Decimal Approximations

Terminating and Non-terminatingRepeating and Non-repeating

Terminating: 5/4 = 1.25 _Repeating: 5/3 = 1.66666666 or 1.6

Do not truncate repeating decimals in the middle of a problem, as this may skew your results.Ex: 3000 * 1/3 = 1000 3000 * 0.3 = 900 3000 * 0.3333333 = 999.9999

Rounding

Most rounding is to the hundredths place: 0. _ _

Look at digit in 1000ths place: 0. _ _ _

If that digit is 0 – 4, just use what you have.If that digit is 6 – 9, add 1 to the 100ths place.If that digit is 5, if there are multiple digits to the right (51-59), increase the 100ths, but if the digit is 5 and there is no digit after it, if the digit in the 100ths place is even, leave it alone; if the digit in the 100ths place is odd, add 1 to the 100ths place.

Word Problems

1. Read the problem.2. Focus on the important phrases and facts. You may find extraneous information in any problem. Filter it out.3. Organize facts: a) as ratios or b) as not ratios.4. Use appropriate labels.

Ratios

Ratios are fractions.

A ratio compares two quantities:fraction form: a/bratio form: a: b

You must reduce final answers: 6:8 => 3:4

Pharmacy Ratios

In pharmacy, a:b always means a grams g b milliliters ml

What is a 1:3 solution? 1 g 3 ml(this is a reduction, not necessarily 3 ml of solution)

Proportions declare that two ratios are equal. a/b = c/da:b = c:d – Matching labels are required.

Nancy Massengale's

Rules for Pharm Tech Math

1. Must use labels.Weight: g (grams), gr (Apothecary unit grains), mg (milligrams)Volume: ml (milliliters), L (liters), tsp (teaspoons)

2. Label position must match. Most ratios will be g/ml or mg/ml.

3. To solve: a. cross multiply. b. divide both sides by the quantity with the x (cancel labels as you go). c. Make sure the answer makes sense.

Metric UnitsVolume

Volume base is liters (L). 1 L = 1000 ml. Usually use milliliters.

To change between ml and L:L to ml: move decimals 3 places to the right.ml to L: move decimals 3 places to the left.

Metric UnitsWeight

Weight: grams (g) 1 g = 1000 mg milligrams (mg).

To change between mg and g:g to mg: move decimal 3 places to the right.mg to g: move decimal 3 places to the left.

Volumes, Weights, and

Concentrations

Volume: liquid measure: ml, tsp, quarts, etc.Weight: dry measure (amount of drug): g, mg, gr, etc.

Concentrations: amount of drug over volume (always a fraction): amount of drug volume

A:B is a concentration of weight over volume.

% Concentration

% Concentration is just a very specific concentration: the amount of drugs in grams over 100 ml. The denominator is always 100 ml.

For the purposes of this class, => indicates reduction.

Common Percent Concentrations

What is the percent concentration of the following?

1:10 10% 1 = x x = 100 10 100 10

1:100 1% 1 = x x = 100 100 100 100

1:1000 0.1% 1 = x x = 100 1000 100 1000

Common Substitution

What is the common substitution?

1 g = 1000 mg = mg1000 ml 1000 ml ml

Concentrations

amount of drugvolume

Concentrations: Look for form requested.

Mg alwaysml reduced g g or %ml 100 ml

in colon form a:b ; in fraction form

ex 30 g of D1 are dissolved in 40 ml. What is the concentration? 30 g/ 40 ml 3:4

Finding Weight Word Problems

Find the amount of active drug – looking for weight of active drug. Method: ratio and proportion.

Steps1. Write a ratio which represents the concentration. x 2. Write the other ratio as volume.3. Solve.

ex: You have 40 ml of a 15% solution. How many grams of active drug? x g = 15 g x g = 40 ml * 15 g = 6 g40 ml 100ml 100 ml

Finding Volume Word Problems

Steps1. Write a ratio for the concentration.2. Write the other ratio as weight x .3. Solve.

Ex: You have 14 grams of D1. You want a 5 g/12 ml concentration. How much sterile water do you use? 14 g = 5 g x ml = 14 * 12 ml = 33.6 ml x ml 12 ml 5 g

Metric System Prefixes

Prefix Meaning kilo 1000 * > basedeca 10 * > basecenti 100 * < base milli 1000 * < basemicro 100000 * < base

Most Common Metric System

Units, Symbols, & Conversion

Factors

Volumekiloliter kl 1000 liters = 1 klliter L liter is base unitmilliliter ml 1000 ml = 1Lcubic cc 1 cc = 1 mlcentimeter

Weightkilogram kg 1000g = 1 kggram g gram is base unitmilligram mg 1000 mg = 1 gmicrogram mcg (µg) 1000 mcg = 1mg

Metric System Conversion

Process

Conversions within the metric system are done by moving the decimal point. Each step down the list* moves the decimal 3 places to the right because you are going from a larger unit to a smaller unit.

