By D. Stan Saundes
Mission Statement This manual is pepaed to help nusing students undestand and pefom the mathematics pat of nusing fo dispensing medications as pe docto s odes, no matte what the dispensing fom of the medication o the units attached to the medication. 2
Knowledge of Abbeviations Medication administation odes ae based on commonly used abbeviations. These abbeviations must be memoized and known because they epesent, among othe things, when, how much, how often, and by what oute dugs ae to be given to the patient. The abbeviations have been gouped fo easie leaning associations by both wods and phases, liquid/volume measuements and weight measuements 3
Wods and Phases Abbeviations a befoe fl Fluid c s with KVO keep vein open p afte pn as necessay without q evey ac befoe meals qs quantity sufficient ss pc afte meals half AM moning stat immediately PM aftenoon supp suppositoy BSA Body Suface Aea susp suspension cap(s) capsule(s) tab(s) tablet(s) DC Discontinue tinct tinctue elix elixi 4
HOUR - MINUTE & DOSES BY HOURS HOUR - MINUTE h hs min hou hou of sleep, at bed time minute DOSES BY HOURS qh q2h q4h q6h q8h evey hou evey two hous evey fou hous evey six hous evey eight hous 5
DOSES TIMES A DAY bid twice a day tid thee times a day qid fou times a day qd qod evey day evey othe day DRUG ROUTES OTHER THAN BY MOUTH ID intademal IM intamuscula IV intavenous IVPB intavenous piggyback SC o SQ SL subcutaneous sublingual 6
Facial Anatomy (When facing the patient you left side is the patient s ight side) AD ight ea AS left ea AU both eas OD ight eye OS left eye OU both eyes PO by mouth NPO nothing by mouth PO 7
Dug Measuement Systems Othe than labeled measuements, thee ae thee common systems of dug measuement that ae used to administe dug doses: The household system Examples: Teaspoon, tablespoon, etc. The apothecay system Examples: Minim, gain, etc. The metic system Examples: millilite, micogam, milligam, gam, etc. 8
METRIC SYSTEM (GENERAL) Quantity Geneal Unit Symbol Length mete m Weight gam g Volume lite L o l Time minute min METRIC SYSTEM PREFIXES Geneal Unit m, g, L o l, min 1 kilo k 1,000 deci d 0.1 = 1/10 centi c 0.01 = 1/100 milli m 0.001 = 1/1,000 mico mcg o μ 0.000001 = 1/1,000,000 9
Equivalents Because thee diffeent bases of dug measuing has come about ove hundeds of yeas, a system of equivalent meshing of the thee systems has evolved. Following ae lists of liquid/volume and weight abbeviations combining the thee systems, afte which the quantity measuement equivalents ae listed. 10
Liquid/Volume Measuement Abbeviations meq milliequivalent ml o ml millilite d dam oz ounce (fluid) gal gallon pt pint gtt(s) dop(s) qt quat IU intenational units tbs tablespoon L o l lite tsp teaspoon M minim U units mgtt micodop Weight Measuement Abbeviations g g kg lb mcg mg oz gam gain kilogam pound micogam milligam ounce (solid) 11
Liquid/Volume Equivalents 1 gtt = 1 M 1 d = 4mL 16 (15*) gtt = 16 (15*) M = 1 ml 1 tsp = 60 M = 5 ml 3 tsp = 1 tbs = 15 ml 2 tbs = 1 oz = 30 ml 240 (250**) ml = 1 measuing cup = 8 oz 480 (500**) ml = 16 oz = 1 pt = 2 cups 1,000 ml = 1 L = 32 oz = 2 pt = 1 qt 4 qts = 1 gal * Use eithe numbe depending on whethe numbes ae odd o even to facilitate easie math ** Use numbe in paenthesis when efeing to cups, pints, and quats othewise use fist numbe fo cc, ml, and othe metic numbes 12
Solid Weight Equivalents (RN & LPN Test: Only use 1 g = 60 mg fo all medications) 1 mg = 1,000 mcg 1 g = 1,000 mg = 1,000,000 mcg 1 g = 60 mg* 5 g = 300 (325**) mg 7.5 g = 450 (500*** ) mg 10 g = 600 (650**) g 15 g = 900 (1,000 ***) mg = 1 g 1 oz = 1/16 lb =.0625 lb 2.2 lb = 1 kg = 1,000 g * Use this elationship up to and including 5 g ** Refes to Aspiin and Tylenol equivalents only *** Real life value 13
