Medical Math
conversions between systems of measurement with the correctly numbered step in the process:
1- Identify an equivalent between the two systems 2- set up a proportion 3- Use X for the unknown value being calculated 4- cross multiply and solve for X 5- Verify the answer is reasonable
What is the metric unit of weight?
grams
Order: ciproflaxin 500 mg P.O (by mouth) once daily The ond hand dose is 250 mg
(x) tablets = (x)/ (x) times (x) tablets 2 tablets (because 2 times 250 is 500 mg) Desire dosage on top (500 mg)/ on hand dosage on bottom (250 mg) TIMES quantity of on hand dosage (1) meaning how many tablets will contain the amount 250 mg (i think)
Order: prednisone 12.5 mg bid (twice a day) on hand dose : 25 mg
(x) tablets = (x)/ (x) times (x) tablets Each tablet is 25gm meaning that in oder to make it 12.5 mg the tablet needs to broken into 1/2 Therefore the require dose is: (1/2) The desire dosage is: 12.5 mg The on hand dosage is: 25 mg The quantity of on hand dosage is: 1 (because 1 table contails 25 mg which need to be broken into half to be properly taken twice a day)
550 milligrams equals how many grams?
0.550 divide the mass value by 1000
What is 1,379 rounded to the nearest thousand?
1,000
Metric Units
grams: measuring weight Liter: measures volume meter: measures distance
1 kg is equal to how many grams?
1000 grams multiply the mass value by 1000
A physician's order says to give 10 mg of a medication per kg of the patient's weight. How much medication should you give to a 220 lbs patient?
1000 mg convert 220 lbs to kg (divide 220/2.2) multiply result by amount of dosage (10)
Calcium carbonate 1000 mg daily is ordered in divided doses bid (twice a day). 250 mg per tablet is available. How many tablets should you administer to the patient per dose?
1000 mg twice a day divide 1000 by 250 = 4 tablets 2 tablets of 250 per dosage
MIlligram
1000 times smaller than a gram. 1 gram paper clip weights 1000 mg A milligram is an extremely small amount
A 250 lbs patient weighs how many kilograms?
116.6 Divide 250 / 2.2 to obtain mass in KG
Match the traditional time with its equivalent in military time.
11:00 pm - 2300 6:45 am- 0645 3:00 am- 0300 5:50 pm- 1750 1:00 pm -1300
How much does a 135 lbs patient weigh in kilograms?
135 lbs divided by 2.2 61.4 kg
A physician's order reads "ampicillin 0.5 grams". The unit dose packet of ampicillin reads "250 milligrams per capsule". How many capsules should you give the patient?
2 multiply the mass value (0.5 g) by 1000 divide result (500) by 250 mg result: 2
To administer 1 ounce of liquid, you would give
2 tablespoons
A hospital emergency room treated 36 people in one day. If 24 of the people were children, what was the ratio of children to adults that day?
2 to 1 or 2:1
Estimating is:
is expressing the approximate answer.
5 teaspoons equals to?
25 mililiters
A physician's order reads "Lasix 60 milligrams". The unit dose packet of Lasix reads "20 milligrams". How many unit doses should you give the patient?
3 multiply 20 x 3 = 60 mg
Question WorkspaceCheck My WorkInterpret the following Roman numeral: MMMDXXXIII
3,533
Match the temperature (either Fahrenheit or Celsius) with its equivalent.
35f = 1.7 c 59 f = 15 c 86f = 30 c 99.6 = 37.6 c
An infant weighs 10 lbs. What is the infant's weight in grams?
4545 multiply the mass value by 454
Equivalent values and measurements
6,000 G = 6 KG (10 ^3) 0.6 L = 600 ml ( 10 ^-3) 0.006 L = 6 ml (10 ^-3) 0.06 g =60 mg (10 ^-3) 6 M = 600 cm ( 10 ^-2) 60 M = 0.06 km (10^3) (divide 60 /1000) 6 g = 6,000,000 mcg (10^-6)
A physician orders 525 milligrams (mg) of an antibiotic suspension for a patient with pharyngitis. The antibiotic is available as 375 milligrams per 5 milliliters (375 mg/5 mL) of solution. How many mL should be given?