Each step up the list moves the decimal 3 places to the left because you are going from a smaller unit to a larger unit.

*Please see the card titled “Most Common Metric System Units, Symbols, & Conversion Factors.”

AbbreviationsWhen

Cc with meals qwk once a weekAc before meals prn as neededPc after meals ut dict as directedHs before sleep act around the clockqd once a day qh every hourbid twice a day c withtid 3 times a day s withoutqid 4 times a dayq4h every 4 hoursqod every other day

Abbreviations Where

po by mouth ID into the skinod right eye IA into the arteryos left eye IT intrathecalou both eyes IC intracardiacad right ear SL under the tongueas left ear rect rectallyau both earsIM intramuscularIV into the veinSC under the skin

Abbreviations How Much

cc cubic centimeterfl fluidg gramgr graingtt drop (from Latin guttae)mg milligramsmcg microgramsaa of eachtsp teaspoonTbs tablespoon

Abbreviations Drug Form

tab tabletcap capsulepul pulvulesyr syrupsusp suspensionel elixirext extracttinct tinctureung ointment (unguent)

3 basic Systems of Measurement

Household – often used in orders to the patient. Volume (liquid): tsp, Tbs, qt, gal, pint Weight (solid): oz, lbMetric – if used in patient orders, give calibrated equipment. Volume (liquid): liters Weight (solid): gramsApothecary – use Roman Numerals for quantity for most of these. Volume (liquid): drams, scruples Weight (solid): grains, scruplesExtra Measures include International Units and milliEquivalents.

Metric to Metric Conversions

milli centi deci base deca hecto kilo 1 1 1 1 10 100 10001000 100 10

kilo kilogram kiloliterbase gram litermilli milligram milliliter (ml or cc*)micro microgram microliter

*cc = cubic centimeter

Non Metric to Metric

Conversions

1. List the conversions (can be an actual list or ratios).2. Set up the proportions.Ex 130 mg = ______ gr

130 mg = 65 mg x gr 1 gr

x gr = 130 mg * 1 gr 65 mg

x = 2 gr

Temperature Conversions

Centigrade (Celsius) to Fahrenheit:

F = (C * 1.8) + 32

Fahrenheit to Centigrade (Celsius):

C = (F – 32) * 5/9

Conversions Metric to Metric

Volume

kiloliter kl 1000 liters = 1 klliter L liter is base unitmilliliter ml 1000 ml = 1 Lcubic cc 1 cc = 1 ml centimeter

Conversions Metric to Metric

Weight

kilogram kg 1000 g = 1 kggram g gram is base unitmilligram mg 1000 mg = 1 gmicrogram 1000 mcg = 1 mg mcg or µg

Conversion Factors Volume

1 gtt (drop) = 1 minim = 0.06 ml1 teaspoon (tsp) = 5 ml1 Tablespoon (Tbs) = 15 ml1 fluid dram (fl dr) = 4 ml = 3 sc = 60 min1 fluid ounce (fl oz) = 30 ml = 8 drams1 pint = 16 fl oz1 quart = 2 pints = 1 L = 960 ml1 gallon = 4 quarts

Conversion FactorsWeight

1 oz = 30 grams = 8 drams1 g = 15.4 gr1 gr (gr I) = 65 mg1 sc (sc I) = gr xx = 1300 mg1 dram = sc iii1 pound (lb) = 454 g = 16 oz (household)1 pound = 12 oz (Apothecary & troy)1 kg = 2.2 lbs

Solid Dose Forms

1. Make sure that the units of the order and the stock match. (Do the easiest conversion, i.e., to what's in stock.)2. Make sure that the answer is within a range of measurement.3. Unit dose – should be the weight of the drug taken in a 24-hour period.

If too many tablets, “See pharm.” If tablets are not scored or capsules or other form that cannot be scored and your answer is not a whole number, “See pharm.”

Solid Dose Forms Method 1 (Ratio)

1. Write ratio of order: order dose2. write the stock ratio: weight of stock weight of stock tab cap3. Set them equal.4. Solve for “dose” (x).

