Chapter 18 Medical Math

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 (continues)

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

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? 240+120+45+60=465 ml of fluid (continues)

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? 214-195= 19 pounds. (continues)

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 (continues)

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

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+13.83 g= 76.64 g fat your recommended amount is 60g, you went over 16.64

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 (continues)

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

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!!

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

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.

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.

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

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

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

18:4 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 (continues)

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)

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 144/12 = 12 feet Look at figure 18-9

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

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 (continues)

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 578-579 1-8

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 18-10 and 18-11 in text

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 18-12 in text