Clinical Mathematics Review We can do this!

SIX rights Pt Dr Dr Right Patient Right Time Right Drug Right Route Right Dose Right Record

24-Hour Clock

Comparison of Traditional and 24-Hour (Military) Clock AM Int’l. Time PM Int’l Time 12:00 midnight 0000 12:00 noon 1200 1:00 0100 1300 2:00 0200 1400 3:00 0300 1500 4:00 0400 1600 5:00 0500 1700 6:00 0600 1800 7:00 0700 1900 8:00 0800 2000 9:00 0900 2100 10:00 1000 2200 11:00 1100 2300

Notation Rules Fractional parts of unit written as decimal (do not write fractions). e.g., 34.5 mg, 2.5 mL, 78.2 kg

Notation Rules Zero placed in front of decimal point when not preceded by whole number Emphasizes decimal point e.g., 0.25 mg, 0.5 g Excess zeros following decimal fraction deleted e.g., 4.500 g = 4.5 g, 2.500 L = 2.5 L

Conversions Metric – metric US – US Metric - US

Conversions: metric - metric

Conversions: metric - metric

Conversions: metric - metric Move decimal to left

Conversions: metric - metric Move decimal to right

Conversions: metric - metric

Conversions: US - metric Length 2.54 cm = 1 in Mass 2.2 lbs = 1 kg

Conversions: US - metric Volume 1 tsp = 5 mL 1 TBS = 3 tsp = 15 mL = 0.5 oz 30 mL = 1 oz 240 mL = 1 cup 2 cups = 1 pint 1 quart = 4 cups = 960 mL

Intake Intake: 1 glass of juice (glass = 6 oz) 200 ml Sprite 75% cup of Jello (cup = 8 oz) ¾ glass of water (glass = 16 oz) How much in ml? And in Liters?

Abbreviations a.c. – before meals ad lib – as desired b.i.d. – two times a day cap – capsule IM – intramuscular IV – intravenous nightly – every night at bedtime OD – right eye OS – left eye OU – both eyes p.c. – after meals per – by PO; orally – by mouth p.r.n. – when necessary/ required stat. – immediately subcut. – subcutaneous tab. – tablet t.i.d. – three time a day daily, once daily, units – must be written out

Oral Doses Most consist of half to three tablets or capsules, or half to double the mL volume in liquid medications

Reading Labels Trade or brand name Generic or official name Capitalized (will have ® symbol) Generic or official name Lowercase if only one name listed, it is generic Strength in metric measure Always has unit of measure

More Label Information The letters USP (United States Pharmacopeia) and NF (National Formulary) on drug labels identify official generic listing

Drug Label Information Manufacturer Lot number Expiration date Must check before administering

Other Label Information If drug in multiple dose containers, number of tablets or capsules in container will be on label

Labels Drug (supply) concentration Route of administration Diluent required Reconstitution instructions

Calculation of doses Read label carefully Identify all information given what unit Identify information needed

Given and Needed Units To solve a problem Identify the given unit Identify the needed unit. Example: A person has a height of 2.0 meters. What is that height in inches? The given unit is the initial unit of height. given unit = meters (m) The needed unit is the unit for the answer. needed unit = inches (in.)

Learning Check An injured person loses 0.30 pints of blood. How many milliliters of blood would that be? Identify the given and needed units given in this problem. Given unit = _______ Needed unit = _______

Solution An injured person loses 0.30 pints of blood. How many milliliters of blood would that be? Identify the given and needed units given in this problem. Given unit = pints Needed unit = milliliters

Problem Setup Unit 1 x Unit 2 = Unit 2 Unit 1 Write the given and needed units. Write a unit plan to convert the given unit to the needed unit. Write equalities and conversion factors that connect the units. Use conversion factors to cancel the given unit and provide the needed unit. Unit 1 x Unit 2 = Unit 2 Unit 1 Given x Conversion = Needed unit factor unit

Setting up a Problem How many minutes are 2.5 hours? Given unit = 2.5 hr Needed unit = min Unit Plan = hr min Setup problem to cancel hours (hr). Given Conversion Needed unit factor unit 2.5 hr x 60 min = 150 min 1 hr Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Learning Check A client is 1.6 m tall. How many centimeters tall is the client? 1) 1600 cm 2) 160 cm 3) 16 cm

Solution A client is 1.6 m tall. How many centimeters tall is the client? 2) 160 cm Given Conversion Needed unit factor unit 1.6 m x 100 cm = 160 cm 1 m

Dosage example Prescriber orders 5 mg of drug, the pharmacy delivers the drug as 10 mg/tablet (tablets are scored). What is the dosage of medication you administer?