7 mL
If a patient's bed is adjusted so that he is sitting in a straight-up position, at what angle is the bed set?
90 degrees
If a pharmaceutical company wants an idea of what percent of the thousands of patients taking a drug have lowered their blood pressure as a result, they would gather data from which of the following?
A sample
Angles
Angles are used in health care when injecting medications, describing joint movement, and indicating bed positions. Angles are always defined by comparison to a reference plane, a real or imaginary flat surface from which the angle is measured. Angles are always defined by comparison to a reference plane, a real or imaginary flat surface from which the angle is measured.
What are the first steps when dividing one decimal into another?
Convert the decimals into whole numbers by moving the decimal point to the right.
What is recommended to make performing calculations with percentages easier?
Convert them to decimals
In the basic formula, D stands for ?
Desired dosage
Which of the following factors would necessitate a reduced drug dose for a geriatric patient?
Diminished metabolism
Order: acetaminophen 10 mg/kg P.O (by mouth) Determine how many milligrams of acetaminophen to administer to a 150 lb adult patient.
Divide 150 lb by 2.2 68.1 = 68 multiply by 10 68x10 = 680 mg
Demerol 60 mg is ordered. You have 75 mg per 1 mL on-hand. How many milliliters should you administer to the patient per dose?
Divide 60mg by 75 mg = 0.8 mL per dose.
Order: ibuprofen 50 mg/kg children's weight is 8 lbs Determine how many milligrams of ibuprofen to administer to an 8 lb infant patient.
Divide 8 lbs / 2.2 3.63 kg multiply by 50 181.5 = 182 mg
A proportion is useful for finding the value of unknowns when you know two of the four terms.
False You must know three of the four terms in order to find the value of the unknown.
Celsius is a measurement of temperature based on a freezing point of 32° and a boiling point of 212°.
False. Fahrenheit is based on a freezing point of 32° and a boiling point of 212°
Military time is based on a 12-hour clock.
False. It's based on 24 hour clock.
Rounding numbers means changing them to the nearest whole number.
False. Rounding numbers means changing them to the nearest ten, hundred, thousand, and so on.
The fraction ¾ is equal to 7.5%.
False. The fraction ¾ is equal to 75%.
Improper fractions have denominators that are larger than their numerators.
False. The numerators of improper fractions are larger than the denominators.
To determine the common denominator you first
Find a number that both denominators divide evenly into
What is the first step when dividing fractions?
Invert the dividing fraction.
Prefixes most commonly used
KILO = (10^3) means 1 thousand of a unit CENTI = (10 ^ -2) means 1 hundredth of a unit MILLI = (10 ^ -3) means 1 thousands of a unit MICRO = (10 ^ -6) means 1 millionths of a unit
Percentages
Percentages are used to express either a whole or part of a whole. The whole is expressed as 100% (percent). example: imagine this as a hot apple pie sliced into 10 equal pieces. The 10 slices together equal the whole, or 100%, of the pie. One hundred divided by ten equals ten. Therefore, each slice represents 10% of the pie. If each slice is 10%, then three slices represent 30% of the pie.
Fractions
Represent parts of a whole. A fraction has a numerator (top number) and a denominator (bottom number). An example of a fraction is , where the 3 is the numerator and 10 is the denominator.
Roman Numerals
The traditional numbering system we use every day is referred to as Arabic numerals (1, 2, 3, . . .). In health care, it is necessary to know Roman numerals because they are used for some medications, solutions, and ordering systems. All numbers can be expressed by using seven key numerals: I = 1 V= 5 X = 10 L = 50 C = 100 D = 500 M = 1000
Temperature conversion
Thermometers using Fahrenheit (F) as the measuring unit are more familiar to people living in the United States, though the Celsius (C) system (also known as centigrade) of measurement is frequently seen in medical practice. One way to start understanding the difference between the two systems is to compare how each one expresses the boiling and freezing points of water. Boiling points: 212 f = 100 c Freezing points: 32 f = 0 c
Ratios show relationships between numbers or like values.
