Basic Math Review

Tyra L. Ousley, RN, MSN

I. PERCENTAGES

Any quantity stated as the proportion per hundred; expressed with % sign meaning “for every hundred”.

A. Convert a percent to a decimal

RULES:1. Delete the % sign2. Divide the remaining number by 100, which is the

same as moving the decimal point 2 places to the left.

Ex: 25% = 25/100 = 0.25 50% = ___________ 75% = ___________ 67% = ___________

B. Convert a decimal to a percentage

RULES:1. Multiply the decimal number by 100 (move

the decimal point 2 places to the right) and2. Add % signEx: 0.25 x 100 = 25% 0.50 = _______% 0.75 = _______% 0.67 = _______%

C. Converting a common fraction to a percentage

RULES– Convert the fraction to a decimal by dividing the

numerator by the denominator 3/8 (0.375)

– Move the decimal point two places to the right, round off if necessary

37.5 or 38

– Add the % sign 37.5% or 38%

Examples

4/52/37/83/4

Convert a percent to a fraction

RULES:

1. Delete the % sign

2. Write the remaining number as the numerator

3. Write the 100 as the denominator

4. Reduce the common fraction to the lowest term

Ex: 25% = __________

50% = __________

75% = __________

II. RATIOS AND FRACTIONS IN PROPORTIONS

Numerical ways to compare items.A proportion is a set of two equal

ratios or fractions

A.Ratios in proportions

Written with a double colon separating the ratios (Example: 3:1 :: 6:2)

The outer numbers (3&2) are the extremes. The inner numbers (1&6) are the means The product of the extremes must equal the product

of the means– Solve for X in this proportion

3:1 :: 6:X 2.5 : 1.2 :: X : 3.2 ¼ : 2 :: 1/3 : X

B. Fractions in proportions

Cross products should be equal 5 X --- = --- 2 4

• Rewrite the problem to multiply cross products• 2 x X = 5 x 4

• Obtain the cross products• 2X = 20

• Solve for X by dividing both sides by 2• Find X (10)

Example:

X = 1

55 2.2

X = 0.5

75 50

80 = 60

10 X

Convert a fraction to a decimal

RULE: To convert a fraction to a decimal, divide the numerator by the denominator.

Ex: 1/ 4 = _________ 2/5 = ____________ 4/10 = _____________

Convert decimal to a fraction

Decimal fractions are fractions with a denominator of 10, 100, 1000 or any multiple or power of 10.

Ex: 0.1 = _________ 0.01 = _______ 0.001 = ___________

SYSTEMS OF DRUG MEASUREMENT

I. METRIC SYSTEM– Basic units of measurement:

Meter (m) – unit of lengthLiter (L) – unit of volumeGram (G, GM, Gm) – unit of weight

METRIC SYSTEM

WEIGHT ABBREV CONVERSION FACTOR

Gram g 1g=1000 mg

milligram mg 1 mg=1000 mcg =0.001 g

microgram mcg 1 mcg=0.001 mg = 0.000001 g

kilogram kg 1 kg=1000 g

Metric Conversions

To convert a smaller unit to a larger one, move the decimal point to the left or divide by the appropriate multiple of 10

– Example: milligrams to grams– 1000 milligrams / 1000 = 1

To convert a larger unit to a smaller one, move the decimal point to the right or multiply by the appropriate multiple of 10

– Example: gram to milligrams– 1 gram x 1000 = 1000 mg

Larger to smaller unit MULTIPLY (L-S-M) Smaller to larger unit DIVIDE (S-L-D) Identify conversion factors Convert 2 grams to equivalent milligrams

– Equivalent conversion= 1g=1000mg– 2 g = 2 x 1000=2000 mg- by multiplication OR– 2.000 = 2000 mg(moving decimal 3 places to right)

II. HOUSEHOLD SYSTEM

Usually used at home– Drop gtt (standard measure varies)– Teaspoon t (tsp) 1 t = 60 gtt– Tablespoon T(tbs) 1 T = 3 t– Ounce(fluid) oz 2 T = 1 oz – Ounce(wt) oz 1 lb = 16 oz– Cup cup 1 cup = 8 oz– Pint pt 1 pt = 2 cups– Quart qt 1 qt = 4 cups = 2 pints– Gallon gal 1 gal = 4 qt

III. Apothecaries’ System

Uses Roman numerals Unit of measurement is placed before the

Roman numeral (Example: 5 grains is written as grains v )

Basic units of measurement– Minim: for liquid volume– Grain (gr): for solid weight

IV. Avoirdupois System

Used for ordering and purchasing some pharmaceutical products and for weighing patients in clinical settings

Units of weight include grains, ounces, pounds

V. Unit System

USP – United States Pharmacopeia Units IU – International Units Common drugs in units

– Insulin– Heparin

VI. Milliequivalent System

Most electrolytes are measured in mEq– Example: Potassium Chloride

APPROXIMATE EQUIVALENTS

1 g = gr(grains) xv = 1 ml = 1 cc

gr 1 = 60 mg 1 t = 5 ml 1 T = 3 t = 15 ml = ½ oz 1 oz = 30 ml = 6 t 1 L = qt I = oz 32 = pt ii = 4 c pt I = = 500ml = oz 16 = 2 cups 1 cup = 240 ml = oz 8 1 kg = 2.2 lbs 1 inch = 2.54 cm

Conversions forOther Clinical Applications:

Time and Temperature

Chapter 5

Time is an essential part of the drug

order

What are some issues related to using the

traditional time method?