Dosage example Prescriber orders 5 mg of drug, the pharmacy delivers the drug as 10 mg/tablet (tablets are scored). What is the dosage of medication you administer? Unit given= Unit needed= Conversions needed=

Dosage example Unit given= mg Unit needed= tablet Prescriber orders 5 mg of drug, the pharmacy delivers the drug as 10 mg/tablet (tablets are scored). What is the dosage of medication you administer? Unit given= mg Unit needed= tablet Conversions needed=10 mg/1 tablet

Dosage example Prescriber orders 5 mg of drug, the pharmacy delivers the drug as 10 mg/tablet (tablets are scored). What is the dosage of medication you administer? Unit given= mg Unit needed= tablet Conversions needed=10 mg/1 tablet Set up: 5 mg x 1 tablet = 10 mg

Dosage example Prescriber orders 5 mg of drug, the pharmacy delivers the drug as 10 mg/tablet (tablets are scored). What is the dosage of medication you administer? Unit given= mg Unit needed= tablet Conversions needed=10 mg/1 tablet Set up: 5 mg x 1 tablet = 0.5 tablet 10 mg

Using Two or More Factors Often, two or more conversion factors are required to obtain the unit needed for the answer. Unit 1 Unit 2 Unit 3 Additional conversion factors are placed in the setup to cancel each preceding unit Given unit x factor 1 x factor 2 = needed unit Unit 1 x Unit 2 x Unit 3 = Unit 3 Unit 1 Unit 2

Example: Problem Solving How many minutes are in 1.4 days? Given unit: 1.4 days Factor 1 Factor 2 Plan: days hr min Set up problem: 1.4 days x 24 hr x 60 min = 2016 min 1 day 1 hr

Check the Unit Cancellation Be sure to check your unit cancellation in the setup. The units in the conversion factors must cancel to give the correct unit for the answer. What is wrong with the following setup? 1.4 day x 1 day x 1 hr 24 hr 60 min Units = day2/min is not the unit needed Units don’t cancel properly.

Using DA What is 6.5 lb in g? STEP 1 Given 6.5 lb Need g STEP 2 Plan STEP 3 Equalities/Factors 1 kg = 2.2 lb 1000 g = 1 kg 2.2 lb and 1 kg 1000 g and 1 kg 1 kg 2.2 lb 1 kg 1000 g STEP 4 Set Up Problem 6.5 lb x 1 kg x 1000 g = 2955 g 2.2 lb 1 kg

Simple calculations for oral meds Dimensional Analysis: dosage ordered x volume = dosage given have Formula: dose ordered x volume = dosage given

Calculating Safe Range Child weighing 22.6 kg prescribed to receive 500 mg of medication in 100 mL of D5W every 12 hours Normal/Safe dosage range 40 to 50 mg/kg/day Determine if dosage prescribed is within normal/safe range

Calculating Safe Range Calculate safe daily dosage range 22.6 kg x 40 mg = 904 mg 1 kg 22.6 kg x 50 mg = 1130 mg

Calculating Safe Range Calculate dosage infusing in 24 hours 500 mg in 12 hr = 1000 mg in 24 hours ( 24 hours = 1 day) 500 mg x 2 doses = 1000 mg 1 dose 1 day 1 day 1000 mg/ day is within 904 to 1130mg/day range

Calculating Infusion Time Divide volume to be infused by mL/hr flow rate

Calculating Infusion Time: Example Calculate infusion time for IV of 1000 mL to infuse at 100 mL/hr

Fractional Hours Converted to min by multiplying 60 min by fractional hour obtained

Fractional Hours: Example Calculate infusion time for 500 mL at 75 mL/hr IV will infuse in 6 hours and 40 min

Calculating Completion Time Add infusion time to time IV was started Military or standard