Solid Dose Forms Method 2

(Order/Stock)

1. order (tab, cap) stock

ex. Order: 60 mg (tab) Stock: 20 mg

60 mg (tab) => 3 tab20 mg

AlligationMixing 2

Solutions of the Same Drug

Desired % must be between larger % in stock and smaller % in stock. If you add water, H2O is a 0% solution.

Liquid Doses Syrup

Syrup homogenous contains drug sugar (60% - 85%) antimicrobial preservative flavoring

Liquid Doses Elixir

Elixir homogenous hydro-alcoholic (both water & alcohol) used with emetics* or potent drugs

*emetic – may induce nausea

Liquid Doses Suspension

Suspension: two-phase system

1. very finely divided particles in solution → insoluble or poorly soluble2. usually stored as a dried powder that needs to be reconstituted or rehydrated.

Vehicles commonly used – sterile water NS = normal saline (0.9%)½ NS = 0.45% D5W = dextrose in a 5% solution G5W = glucose in a 5% solution

Situations Involving Liquid

Doses

1. Enlarging or reducing quantities (% remains the same)2. Dilutions or Concentrations3. Alligation & Alligation Medial4. Filling Prescriptions

Liquid Doses Enlarging or

Reducing Quantities

No change in % concentrationAs the volume increases, the amount of drug increases.As the volume decreases, the amount of drug decreases.

1. Find given. amt drug2. Write proportion. ml3. Solve.

Liquid Dose Dilutions &

Concentrations(indirect proportion)

1. Find the amount of drug.given % x g 100 ml vol orig. solution2. Find the new volume. a) If given, use it. b) If “evaporated to” → Concentration after “to” is new volume. c) If “evaporated by”, the amount referenced is removed and the new volume is the remainder.3. Set up a proportion and solve it.

Assume 100 ml if given %.

Liquid Doses Alligation

Desired % must be between larger % in stock and smaller % in stock. If you add water, H2O is a 0% solution.

L% or S% * Multiplication Factor = Associated Volume(D% - S%) + (L% - D%) * Multiplication Factor = Total Volume

Liquid Doses Alligation Medial

Combine 3 or more solutions of the same drug.

1. Find the amount of drug in each and find the sum.2. Find the new volume (either the sum of the old volumes or it is given).3. Solve. x g = sum of drug (g) 100 ml new volume (ml)

Liquid Doses Prescriptions

Dose is in ml.Same process as tablets and capsules.If stock is in mg/ml, can use either ratio or order/stock method.If stock is in mg/# ml, then use only ratio method.

Pediatric Doses(computation of Adult Dose

by Body Weight)

Label expressed as mg/kg; no set conversion, depends on manufacturer.

Ex: an adult weighs 75 kg – recommended adult dose (RAD) is 10 mg/kg.

x mg = 10 mg x = 75 kg * 10 mg = 750 mg75 kg 1 kg 1 kg

If drug does not mention pediatric dose, check with pharmacist to be sure it can be used with kids.

Pediatric Doses(Standard formula)

IF NO OTHER METHOD IS GIVEN:

Child dose = Adult dose ÷ 1.7

If pediatric medication, follow label instructions for child dose.

Pediatric Doses: Body Surface Area (BSA)

Body Surface Area (BSA): See nomogram example at the end of this document.

Potential Exam Question: What graph is used to determine the BSA?

Answer: Nomogram.

BSA always given as m2. Most doses are usually mg/m2 .

Pediatric Doses Young's Rule

Young's Rule: For children 1 – 12 years of age:

Child dose = age of child * adult dose age + 12

Pediatric Doses Clark's Rule

Clark's Rule

Child dose =

weight of child * adult dose weight + 150

Pediatric Doses Drilling's Rule

Drilling's Rule

Child dose = age * adult dose 12

Pediatric Doses Fried's Rule

Fried's Rule: Age in months for infants < 2 years old

Child dose =

age in months * adult dose 150

Pediatric Doses Webster's Rule

Webster's Rule

Child dose =

age in years + 1 * adult dose age in years + 7

Dispensing Liquid Medications

Used by very old and very young – those who cannot swallow pills.

Dosed by teaspoons, tablespoons, fluid ounces, or milliliters. Include dosing cup or syringe for fl oz or ml.

DO NOT shake medicine vigorously – gently rotate to avoid bubbles.Some can be crushed and added to apple sauce, tuna, or ice cream.

Do not break coated capsule or time-release capsules.

SAFE DOSE Recommended

Daily Dose (RDD)

The Safe Dose is what is allowed for a 24-hour period.

If there is no recommended dose for children, check with pharmacist to make sure it is safe for a child.