24-Hour Clock

Traditional and 24-Hour ClockAM Int’l. Time PM Int’l Time

12:00 midnight 2400 12:00 noon 1200

1:00 0100 1:00 1300

2:00 0200 2:00 1400

3:00 0300 3:00 1500

4:00 0400 4:00 1600

5:00 0500 5:00 1700

6:00 0600 6:00 1800

7:00 0700 7:00 1900

8:00 0800 8:00 2000

9:00 0900 9:00 2100

10:00 1000 10:00 2200

11:00 1100 11:00 2300

What Time Is It?

• 3:15 p.m.• 4:45 a.m.• 5:30 p.m.• 10:10 p.m.• 12:35 a.m.

• 0017• 1010• 1730• 2310• 0635

What Is Wrong?

Give two Tylenol at 9:00 Blood pressure to be taken at 2510 Insulin given at 23:10 p.m.

Celsius and Fahrenheit Scales

Convert between Fahrenheit and Celsius temperatures:

1.8

32FC

32C1.8F

Celsius and Fahrenheit Scales

IMPORTANT FORMULAS

TEMPERATURE CONVERSIONS– Celsius °F-32

°C = ----------- OR 5/9 ( °F – 32) 1.8

Example: 101 °F (101 – 32)

------------ OR 5/9 (101 – 32) 1.8 = 69 /1.8 OR (5 x 69)/9 = 38.3 °C

TEMPERATURE CONVERSION

FAHRENHEIT– ° F = 1.8 °C + 32 OR 9/5 °C + 32

Example: 38.3 °C

1.8 x 38.3 + 32 OR (9 x 38.3)

------------ + 32

5

= 100.9 °F

Calculate the Temperatures

40˚ Fahrenheit 75˚ Fahrenheit 18˚ Celsius 65˚ Celsius

ORAL DOSAGE FORMSSteps:

1. Ensure that all measurements are in the same system of measurement and the same size unit of measurement. If not, convert.

2. Calculate using this formulaD = desired amount or orderH = available or have on handQ = quantity D

H=

Amount to be givenX Q

Oral Dosage Forms: Liquid Preparations

Steps:

1. Ensure that all measurements are in the same system of measurement and the same size unit of measurement. If not, convert.

2. Calculate using this formula D

HX Q= Amount to be given

Converting between measurement systems

Example: grains to milligrams Order: Aspirin gr v Available : Aspirin in mg. Set up the first ratio with the conversion factor

1 gr : 60 mg Set up the second ratio with the unknown quantity in the appropriate

position 5 gr : X Use these ratios in proportion

1 gr:60 mg :: 5 gr: X Solve for X (unknown) based on the principle that the product of the

means equals the product of the extremes 1 gr x X = 60 mg x 5 gr X = 300 mg

Pounds to kilograms

A patient weighs 217 pounds. Convert to kg to compute the amount of medication to be given– 1 kg : 2.2 lb– X kg : 217 lbs– 1 kg : 2.2 lb :: x kg : 217 lb– 2.2 lb X = 1 X 217 lb– X = 217/2/2– X = 98.6 kg

Examples

The physician writes an order for secobarbital 0.2 gm every 6 hours prn for sleep. Each secobarbital capsule is labeled 100 mg. The nurse should administer______ capsules per dose.

Examples

The physician orders 500 mg of amoxicillin by mouth to be given every 6 hours. Available are 250 mg of amoxicillin capsules. The nurse should administer _________ capsule(s) for each dose.

Examples

The physician writes an order for acetaminophen 240 mg po for an elderly adult. You have on hand 80 mg acetaminophen oral liquid in 0.8 ml. The nurse should administer _________ ml per dose.

Examples

The physician orders amoxicillin 250 mg po. The pharmacy supplies amoxicillin suspension 250 mg/5 ml. in a 50 ml. bottle. The nurse should instruct the client to take _________ ml per dose.

Practice Questions:

A physician’s order reads 2 Tbs milk of magnesia. How many milliliters will the nurse administer?

The Physician’s order reads Tylenol supp. Gr x every 4 hrs p.r.n. for temp. > 101 F. The package label states that each suppository contains 10 grains of Tylenol. How many suppositories should the nurse administer?

The order states Lithium Carbonate gr x p.o. tid. The drug is labeled Lithium Carbonate 300 milligrams/capsule. How many capsules should the nurse give?

The order for Coumadin is 5 mg. It is available in 2.5 mg tablets. How many tablets should be given?

The physician’s order is Ferrous Sulfate 300 mg p.o. tid X 1 week. How many tablets in total should be dispensed for the patient?

Calculation for individualized drug dosing

Based on actual body weight Used to individualize medication

administration for children and adults

Steps

Convert pounds(lbs) to kilograms (kg) Determine the drug dose per body weight by multiplying drug

dose X body weight X frequency Choose one of the four methods of drug calculation for the

amount of drug to be given– Basic formula– Ratio proportion– Fraction equation– Dimensional analysis

The physician orders morphine sulfate 1.8 mg IM stat.

The child weighs 79 lbs. Is the dose safe?

Verifying Safe Dosages

Verifying Safe Dosages

Convert 1 lb to kg

kg 35.9 2.2 79 lb 79

Verifying Safe Dosages

Calculate mg/kg as recommended by a drug resource– Resource indicates the usual IM/SC dosage may

be initiated at 0.05 mg/kg/dose

mg/dose 1.8 kg 35.9 X mg/kg/dose 0.05 :dosePer

• The dose is safe

Kee, pp. 98 -109

REFERENCES

Broyles, B. (2003) Dosage Calculation Practice for Nurses. Canada: Delmar

Erickson, B. ( 1991). Nurse’s Clinical Guide Dosage Calculations. Pennsylvania: Springhouse Corporation

Kee, J and Marshall, S.(2004). Clinical Calculations. 5th Edition. Missouri: Elsevier

Pickar, G. ( 2008). Dosage Calculations. 8th Edition. Canada: Delmar