Download Medical Mathematics

MEDICAL
MATHEMATICS
HEALTH SCIENCE 1
OBJECTIVES
• Perform basic math calculations on whole numbers,
decimals, fractions, percentages and ratios
• Convert between the following numerical forms:
decimals, fractions, percentages and ratios
• Round off numbers correctly
• Solve mathematical problems with proportions
• Express numbers using Roman numerals
• Estimate angles from a reference plane
• Use household, metric and apothecary units to express
length, volume, and weight
• Convert between the Fahrenheit and Celsius temp
• Express time using the 24-hour clock (military time)
INTRODUCTION
• Working in health care requires the use of various
math skills to measure and perform various types of
calculations. Some common applications used
include:
• Calculating medication dosages
• Taking height and weight readings
• Measuring the amount of intake (fluids consumed or
infused) and output (fluids expelled, e.g., urine, vomit)
• Billing and bookkeeping tasks
• Performing laboratory tests
• Mixing cleaning solutions
IMPORTANCE
• Errors in math can have negative effects on
patients.
• Ex: administering the wrong dosage of medication is a
serious mistake and can harm or even kill a patient
• Health care workers must strive for 100% accuracy. If
there is any doubt, it is essential to ask your
supervisor or a qualified co-worker to double-check
math calculations
BASIC CALCULATIONS
• Essential to be able to add, subtract, multiply and
divide whole numbers, decimals, fractions and
percentages.
• Best to know how to do it “long hand” (without a
calculator) One may not always be available or
can quit working
• Professional exams required for licensure or certification DO
NOT allow the use of calculators
• Also need to understand equivalents when using
decimals, fractions, and percentages
• Ex: ½=.5=50%
WHOLE NUMBERS
• Used traditionally to count. They do not contain fractions
or decimals
• Ex. 1,2,3,4……
• Addition of whole numbers: adding 2 or more numbers
together to find the SUM, or total.
• Few examples of addition being used in the health care:
Counting and totaling supplies for an inventory
Adding oral (by mouth) intake
Adding intravenous, or IV (into vein), intake
Measuring and totaling output from the body such as amounts
or urine
• Completing statistical information such as the total of number
of patients diagnosed with lung cancer or the total number of
surgeries performed in a hospital in one–year period
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WHOLE NUMBERS
• Add whole numbers together, the numbers are
placed in a column and lined up on the right side.
• Ex. A nurse assistant must encourage a patient to drink large
amounts of fluid. For lunch, the patient drank 240cc of milk,
120cc of coffee, 45cc of water, and 60cc of juice. What is
the total amount of fluids the patient drank?
240
120
45
+ 60
465
SUBTRACTION OF WHOLE NUMBERS
• Subtraction is the process of taking a number away
from another, number to find the difference, or
remainder, between the numbers.
• A few examples of how subtraction is used in health
care includes:
• Determining weight loss or gain
• Maintaining an inventory of supplies
• Calculating a pulse deficit (difference between the number
of times a heart betas and the actual pulse it creates)
• Performing laboratory tests
• Reporting statistical information such as the number of
deaths from a particular disease
SUBTRACTION OF WHOLE NUMBERS
• To subtract whole numbers, the number to be
subtracted is placed under the number from which
it is to be subtracted. Both numbers must be lined
up on the right-hand column. Starting at the right
side, the bottom number is subtracted from the top
number.
• Ex. A patient with a heart condition is on a weight-reduction
plan. Last month the patient weighed 224 lbs, this month the
patient weighs 195 lbs. How much weight did the patient
lose?
224
- 195
29
MULTIPLICATION OF WHOLE NUMBERS
• Multiplication is actually a simple method of addition.
• Ex. If three 7’s are added together, the answer or sum is 21.
(7+7+7=21) If the number 7 is multiplied by 3, the answer or
product is 21. (7x3=21)
• A few examples of how multiplication is used in health
care include:
• Maintaining payroll records, including hours worked and salary
earned
• Performing laboratory tests
• Determining the magnification power of a microscope
• Calculating prescription amounts such as the number of pills a
patient should receive for a 30-day supply of medication
• Calculating caloric requirement based on body weight
MULTIPLICATION OF WHOLE NUMBERS
• To multiply whole numbers, write the number to be
multiplied first (multiplicand). If possible, use the
largest number. Under that number, write the
number of times it is to be multiplied (multiplier),
making sure the numbers are lined up on the right
side. Then multiply every number in the multiplicand
by every number in the multiplier. After all the
multipliers are used, the products obtained are
added together to get the answer.
MULTIPLICATION OF WHOLE NUMBERS
• Example:
• A medical laboratory technician is preparing agar slant
tubes. The tubes are used to grow microorganisms so the
cause of the disease can be identified. He needs a total of
24 tubes. For each tube he needs 30 milliliters (mL) of broth
and 15 (mL) of agar. What is the total amount of broth
needed and the total amount of agar needed?