Ex: 1 Safe dose range “0.2 mg to 0.8 mg” – POTENT DRUG2 “150 mg – 250 mg” freer – need to see pharm3 Given as signal value – “safe dose is 300 mg”; <300 okay.

milliEquivalents(mEq)

Our body needs salt to operate our muscles.

MilliEquivalents are the number of positively charged ions per liter of salt solution.

Concentrations are expressed in equivalents per liter (Eq/L) or milliEquivalents per liter (mEq/L).

1 Eq = molecular weight of the salt (g) ionic charge (valence)

1 Eq = 1000 mEq

1 mEq = Eq in mg

Converting Eq to mEq

1 Eq = 1000 mEq

Ex:1Eq = 74 g1 mEq = 74 mg

Change g to mg – DO NOT move decimal.

Some Common Elements with

milliEquivalents

Element Atomic Weight ValenceSodium Na+ 23 1Potassium K+ 39 1Magnesium Mg++ 24 2Aluminum Al+++ 27 3Chloride Cl- 35.5 (or 35) 1Calcium Ca++ 40 2

Atomic Weight and Valence

1 Eq = Atomic Weight/Valence g

1 mEq = Atomic Weight/Valence mg

ex: Find the mEq of a calcium ion.

40 = Atomic Weight 2 Valence

1 mEq = 20 mg

mEq Word Problems

Easy: Simple Order Problem

Ex: Potassium chloride is available in a concentration of 40 mEq in 30 ml. A patient is to receive 20 mEq of KCl. What do you administer?

40 mEq = 20 mEq x = 30 ml * 20 mEq 30 ml x ml 40 mEq

x = 15 ml or 1 Tbs

mEq Word Problems

Hard: Step 1 2 3

1 Find the amount of drug. a) could be given b) set up a proportion – to find concentration or to find volume; x will always equal the amount of drug.2 Find the mEq => mg (based on atomic weight and valence: 1mEq = x mg)3 Use a proportion: 1 mEq = mEq __ mg mg

1 mEq = x mEq OR 1 mEq = # mEq # mg __ g __ mg x mg

3-Step mEq Word Problem Example

Ex: What is the number of mEq in 5 ml of a 2% solution of CaCl2?

1 2 g = x g 2 40 3 1 mEq = x mEq 100 ml 5 ml 35.5 55.5 mg 100 mg 35.5x g = 2 g * 5 ml 110 / 2 = 55.5 mg 100 ml x = 1 mEq * 100 mg 55.5 mg

x = 1.82 mEq

Reconstitution

Two types of measuring equipment:

1 Liquids2 Solids

Use the most accurate device.

Measuring Liquids

Syringe => <10 mlGraduated cylinder => >10 ml

Want to measure a solution in the least number of containers you can.

Temperature does affect accuracy:*Warm liquids expand, meaning less drug delivered.*Cool liquids contract, meaning more drug delivered.

LiquidsGlass vs Plastic

A glass cylinder is harder to read than plastic. Plastic: read on the line. Glass: read on the bottom of the meniscus.

Meniscus – found on glass – little tiny refraction of light.

To calibrate a cylinder, weigh it with 1 ml of H2O. 1 ml of H2O should weigh 1 gram at 25o C (@ 77o F).

Syringe

3 ml or 3 cc syringe

Use Top of plunger for reading

IV = intravenousIM = intramuscular

Types of Syringes

Syringes may contain minims (minim or m).Increments are often in 0.1 ml or 100 mcl (equal).

Other syringesTuberculine or TB syringe: 1 ml syringeMeasured in 0.01 ml or 10 mclUsed for allergy testing; sometimes for pediatric doses. Much smaller syringe with much smaller needle.

Insulin Syringe

Insulin Syringe – calibrate for IU or U (units)specific to the concentration of normal insulin100 U = 1 ml volume (comes with 30-gauge100 U ᵙ 1 ml volume needle attached)

Needles: 30-gauge is for insulin25-30 gauge fine needle: allergy testing pediatrics, subcutaneous injections16-18 gauge large-bore needle for IV or IM

Other Liquids Tools

Other Liquids ToolsCalibrated DropperCalibrated SpoonOral SyringeDosage Cup – Dosage Cups are hard to read

Accurate to 4 ml or 1 dram30 ml 1 fl oz dramsml fl

Solids Double Pan

BalanceCan be used for 1 gram or morePut material to be weighted on one pan and a counterbalance on the other.Use padded forceps to pick up weights – oils from fingers could accumulate, leading to inaccurate readings.Use paper called glassine – low static electricity, low adherence.