Time Equivalency 60 minutes = 1 hou Non-Specific Unit Delivey Systems Milliequivalent (meq), Intenational Units (IU), and Units ae quantities in medication delivey systems such as milliequivalent pe tablet o IU s pe capsule not given usual units of measuements as to weight o volume as shown on the equivalent tables. As new dugs ae developed they maybe given any unit values o names. 14
Analysis of Equivalents by Ratio/Popotion 1 2 3 8 10 2 4 6 16 20 1 2 5 20 5 10 25 100 3 9 27 13.5 2 6 18 9 7 28 14 15 60 30 In geneal, factions ae not only abstact popotions. Most times, factions have dimensional units associated with them. When the numeato and denominato have the same units (dimensions), they ae called popotions such as elating two pieces of lumbe of diffeent sizes. When the numeato and denominato ae dimensioned diffeently, as in miles pe gallon o quates pe dolla, they ae called popotional ates. The setup of the initial equivalency equation must have the same units in the numeato and the denominato espectively. Pocalc math uses popotional ates to administe dosages of medicine. On the following pages, 3 methods will be shown to explain how to wok Pocalc poblems. To illustate these methods, examples will be shown using dollas and quates pe dolla fo the dimensions. Afte the illustations, pactical Pocalc poblems will be woked. 15
Solving by Equivalents (Method 1) Relationship 4/1 Relationship 1/4 4 Quates = 1 Dolla O 1 Dolla = 4 Quates How many quates equal 6 dollas? This is a diect elationship 4 Quates X Quates 1 Dolla 6 Dollas O 1 Dolla 6 Dollas 4 Quates X Quates How many times do we have to multiply the one dolla to get to the 6 dolla figue? 6 times O Do the same opeation to the numeato, multiplying by six and get the equivalent value fo the second atio 4 Quates 24 Quates 1 Dolla 6 Dollas o 1 Dolla 6 Dollas 4 Quates 24 Quates X = 24 Quates 16
Solving by Coss Multiplication (Method 2) The popotion that was setup in the equivalent Method 1, is the basis of the othe two methods of solving. 4 Quates X Quates 1 Dolla 6 Dollas Coss Multiply 4 Quates (6 Dollas)=X Quates (1 Dolla) Solve fo X 24 Quates = X Quates Being able to cancel the dolla units in the numeato and denominato is the basis of the thid method, solving by dimensional analysis. 17
Solving by Dimensional Analysis (Method 3) The key to this method is to know the pope atios that elate one dimensional unit to anothe. X = The amount of quates needed. To find X, multiply the dolla equivalence needed, so that this atio will set up the denominato units to cancel the units of the given dollas, in the numeato leaving the units of the numeato to be the esult equied to answe the question. Note: This is the same equation fom the coss multiplication in Method 2 18
Applying Method 3 Diectly to Dug Applications In the pevious example, the 6 Dollas epesents the pescibed amount and the 4 Quates pe 1 Dolla epesents the inveses of 1 Dolla pe 4 Quates as the available equivalency is geneally pesented. The equied units, based on the poblem, is to find quates. One would have to use the equivalency so that the Dollas would cancel out and the Quates would emain in the numeato to obtain the equied answe. Note: Thee ae two equivalencies elating to the Quates and Dolla. These ae, 1 Dolla pe 4 Quates o 4 Quates pe 1 Dolla. As shown, the numeatos and denominatos ae diffeent. Since we wee tying to find the numbes of quates in six dollas, it is necessay to cancel Dollas with Dollas. Theefoe, we need to use the equivalency of 4 Quates pe 1Dolla to be able to cancel Dollas and emain with Quates in the numeato to get the pope esults. Applying this method to dug applications, the equation would be as follows: Available Equivalency A X =Pesciption =P equied units units u Available Equivalency units Au 19