• 30
x 24
120
+60
720 mL broth
15
x 24
60
+30
360 mL agar
DIVISION OF WHOLE NUMBERS
• Division is a simple method of determining how
many times one number is present in another
number. A few examples of how division is used in
health care include:
• Calculations of diet and amounts of nutrients allowed
• Determining cost per item while ordering bulk supplies or
equipment
• Performing laboratory tests
• Compiling statistics on diseases and death rates
• Calculating budgets and salaries
DIVISION OF WHOLE NUMBERS
• Division involves the use of 2 numbers: a dividend
and a divisor. The number to be divided is the
dividend. The divisor is the number of times the
dividend is to be divided. It is important to position
these numbers correctly in order to obtain an
answer or quotient.
• Ex. A student doing research learns that statistics show
526,704 people die of cancer each year. On average, how
many people die of cancer each month? (Hint: 12 months
in a year.)
•
43892
• 12√526704
DECIMALS
• Decimals are one way of expressing parts of
number or anything else that has been divided into
parts. The parts or expressed in units of 10. That is
decimals represent the number of tenths,
hundredths, thousandths and so on that are
available.
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0.5 is read “five tenths”
1.5 is read “one and five tenths”
1.50 is read “one and fifty hundredths”
1.500 is read “one and five hundred thousandths
1.5000 is read “one and five thousand ten thousandths
DECIMALS
DECIMALS
• A few examples of how decimals are used in health
care include:
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Determining medication dosages
Performing laboratory tests
Calculating dietary requirements or restrictions
Measuring respiratory function
Maintaining payroll records
Billing charges on patient accounts
Determining exposure to radiation
Totaling the cost of supplies and equipment orders
DECIMALS
• Example:
• A dietitian is teaching teenagers about the high levels of fat
in fast food. She notes that there are 44.51 grams (g) of fat
in a bacon cheeseburger, 18.3 g in a large serving of fries,
and 13.83 g in a milkshake. How many grams of fat does this
meal contain? (Remember to line up the decimal points to
add the numbers together.)
44.51
18.3
+ 13.83
76.64 g of fat
FRACTIONS
• Fractions are another way of expressing numbers
that represent parts of a whole. A few example of
how fractions are used in health care include:
Measuring solutions for laboratory tests
Calculating height and weight
Measuring head circumference on an infant
Measuring solutions such as disinfectants for infection
control
• Preparing dental materials and trimming dental models
• Mixing infant formulas or tube feeding
• Calculating dosages for certain medications
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FRACTIONS
• Fractions have a numerator (top number) and a
denominator (bottom number)
• An example of a fraction is 3/10 where
PART
3
WHOLE
10
FRACTIONS
• Reducing fractions – some fractions must be
reduced to their lowest terms
• Ex: 4/8 = ½
• Improper fractions have numerators that are larger
that the denominators. To reduce these fractions,
divide the denominator into the numerator. The
result will be a whole number or a mixed number
• Ex: 12/4 = 3
• Ex. 11/4 = 2 ¾ (11 - 4=2 ¾ )
DIVIDING FRACTIONS
• Dividing fractions requires the dividing fraction to be
inverted (turned upside down). The new upside-down
fraction is called the reciprocal. The numerators and
denominators are then multiplied to get the answer.
• Ex. ½ ÷1/2 =1/2 X 2/1 = 2/2 or 1
• Ex. A dental assistant has ½ ounce of disinfectant solution in
one bottle and 2/3 ounce in a second bottle. Can the 2
bottled be combined in a 1 ½ ounce bottle? To solve this, add
½ and 2/3 together using the following steps.
• Think of a number that both 2 and 3 divide into evenly. Answer is 6
• 6÷2=36÷3=2
Then multiply the numerator by the number of times the
old denominator goes into 6
• 1X3=3
½=3/6
2/2 = 4
2/3=4/6
• Now add the 2 numerators together and place the answer over the
common denominator
3/6 + 4/6 = 7/6
DIVIDING FRACTIONS
• 7/6 is an improper fraction because the numerator
is larger than the denominator. Divide the
denominator in the numerator
• 7÷6=1 ⅙ ounces
• Will 1 ⅙ ounces fit into a 1 ½ ounce bottle?
• Change the ½’s to 6ths.
• 6÷2=3
3×1=3
½=3/6
• ANSWER: This bottle will hold 1 3/6 ounces so 1 ⅙ ounces will fit into
the bottle!
DIVIDING FRACTIONS
• Example 2: A pharmacist must prepare 24 ounces
of a tube feeding for a patient. The mixture is 1/3
formula and 2/3 water. How much formula should
the pharmacist use? How much water?
• To determine the amount of formula, multiply 24 (write the
fraction 24/1) by 1/3
• 24/1X1/3=?
• Multiply the numerators: 24X1=24
• Multiply the denominators: 1X3= 3
• New numerator of new denominator: 24/3
• 24÷3=8
• Pharmacist will need 8 ounces of formula
• How Much water will the pharmacist need?
PERCENTAGES
• A few examples of how percentages