Prescription Balance

Prescription Balance can be used for from 5 to 6 mg to 120 grams.

Temperature is important because of air currents in the room. Should not work directly beneath a vent.

Torsion Balance

Torsion balance is very rare.

Ways of Administering

Drugs

Parenteral: bypasses the digestive tract; anything injected.

IV intravenous IA intra-arterialIM intramuscular IT intrathecalSC subcutaneous IC intracardiac

IV bolus – all at onceIV drip – over a period of timeCalculations: concentrations, ratio, %, weight/volume, :From Manufacturer labelBolus injection: most < 3 ccs

Bolus Calculations

Example

Order: 25 mgStock: Contains 100 mg of active drug once you add 5 ml

25 mg = 100 mg x = 25 * 5 ml x 5 ml 100 mg

x = 1.25 ml

5 ml – 1.25 ml = 3.75 ml remainder to be stored

Rehydration & Reconstitution

Rehydration & Reconstitution

Many drugs are unstable with water – mixed right before use.Usually supplied with saline solution (0.9%).

Rehydration – use water only.Reconstitution – may use water or NS (0.9%), ½ NS (0.45%), or ¼ NS (0.225%).

D5W: 5% dextrose.Ringer's Solution: lot of salts, NaCl, KCl, CaClLactated Ringer's: Ringer's Solution plus sodium lactate.

AdmixtureAdmixture: Drug or other therapeutic substance added to an IV.

Reconstituted Liquids

Reconstituted Liquids can be used in large amounts in an IV or with an admixture.

5 Different Math Problems for

Rehydration & Reconstitution

1 Reconstitution & Rehydration2 Concentration of Drug in IV3 Flow Rate, Drop Factor, and Drop Rate4 Correcting Mistakes5 Dose Per Time

Single Strength Solution

Calculations

1 Find the directions and read the label.2 Use sterile syringe and aseptic techniques.3 Weight of the powder in the vial IS NOT the weight of the active drug.

Minimize air bubbles by adding water slowly. Rotate gently – DO NOT VIOLENTLY SHAKE. Withdraw what you need, label the remainder with date, concentration of drug, amount of drug, storage information, and your name or initials.

Single Strength Solution Example

Ex: Order: 200 mg of drug; IM; directions on label of vial containing 1 g of powder indicate that adding 7.2 ml will yield a concentration of 125 mg/ml.Stock: 125 mg/ml

What do you do?

200 mg = 125 mg x = 200 mg * 1 ml x = 1.6 ml x ml 1 ml 125 mg

7.2 ml – 1.6 ml = 5.6 ml

Administer 1.6 ml of reconstituted drug.Label remainder as 5.6 ml of 125 mg/ml solution, stored as given on label. 10/16/09 BF

Multiple Strength Solutions

(usually with multiple strength directions)

A bottle of penicillin may contain a dilution table:23 ml provides 200000 U/ml18 ml provides 250000 U/ml 8 ml provides 500000 U/ml 3 ml provides 1000000 U/ml

1 See order.2 Order/Stock for each line.3 Evaluate answers for best choice.

Criteria: <3 ml, as few decimals as possible.

Multiple Strength Solution

Example*

*See Multiple Strength Solutions card for dilution table for this example

Ex: Order: 500000 U*

500000 U = 2.5 ml 500000 U = 2 ml200000 U 250000 U

500000 U = 1 ml 500000 U = 0.5 ml500000 U 1000000 U

8 ml => 8 ml – 1 ml = 7 ml

Add 8 ml to vial – use 1 ml to fill order.Label 7 ml of 500000 U/ml on 10/16/09, per label storage instructions. BF*All 4 dilutions could work.

Intravenous Flow Rates

IV drip – dispenses liquid over a period of time: 30 minutes to 24 hours.

Flow rate – fluid flows at a certain rate.

In mathematics, rate is over time. Volume TimeSet by a device called an infusion set. Can be set, altered, and monitored by a computer, tech, or nurse.Calibrated to deliver a certain number of drops (gtt) per ml.

Common Infusion Sets

#10 infusion set: 10 gtt/ml => macro drip#15 infusion set: 15 gtt/ml #20 infusion set: 20 gtt/ml #60 infusion set: 60 gtt/ml => micro drip

Isotonic

If salt concentration in the blood is too high, water is drawn from the cells and they smush up, which is not good.

If salt concentration is too low, it will drive water into the cells and they might rupture, which is also not good.