True
When adding or subtracting fractions, the first step is to change all the denominators to the same number.
True
A proportion statement states that two ratios are equal.
True.
Estimating should be used to determine if the calculations made are reasonable.
True.
To convert a fraction to a decimal, divide the numerator by the denominator.
True.
The decimal 0.85 is equal to 85%?
True. Change decimals to percentages by moving the decimal point two places to the right.
Metric system
Used in medical field has 3 units of measurement expressed by the power of 10
Kilogram
a kilogram is 1000 larger than a gram 1 KG = 1,000 X 1 GRAM if a book weights 1 kg and a paper clip weights 1 gram we would need 1000 paper clips to equal the weight of the book
What is the prefix for one 100th of a unit?
centi
A premature infant weighing 3 lbs is ordered 1 milligram per gram of a drug. How many milligrams should you administer to the patient?
convert lbs to grams multiply the mass value by 454 3 lbs x 454= 1362
Converting metric units
converting btwn metric units is as easy as moving the decimal point to the right or left . Example: to convert kilograms to grams, the decimal point is after the 1 = 1.000 kg to convert it to grams you need to move 3 places to the right to get to grams.
Which of the following is expressed as a ratio? a. 0.25 b. 40% c. 0.40 d. 2:5
d) 2:5
Match each metric system prefix with its meaning.
deci: 1/10 centi: 1/100 milli: 1/1000 micro: 1/1,000,000
Tylenol elixir 650 mg is ordered. You have 125 mg per 1 mL on-hand. How many milliliters should you administer to the patient per dose?
divide 650 mg by 125 mg = 5.2 5.2 milimeters
To convert Lbs to KG
divide number of pounds by 2.2 Infants and smaller children often need more smaller dosages and require a conversion to grams for certain medications.
All measurements in the metric system are based on units of five.
false. Units of ten.
Statistics
is the collection and analysis of large amounts of numerical data and, when organized, are commonly presented as percentages and averages. Statistics help health care providers, insurance companies, health care administrators, researchers, pharmaceutical companies, and others make decisions about providing care and services to patients. a few examples of health care statistics: - Percentage of overweight or obese patients who develop diabetes - Percentage of smokers who develop lung cancer - Average age of death of a female born in 1945 - Increase in number of patients using the emergency room of the local hospital - Success rate of heart transplant surgery in New York - Percent of patients in a clinical trial whose condition is improved by taking a particular drug
What is the metric unit of measure for volume?
liter
Proportions are commonly used in health care to calculate
medication dosages
On which whole unit would a patient's height be measured using the metric system?
meter.
What does the abbreviation "mcg" stand for?
microgram
Which is one millionth of a meter?
micrometer
DRUG DOSAGE FORMULA
required dose = desired dose/ on hand dose TIMES (x) quantity of on hand dose
The collection and analysis of numerical data about the number of people who receive influenza vaccinations is known as
statistics
When multiplying fractions, it is not necessary to find a common denominator.
true
A technique to make estimating easier is to round the numbers in the calculation.
true.
In military time, seven in the morning is written as 0700.
true.
In the metric system, the unit of measuring distance or length is the meter.
true.
More than 50% of medication errors caused by misreading numbers are caused when the numerals 1 and 7 are confused.
true.
One gallon is equal to four quarts?
true.
The gream is used as the base unit to measure mass and weight in the metric system.
true.
The oldest and least used of the three systems of measurement in the text is the apothecary system.
true.
The reason for using military time in health care is to avoid confusion when recording day and night times.
true.
To convert measurements from one system to another, set up a proportion and solve for the unknown quantity.
true.
Bumex 4 mg is ordered bid (twice a day) . You have 2 mg tablets on-hand. How many total tablets will you need for the patient that day?
you need to give the patient 4mg twice a day. Meaning 8 mg total dosage. divide the amount of dosage (4 mg bid = 8mg) by the amount of tablets on hand (2 mg tablets)