Rounding The chat above shows the names of some of the columns fo numbes that include decimals. To calculate an answe fo a poblem, use all decimal places given in the poblem when adding, subtacting, multiplying, and/o dividing to get any answe. Than efe to the infomation below to the find the necessay numbe of decimal places fo the categoy of the calculations. To ound any numbe fo the categoy needed, look to the column to the ight of the column fo the necessay numbe of decimal places. If the column to the ight has a numbe five o geate, incease the pevious column by one unit; if the numbe in the column to the ight is fou o lowe, dop that numbe and emain with numbe that is the pevious column. Rounding Paametes oz do not ound Kg always ound to tenths ml fo pepaing oal liquids o injectables: <1 to hundedths, >1 to tenths ml fo IV infusions (pumps):<10 to tenths, >10 to whole numbes mcg ound to whole numbes mg, gams, units, meq: <1 to thousandths 1-10 to tenths >10 to whole numbes Rounding Examples 1. Round to whole numbes a) 35.52 = 36 b) 156.2 = 156 2. Round to tenths a) 15.173 = 15.2 b) 20.54 = 20.5 3. Round to hundedths a) 25.337 = 25.34 b) 112.524 = 112.52 4. Round to thousandths a) 155.3254 = 155.325 b) 32.8756 = 32.876 20
Metic convesions, mcg, mg, g 3 g of Ceptaz (Ceftazidime) must be pepaed.ceptaz is available in mg. How many mg of Ceptaz should be pepaed? Hint: 1 g = 1,000 mg Equivalent Method 1: Coss Multiplication Method 2: Dimensional Analysis Method 3: X P u A A u 1000mg Xmg 3g 3000mg 1g 21
Metic convesions, mcg, mg, g Supax (Cefixime) is available in mg. 0.2 g of Supax must be pepaed. How many mg Supax should be pepaed? Hint: 1 g = 1,000 mg Equivalency Method 1: Coss Multiplication Method 2: X Dimensional Analysis Method 3: A P u A u 1000mg Xmg.2g 200mg 1g 22
Metic convesions, mcg, mg, g An IV solution contains 2 mg of Epinephine. 2 mg of Epinephine is equivalent to how many mcg? Hint: 1 mg = 1,000 mcg Equivalency Method 1: Coss Multiplication Method 2: Dimensional Analysis Method 3: X P u A A u 1000mcg Xmcg 2mg 2000mcg 1mg 23
Metic / apothecay convesions - g, mg 10 g of Feous Gluconate must be pepaed. Feous Gluconate is available in mg. How many mg of Feous Gluconate should be pepaed? Hint: 1g = 60mg Equivalency Method 1: Coss Multiplication Method 2: 10g(60mg) 1g(Xmg)=10g(60mg) Xmg = X=600mg 1g Dimensional Analysis Method 3: X P u A A u 60mg Xmg 10g 600mg 1g 24
Metic / apothecay convesions, g, mg Atopine Sulfate is available in mg. 1/150 g of Atopine Sulfate must be pepaed. How many mg of Atopine Sulfate should be pepaed? Hint 1g = 60 mg Equivalency Method 1: Coss Multiplication Method 2: 1 g(60mg) 1 150 60 2 1g(Xmg)= g(60mg) Xmg = X mg mg.4mg 150 1g 150 5 X Dimensional Analysis Method 3: A P u A u 1 60mg 60 2 Xmg g mg mg.4mg 150 1g 150 5 25
Metic / household convesions tsp, ml 2 tsp of cough medicine has been pescibed. A measuing device maked in ml is being used. How many ml should be administeed? Hint 1 tsp = 5 ml Equivalency Method 1: Coss Multiplication Method 2: 1 tsp( XmL) 2 tsp(5 ml) XmL 2 tsp(5 ml) 1tsp X 10ml Dimensional Analysis Method 3: X A P u A u 5ml Xml 2tsp 10ml 1tsp 26
Metic / household convesions tsp, ml 2.5 mg of liquid Uecholine ( Bethanechol Choloide) have been pescibed. A measuing device maked in tsp is being used. 2.5 ml is equivalent to how many tsp? Hint 1 tsp = 5 ml Equivalency Method 1: Coss Multiplication Method 2: X Dimensional Analysis Method 3: A P u A u 1tsp Xtsp 2.5 ml.5tsp 5ml 27