Flow Rate isVolume

Time

Flow rate is volume over time. L L ml ml gtt gtt = Drophour min hour min hour min rate

A flow rate done with gtt/min is a drop rate. All drop rates are flow rates; not all flow rates are drop rates. Flow rate is to “dog” as drop rate is to “Labrador retriever.”

Flow Rate * Drop Factor = Drop rate ex: ml x gtt = gtt min ml minALWAYS MAKE SURE LABELS CANCEL.

Flow RateWord Problems

FR = Flow RateDF = Drop Factor DR = Drop Rate

1 Read the problem.2 Find the volume.3 Find time.4 Reduce flow rate: ex: 2 L/4 hours = 1 L/2 hours = 1000 ml/120 min = 8.33 ml/min = Flow Rate.5 Find the drop factor. Usually given in problem – infusion set, microdrip, macrodrip.6 Plug into formula: FR * DF = DRRound answer (often to the next highest whole number).

Flow RateWord Problem

Example

100000 U of penicillin (D1) is added to a 1 L bag of NS and infused over 5 hours. The Drop Factor is 10 gtt/ml.

Find the Flow Rate in gtt/min.

1000 ml => 3.3 ml * 10 gtt = 33.33 gtt 300 min min ml min

34 gtt min

Admixtures

A drug or other therapeutic substance added to a large-volume IV. WE DO NOT IGNORE THE ADDED VOLUME.

IV piggyback: A separate IV that goes through the main IV.*May interrupt main IV. (Depending on

*May blend into IV. Doctor's orders)

Operates via the law of gravity.

IV Diagram

IV Admixture

IV CalculationsUsually expressed as mg/ml – could be as high as 100 ml. Amount added to IV is often very small.

Give the answer in the form requested. Results may differ slightly from State Test.

1 Compute what is needed to fill the order.2 Reconstitute or rehydrate stock (prefer <3 ml, but may be more).3 Find the amount of drug (g, mg, gr, U, mEq).4 Add the volume of the vial to the volume of the IV to derive new volume.5 Find the concentration: amount of drug * x g new volume 100 ml(IV conc. differs from vial conc.).

IV Calculation Example

Add 10 ml of a 5% solution to a 1 L bag. Find the concentration of the IV in mg/ml.

x g = 5 g x = 500 mg 10 ml 100 ml

10 ml + 1000 ml = 1010 ml

500 mg = 0.495 mg 1010 ml ml

Correcting Mistakes Example

Mistakes happen. Inform the pharmacist.

You may be able to recover.

If you add too little drug, simply add the difference.

Ex: If you add too much drug:Stock: Label: “Add 8 ml of D5W to get 250 mg/ml.” You add 10 ml by mistake. Tell pharmacist.

250 mg = x mg x = 2000 mg 1 ml 8 ml

2000 mg = x g x = 200 mg/ml 10 ml 100 ml x = 20%

Dose Per Time(could be called Dose Rate)

Dose per time is the amount of drug a patients gets over time in an IV.

amount mg g gr U mEq time min hour hour min min

Dose Per Time CalculationMethod 1

Method 1 always works.

Concentration * Flow = Dose Rate Time

mg * ml = mg ml min min

Dose Per TimeMethod 1

1 Find concentrationOrder: amount of drug.New Volume: IV + Admixture2 Find Flow Rate: volume/time.The volume is typically the same as the new volume. Time is the time the IV runs. To find FR, try FR * DF = DR if you are given gtt.3 Labels: make sure the problem is set up to cancel. Find labels of given and unknown.

Dose Per Time Method 1 Example

A L bag contains 1.5 g of D1 to be infused at a rate of 100 ml/hour. What is the hourly dose? Find the dose per time in ml/hour. FR = 100 ml/hour. Amount of drug = 1.5 g

1000 ml = 100 ml 1.5 g => 1500 mg x hour 1 hr 1000 ml 1000 ml=> 1.5 mg/ml

Concentration * Flow Rate = Dose/Time 1.5 mg/ml * 100 ml/hr = 150 mg/hr

Dose Per TimeMethod 2

(shortens time for strong math students)

1 Find the amount of drug.Ex: 30 ml of 2 mg/ml solution x mg = 2 mg = 60 mg30 ml 1 ml2 Find time. Volume = vol of IV Time x time3 Put amount . Simplify. Time

Dose Per TimeMethod 2 Example

A 1 L bag contains 1.5 g of D1 to be infused at a rate of 100 ml/hr. What is the hourly dose? Find the dose per time in ml/hr.

