# Medical Mathematics

## 42 terms · Math Review And Medication Administration

you must find the lowest common denominator

### Multiplying and Dividing Fraction

To multiply two fractions, no conversion is necessary. Simply
multiply the numerators together, and then multiply the
denominators together

prescribe drugs. The next step is then to fill the prescription,
which is done by either a veterinary nurse or a veterinary
technician. Lastly, the drug is then administered to the
patient by a veterinary technician or a nurse.

### drug

is any chemical substance that acts on the physiological processes in the body.

### drug can be identified in one of two ways:

generic name is the officially accepted
name of a drug that's listed in the U.S. Pharmacopeia.
There's only one generic name for any given drug, and the
generic name must be on the drug label. The trade name,
however, is usually the name given by the company that
manufactures the drug, and the trade name is followed by a
trademark (™) or registration symbol (®)

### Right Dose

Drug dosage is calculated based on the animal's weight and
the recommended dosage. It can also be calculated via body
surface area (BSA)

### surface area (BSA)

which is an estimate of total skin area of
an animal measured in meters squared (m2
).

### Oral medication

are administered by the mouth (usually abbreviated PO). These drugs can be found in either solid or liquid
form including tablets, capsules, caplets, elixirs, syrups, and
suspensions.

### Parenteral medications

are injected into the body by one of
the following routes: intramuscular (IM), subcutaneous (SQ),
intravenous (IV), intradermal (ID), and intracardiac (IC).
Intraperitoneal (IP), which is rarely used in human medicine
but is still used in some species in veterinary medicine, is the
injection of a substance into the peritoneum or body cavity

### Cutaneous medication

s are administered through the skin
or mucous membranes. These routes can include topical,
transdermal, inhalation, optic, nasal, otic, or rectal. The
form of medication can include liquids, ointments, creams,
or suppositories.

### Right Time

once a day
(s.i.d.), twice a day (b.i.d.), three times a day (t.i.d.), four
times a day (q.i.d.), and as needed (prn).

### Drug Label

e it contains the generic
and trade names, as well as other important information that
you'll need to help ensure correct administration. The form
of the drug is indicated on the label
Other forms would include oral
solution, topical cream, and so on. Next, the dosage strength
tells the amount of the drug in a measurable unit.
The expiration date is also found on the label to ensure the drug is still
viable. Lastly, some labels have specific storage instructions
such as controlled temperature, refrigeration, away from
direct light, and so on.

### Drug Package Insert

found with the drug is also helpful, as
sometimes the information you're seeking won't be found on
the actual label. This is most common when reconstituting a
powder into a liquid form. The package insert gives instructions on what type of constitute (sterile water, sterile saline,
and so on) and how much to use. The insert also tells how
long the product is good for (10 days, two weeks, and so on).
There's also the information on safe dosages, ranges, indications, contraindications, warnings, side effects, and adverse
reactions.

### dimensional analysis

s refers to the ability to solve
problems using unit cancellation. Since only one equation is
needed, it eliminates the need to memorize formulas.

### dimensional analysis has two main concepts:

(1) when a nonzero quantity is divided by the same
amount, the result is one, and (2) when a quantity is multiplied by one, the quantity is unchanged.

### When using the dimensional-analysis method, the conversion factors should be written in fraction format.

We'll use the equivalent 1 L = 1,000 mL.
This can be written as either:
1 L/1,000 mL or 1,000 mL/1 L

### You would like to order Gentamicin 3 g IV s.i.d. It's available as Gentamicin 100 mg/mL

2. Set up the problem in fraction format
x(mL) =1 mL/100 m
3. A conversion is necessary since the order is in grams
and the medication is available in milligrams. A second
fraction can be added to the equation.
x(mL)=1 mL/100Mg X1,000Mg/ 1g

4. The amount of drug needed can now be placed in the
equation and should match the denominator of the
fraction immediately before it.

x(mL)=1ml/100mg X 1,000mg / 1g X 3g/1g

5. Like units can be canceled and the remaining unit
should be what's desired

x = 30 mL of Gentamicin

### metric system

is a system of measurement in which all
the units are based on powers of 10. The metric system has
only three basic units for weight, volume, and length: gram
(g), liter (L), and meter (m).

