1. Clinical Mathematics Review
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2. SIX rights Pt Dr Dr Right Patient Right Time Right Drug Right Route
Right Dose
Right Record

3. 24-Hour Clock

4. Comparison of Traditional and 24-Hour (Military) ClockAM
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

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

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

7. Conversions
Metric – metric
US – US
Metric - US

8. Conversions: metric - metric

9. Conversions: metric - metric

10. Conversions: metric - metric
Move decimal to left

11. Conversions: metric - metric
Move decimal to right

12. Conversions: metric - metric

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

14. 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

15. 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?

16. 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

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

18. 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

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

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

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

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

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

24. 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.)

25. 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 = _______

26. 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

27. 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 x Unit 2 = Unit 2
Unit 1
Given x Conversion = Needed
unit factor unit

28. Setting up a Problem How many minutes are 2.5 hours?
Given unit = 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 hr
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29. Learning Check
A client is 1.6 m tall. How many centimeters tall is the client?
1) cm
2) 160 cm
3) 16 cm

30. 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 cm = 160 cm
1 m

31. 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?

32. 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=

33. 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

34. 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

35. 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

36. 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 x Unit x Unit = Unit 3
Unit Unit 2

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

38. 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 hr
24 hr min
Units = day2/min is not the unit needed
Units don’t cancel properly.

39. 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 g = 1 kg
2.2 lb and kg g and 1 kg
1 kg lb kg g
STEP 4 Set Up Problem
6.5 lb x kg x g = g
2.2 lb kg

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

41. 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

42. 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

43. 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 day day
1000 mg/ day is within 904 to 1130mg/day range

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

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

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

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

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