1 1.5 g = amount of drug2 100 ml/hr = 1000 ml / x hours = 10 hours3 1.5 g = 1500 mg = 150 mg 10 hrs 10 hrs hr

Insulin

Insulin injections are for diabetic patients.

Units of activity U-10 = 10 U ml 1 ml

Insulin for Type 1 Diabetes Standard Dose: 100 U/ml

3 Typical Syringes1 3/10: measures up to 30 U2 ½: measures up to 50 U3 1 cc or 1 ml: measures up to 100 U

Insulin Syringe

When using insulin, attempt to avoid IV injection – absorption can occur in the container or in the plastic tubing.

Insulin syringe:1 Order is given in Us or IUs and an insulin syringe is available.2 Order is given in units and you need to derive the volume administered in ml.

Ex: A doctor orders 300 U of U-100. 100 U = 300 U x = 3 ml 1 ml x ml

InsulinUnits by Weight

Most orders are in U/kg.

1 Find the weight in kilograms.2 Find the order.3 Find the stock volume needed to fill the order.

Ex: Find the total daily insulin in U if the order is 1.5 U/kg and the patient weighs 160 lbs and uses U-100. 1 kg = x kg 1.5 U = x U = 109.09 U2.2 lbs 160 lbs 1 kg 72.73 kgx = 72.73 kg 109.09 U = 100 U x = 1.09 ml x ml 1 ml

Insulin for Type 2 Diabetes

Type 2: mg %: Blood glucose is given as mg %, using actual reading & desired reading.

1 Find the difference between the two (actual & desired) for every or each reading (usually morning & evening).2 Use the given ratio for adjustment.3 Solve proportions.

Mg % Example

Order is for 0.4 ml for every 30 mg % or blood glucose over 170 mg % for each morning and evening reading. Actual readings: 300 mg % and 350 mg %. What volume is dispensed?

300 350 0.4 ml = x ml 0.4 ml = x ml -170 -170 30 mg% 130 mg% 30 mg% 180 mg% 130 180 x = 1.73 ml x = 2.4 ml

1.73 ml+2.40 ml 4.13 ml

Tuberculine Syringe

(Not Recommended)

Standard Dose: 100 U = 1 ml

ex: Order is for 70 U of U-40 insulin.

40 U = 70 U x = 70 U * 1 ml 1 ml x ml 40 U

x = 1.75 ml

HeparinRed-label drug

used for thinning blood

Heparin is a very dangerous drug. It is measured in units. It is used for thinning blood. It is available in ½ to 1 ml ampules, measured in U/hour.

Adult dose is 20000 U to 40000 U/day.

Dilute with NS, D5W, or Ringer's lactate. Stored at room temperature. Heparin usually has a different density than its admixtures. Mix thoroughly – rotate bag 6 or 7 times. It is a red-label drug – can cause death. Be careful. Usually restricted to hospital use.

HeparinCautions for Patient

1 Watch for any symptoms of bleeding.

2 Strict adherence to dosage schedule.

3 No aspirin.

Heparin Word Problems

Find ml.

Heparin orders often per kg.A dose of 90 U/kg is ordered. How many ml containing 5000 Hep U/ml for a 180-lb patient?

x kg = 1 kg x = 81.81 kg180 lb 2.2 lb

81.81 kg = 1 kg x = 7363.6362 U x U 90 U

7363.6362 U = 5000 U x =1.4727272 ml x ml 1 ml

HeparinWord Problems

Find U.

An IV of 1000 ml contains 60000 U of heparin. 60 U/ml has been ordered to infuse at 20 ml/hour.

20 ml = x ml x = 480 ml hr 24 hr

x U = 60000 U 480 ml 1000 ml

x = 60000 U * 480 ml 1000 ml

x = 28800 U

HeparinWord Problems

Dose/Time & Drop Rate

A patient gets IV drip of Sodium Heparin: 50000 U/1000 ml ½ NS.

a) How many ml/hour to get 20000 U/hour?

2000 U = 50 U x = 40 ml x ml 1 ml

b) With a macrodrip, find the drop rate.

40 ml/hour => 0.666 ml/min0.666 ml/min * 10 gtt/ml = 6.67 gtt/min => 7 gtt/min

HeparinPediatric Dose

x kg = 1 kg x = 33 kg66 lb 2.2 lb

Pediatric Dose must be intermittent – does not flow constantly. Range: 60 – 80 U/kg every 4 hours (6 times per day). Answer is a range with upper and lower values.