### Designations for volume in the apothecary system include:

minims, fluid drams, fluid ounces, pints, quarts, and gallons. The units for weight in the apothecary systems are grains, scruples, drams, ounces, and pounds. The avoirdupois measures of weight include pounds, ounces, and grains. Although some of the units have the same name, the only common unit of designation between the two systems is the grain.

### dosage calculation problems usually involve the following three parameters:

1. The patient's weight
2. The prescribed dose of medication
3. The concentration (strength) of the medication

### A 100-pound patient requires a dose of 25 mg/kg of a drug. The solution you have available contains a drug concentration of 100 mg/mL. What volume of the drug solution (in milliliters) should be administered to the patient?

First, since the patient's weight is given in pounds and the
dose is given in mg/kg, you'll need to convert the weight to
kilograms.
100 lb / 2.2 lb/kg = 45.45 kg
Next, calculate the amount of drug needed for this patient's
weight.
patient's weight  dose = weight of drug needed
45.45 kg X 25 mg/kg = 1,136.25 mg
Finally, calculate the volume of solution needed.
weight of drug needed  concentration = volume of solution needed
1136.25 mg /  100 mg/mL = 11.3625 mL

### If a clinician prescribes one teaspoon of Benadryl to be given twice a day for 10 days, how many milliliters must be dispensed in total? To answer, multiply the number of doses needed by the size of each dose.

l tsp = 5 mL
5 mL X twice a day = 10 mL per day
10 mL per day for 10 days = 10 mL X  10 = 100 mL
You may also need to determine the number of doses that
can be obtained from a given volume of medication. To do
this, you'll divide the total amount of solution by the size of
each dose. So, for example, how many 5 mL doses can be
obtained from 20 mL of a drug? When you divide 20 mL
by 5 mL, you get a result of 4 doses.

### calculating dosages by BSA, which isn't routinely done in animal medicine. BSA is used mostly for chemotherapy medications, which at present are administered by only a veterinarian (laws may change as to who can give in the future). It's important you understand the concept but the actual calculation is based not on body weight and height (as in humans) but actually on the following equation:

BSA (in m squared) = k X  BW to the x
k is a constant (0.101 in dogs, 0.1 in cats)

BW is body weight in kg
x = 2/3or 0.67

So, for a 5 kg dog BSA would be

BSA = 0.101  5 to the 0.67

BSA = 0.29 m squared

### All syringes have

a barrel, plunger, and tip.

a hub and shaft

### The needle shaft is measured

in length and gauge and contains a beveled edge.

### The syringe is measured

according to the amount of fluid it can hold (cc, mL, or units).

### . In large animals, the smaller capacity syringes are used for

injection of medications into the SQ or IM space

### In large animals,The larger capacity syringes are used

to collect blood or other fluid samples and
for medications requiring larger amounts

### In small animals, the smaller capacity syringes are used for

both medication administration and blood collection. Larger syringes are used less frequently.

### Insulin

is a medication that's measured in its own way via
units per one mL.

### In veterinary medicine, two types of insulin measurements are used:

: U-100 and U-40. This means that there are either 100 units per mL or 40 units per mL, respectively. The syringes used are therefore based on either this U-40 or this U-100 measurement.

a=c X b/d
d


### nasoesophageal tube

(a tube placed into the nasal passages bypasses the mouth to end in the esophagus),

### esophagostomy tube

e (a tube placed directly
into the esophagus through the skin of the neck),

### gastrostomy tube

(a tube placed directly into the stomach through the
skin

### jejunostomy tube

(a tube placed directly into the
jejunum through the skin)

### The flow rate

is the speed at which an IV will infuse a patient with fluid.

### The drop factor

is the number of drops per milliliter; this factor depends
on the specific fluid therapy tubing being used

### The drip rate

is the number of drops to be infused per minute.

### To calculate the drip rate, you would

divide the total milliliters
needed by the total time prescribed for the infusion, and then
multiply that figure by the drop factor.

### If a patient is to be infused with 1,000 milliliters of fluid over a 12-hour period, and your fluid administration set has a drop factor of 15, you can calculate the drip rate as follows.

12 hours x  60 minutes = 720 minutes of infusion time
(1,000 mL / 720 minutes) x 15 = drip rate
(1.39) x 15 = 20.85 drip rate
(round this result up to 21 drops)