1. Chapter 18
Medical Math

2. Introduction
Math skills are a requirement for working in a health care occupation
Calculations are needed for
Correct medical dosages
Recording height and weight
Intake and output measurement of fluids
Administrative tasks such as bookkeeping and billing
Tests performed in the lab
Mixing of cleaning fluids
Health care workers must make every effort to achieve 100% accuracy
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3. 18:1 Basic Calculations
It is necessary to be able to add, subtract, and divide whole numbers, decimals, fractions, and percentages
Understanding of equivalents when using decimals, fractions, and percentages
When taking professional exams for licensure or certification, calculators are sometimes not allowed

4. Whole Numbers Do not contain decimals or fractions
Addition—adding numbers together to find the total amount
Several uses in health care
Inventory records
Statistical information on patients
Example: You are to record and total the amount of fluid intake
A patient drank 240 ml. milk, 120 ml coffee, 45 ml water, and 60 ml juice…what is the total?
=465 ml of fluid
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5. Whole Numbers (continued)
Subtraction—taking a number away from a number to find the difference
Several uses
Weight loss
Pulse deficit calculation
Example: A patient with a heart condition is on a weight reduction plan. Last month he weighed 214 pounds and now weighs 195 pounds, how much weight was lost?
= 19 pounds.
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6. Whole Numbers (continued)
Multiplication—same as addition or multiplying to find the quantity
Several uses include
Payroll records (salary amount paid for number of hours worked)
Microscope power magnification
Example: You need a total of 24 agar slant tubes, each tube you need 30ml of broth and 15 ml of agar, how much of each do you prepare?
30ml x 24 = 720
15 ml x 24=360
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7. Whole Numbers (continued)
Division—finding how many times a number is contained in another number
Finding cost of one item
Determining amount of diet nutrients
Example: 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?
526,704/12=43892

8. Decimals Decimals—are based on the number 10
Represent the number of tenths, hundredths, thousandths, and so on
Are added, subtracted, multiplied, and divided the same as whole numbers
Always check the placement of the decimal point to avoid mistakes
Examples (See Table 18-1 in text) A dietician has you add up the grams of fat you have eaten:
44.51 g+18.3 g g= g fat your recommended amount is 60g, you went over 16.64

9. Fractions
Fraction—a quantity less than a whole number expressed as a decimal
Has a numerator (top number) and a denominator (bottom number)
Some fractions need to be reduced to their lowest term. 4/8 =1/2
See Table 18-2 in text
Examples: do example on page 567
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10. Fractions (continued)
Improper fractions—numerators are larger than denominators
Converting fractions is used for addition and subtraction: have to have the same denominator!
Multiplying fractions
Dividing fractions—needs to be inverted (reciprocal) and then multiplied
Examples : Go over the two examples on page 568

11. Percentages Percentages—whole or proportion of a whole (100%)
Part/whole x 100= %
Advantage is to convert the percentage to a decimal before adding, subtracting, multiplying, and dividing
Examples: Do examples 1&2 on page 569!!

12. Ratios Shows relationship between like values or numbers
Health care workers use ratios for strengths of solutions
50 percent strength solution is 1:2 ratio

13. Converting Decimals, Fractions, Percentages, and Ratios
Decimals, fractions, and percentages represent parts of a whole
There are specific methods of conversion from one to another
See Table 18-3 in text: go over this table and look at the examples on how to do each calculation.

14. Rounding Numbers
This requires changing them to the nearest ten, hundred, thousand, and so on
Depends on degree of accuracy
Refer to Table 18-4 in text
Examples : go over examples on page 571.

15. Solving Problems with Proportions
Proportion—equality between two ratios (“two is to six as three is to nine”)
For converting from one unit to another when three in the proportion are identified
Examples: Go over examples pg. 572

16. 18:2 Estimating
Estimating—a reasonable approximate calculation of the answer
Errors can occur with numbers in wrong order or decimal points misplaced
Practice and thought is needed when learning to estimate answers and detecting incorrect answers

17. 18:3 Roman Numerals
Numbers used today are known as Arabic numerals (1, 2, 3, and so on)
In the health care field Roman numerals are used for specific reasons
Study Table 18-5 in text

18. 18:4 Angles Used in health care for Indication of bed positions
Injection of medications
Description of joint movements
Indication of bed positions
Angles are made when two plane surfaces meet along a line
The distance between the plane and line of the angle is measured in degrees
See Figure 18-6 in text
Do Examples on page 574
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19. 18:5 Systems of Measurement
Various systems of measurement used in health care
Terminology in each system
Distance (length)
Capacity (volume)
Mass (weight)
Each system has its own method of naming (nomenclature)

20. Household System Used in the United States Discuss Table 18-6 in text
With basic equivalents known then unknown measurements can be found by using proportions
12in/1ft =144in/x feet /12 = 12 feet
Look at figure 18-9

21. Metric System More accurate than the household system Metric units
Distance/length: meter (m)
Capacity/volume: liter (l or L)
Mass/weight: gram (g or gm)
See Table 18-7 in text: know prefixes!!
Metric system based on multiples of tens
Go over examples 1-3 and 1-2 pg. 577

22. Apothecary System
Oldest and used less than the metric or household systems
Still used by some doctors
Necessary for health care workers to be able to convert within the system
See Table 18-8 in text
Use of lowercase and uppercase Roman numerals sometimes used along with this system
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23. Converting Systems of Measurement
Health care workers need to be aware of equal values between units
Not an exact science when converting
The answer is considered to be approximately the same
Discuss Table 18-9 in text
Go over Examples page

24. 18:6 Temperature Conversion
Use of the Fahrenheit (F) thermometer scale in the United States
Centigrade (Celsius) or C is often used in health care
Conversion charts and formulas (using fractions or decimals) are available
See Tables and in text

25. 18:7 Military Time Traditional system of correct time uses
A.M. and P.M. (12 hours)
Errors can occur if time is misread
Accuracy of time is critical in health care
Military time is based on a 24-hour day
Avoids any confusion
See Table in text