Ex: For a 66-lb child, calculate the range in ml of a heparin injection containing 5000 U/ml to be administered daily.lower upper60 U = x U 80 U = x U 1 kg 30 kg 1 kg 30 kgx = 1800 U x = 2400 U*6 = 10800 U *6 = 14400 U10800 U = 5000 U 14400 U = 5000 U x ml 1 ml x ml 1 mlx = 2.16 ml x = 2.88 mlUnit Dose Unit Dose

Bulk Compounding

Bulk compounding is a process which allows you to make a batch by following a formula or procedure.

Bulk CompoundingReducing &

Enlarging Formula

1 Conversion New Mix Wt Factor: Formula Wt

2 Multiply each step by the conversion factor.

Reducing & Enlarging Formula

Example

Procedure for 500 g of Antibiotic Ointment:Neomycin 2.5 gBacitracin 4.0 gPolymixin B 320 mgLiquid Petrolatum 150 gWhite Petrolatum 343.18 g

Want to make 1500 g of antibiotic ointment. How much polymixin B do I need?1500 g = Conversion Factor = 3 500 g 3 * 320 g = 960 mg of polymixin B

Bulk Compounding Using Percent

Change % to amounts.

Ex: D1 is 6%. Total weight is 400 g. How much D1?

6 g = x g x = 6 g * 400 g = 24 g100 g 400 g 100 g

Making Preparations by

Percent

1 Convert to amounts.2 Derive Conversion Factor.3 Multiply each step by the Conversion Factor.

Bulk Compound Percents

When you double a recipe given in percent, the amount will double but the percent will remain the same.

Aliquot MethodBalance of Sensitivity comes from manufacturer.Permissible Margin of Error determined by whoever controls the pharmacy.

If you are measuring very small amounts, the scale may not be sufficiently accurate due to its margin of error.

1 x Balance Sensitivity Permissible Margin of Error

Ex: A class A balance has a sensitivity of 6 mg. According to the pharmacist, the order can have up to a 2% margin of error.

1 * 6 mg = 300 mg Under 300 mg should NOT 0.02 be measured via this scale.

Pharmacy Business

MathematicsMark-Up

Mark-up can be written as an amount or as a percent.

How much “profit” is made on a sale?

“Profit” is the difference between cost and selling price.

“Profit” = Selling Price – Cost

Mark-Up as an Amount Example

The cost is $8.00. The mark-up is $20.00. What is the selling price?

Cost + Mark-Up = Selling Price$8.00 + $20.00 = $28.00

Mark-Up as a Percent

Mark-up expressed as a percentage is the amount of mark-up for each $100 of Cost:

% Mark-Up = Amt of Mark-Up 100 Cost

Mark-Up as a Percent Example

If the mark-up is 30% and the item cost is $60, what is the amount of mark-up?

30 = Mark-Up100 60

Mark-Up = 30 * 60 = $18.00 100

Selling Price = $60 + $18 = $78

Increase by a Percent: From Cost to Selling

Price

1 Add 100% to percent mark-up.2 Change to a decimal (move decimal 2 places to the left).3 Multiply by cost.

Increase by a Percent Example

Cost is $40. % Mark-Up is 80%. What is the price?

100% + 80% = 180%180% => 1.81.8 * $40 = $72

Be sure to use labels ($).

Gross and Net Profit

(Cost + Incidental Expenses) * (100% + % Mark-Up) = Selling Price

Gross Profit = Selling Price - (Cost + Incidental Expenses)

Net Profit = Gross Profit * (Net Profit Expressed as a % of Gross Profit)

“Discount” or Sale Price (Mark-Off)

1 Subtract % Mark-Off from 100.2 Change to a decimal by moving decimal 2 places to the left.3 Multiply by Selling Price.

Sale Price Example

Lotion is marked 30% off. The original Selling Price is $12.50. What is the new Sale Price?

100 – 30 = 7070 => 0.70.7 * $12.50 = $8.75

Sequential Discount vs Aggregate Discount

A sale offers a 20% Discount. You have a 10% coupon. What happens if you get both discounts in either order versus combining discounts?

$1.00 * 0.8 = $0.80 * 0.9 = $0.72$1.00 * 0.9 = $0.90 * 0.8 = $0.72$1.00 * 0.7 = $0.70

Mark-Up Profit,Mark-Off Profit or

Loss Example

An item costs $400.00. Store policy is a 50% Mark-Up. After 1 month the item is marked off 50%. What is the profit or loss if an item sells immediately versus after 1 month?

$400 * 1.5 = $600 ( - $400 = +$200)$600 * 0.5 = $300 ( - $400 = -$100)