Metic / apothecay convesions, g, Kg, lbs, oz An infant weighs 13 lbs, 13 oz. You detemine that 13 lbs, 13 oz. is equivalent to kg. Hint: 16 oz = 1 lb " Y " oz lb " Y " " Y " oz 16oz 16oz 16 lb Hint: 1oz = 1/16 lb =.0625 lb Xlb.0625 lb Xlb " Y " oz(.0625 lb).0625" Y " Xlb 1 oz " Y " oz 1oz NOTE:"Y" is good fo any amount of ounces Add the esult to the whole numbe of pounds, given in the poblem, to get the total weight in pounds. 13 oz.0625(13) oz.8125lb 13 lb.8125lb 13.8125lb Convesion of pounds to kilogams: 2.2 lb pe kg 2.2 lb kg 13.8125lb lb 2.2 kg 6.3kg 28
Common Faction, Decimal, and Pecent Equivalents 29
Metic / apothecay convesions, g, Kg, lbs, oz A adult weighs 172 lb, 7 oz. You detemine that 172 lbs, 7 oz is equivalent to kg. Hint: Convet ounces to pounds 7oz a) lb.4375lb oz 16 lb b) lb.0625(7 oz).4375lb 172 lb.4375 lb 172.4375lb 172.4375 lb (1 kg) 2.2lb 78.4 kg ( ounded ) 30
Labeled Pesciption: mg and tabs Ode: Decadon 2 mg PO. In med cat: Decadon (dexamethasone) 0.25 mg scoed tablets. What is the coect numbe of tablets to give the client? Hint: Label Equivalent.25 mg pe scoed tablet o.25mg/1tab Equivalency Method 1: Coss Multiplication Method 2: Dimensional Analysis Method 3: A X Pu Au 1tab 1tab Xtabs Xmg = 2mg 8 tabs o 2mg 8tabs.25mg 1 mg 4 31
Labeled Pesciption: Units and ml A patient has an ode fo Hepain 4,000 Units SQ Q AM. The hepain sodium pe-filled disposable syinge is labeled 5,000 U/mL. How many ml should the nuse administe? Hint: The labeled equivalency equals 5,000 Units pe ml Equivalency Method 1: Coss Multiplication Method 2: X Dimensional Analysis Method 3: A P u A u 1ml Xmg 4000 U.8ml 5000U 32
Labeled Pesciption: Units and ml 594 mg of Cefizox (Ceftizoxime) must be pepaed. The Cefizox is available in vial of powdeed dug containing 1 g. Diections accompanying the dug state: Add 3 ml of diluent to yield 270 mg in 1 ml. How many ml should be administe? Hint: The labeled equivalency equals 270 mg pe 1 ml. Equivalency Method 1: Coss Multiplication Method 2: Dimensional Analysis Method 3: 33
Labeled Pesciption: g, mg, and ml Odeed Tylenol 5 gains. Have Tylenol in 80 mg in.8ml. How many ml will you give? Hint: 60mg = 1g Equivalency Method 1: Coss Multiplication Method 2: 80 mg( XmL) 300 mg(.8 ml) 300 mg(.8 ml) 240mL XmL = 3mL 80mg 80 Dimensional Analysis Method 3: X P u A A u 60 mg.8ml 240ml Xml 5g 3ml 1g 80mg 80 34
TYPE 14 DRUG USAGE PER VOLUME In this type of poblem, you ae elating a unit popotion to a full popotion of the same dug solution. A unit atio occus when the numbe value of the denominato dimension is 1, as in 1 ml. You will be given one whole popotion and one pat of the othe and asked to find the missing value. PRACTICE PROBLEM 400 mg of Aminophylline has been added to D5W. The final solution has a volume of 500 ml. You ealize that the IV solution contains mg of Aminophylline pe ml. Set up the final solution stength as a atio with dimensions, equal to the unknown unit atio with the dimensions in the same positions espectively. Fill in the amounts given fo each pat of the equation using 1 fo the unit amount and x fo the missing amount. SOLUTION METHOD 1EQUIVALENCY 500 400mg Xmg 400mg X mg.8mg 500ml 1ml 500 500 SOLUTION METHOD 2 CROSS-MULTIPLICATION METHOD 400ml 400mg 1ml 500ml Xmg Xmg 1 mg.8mg 500ml 35
Conclusion Knowledge of the pocedues of this manual will simplify the math fo dispensing medication in the LPN pogam and will be an excellent pepaation fo the math fo the RN pogam. 36