Chapter 18 Medical Math 2009 Delmar Cengage Learning

Chapter 18 Medical Math © 2009 Delmar Cengage Learning

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 (continues) to achieve 100% accuracy © 2009 Delmar Cengage Learning

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 © 2009 Delmar Cengage Learning

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? (continues) – 240+120+45+60=465 ml of fluid © 2009 Delmar Cengage Learning

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? (continues) • 214 -195= 19 pounds. © 2009 Delmar Cengage Learning

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 30 ml of broth and 15 ml of agar, how much of each do you prepare? • 30 ml x 24 = 720 (continues) • 15 ml x 24=360 © 2009 Delmar Cengage Learning

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 © 2009 Delmar Cengage Learning

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 60 g, you went over 16. 64 © 2009 Delmar Cengage Learning

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) © 2009 Delmar Cengage Learning

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 © 2009 Delmar Cengage Learning

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!! © 2009 Delmar Cengage Learning

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 © 2009 Delmar Cengage Learning

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. © 2009 Delmar Cengage Learning

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. © 2009 Delmar Cengage Learning

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 © 2009 Delmar Cengage Learning

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 © 2009 Delmar Cengage Learning

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 © 2009 Delmar Cengage Learning

18: 4 Angles • Used in health care for – 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 (continues) • Do Examples on page 574 © 2009 Delmar Cengage Learning

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) © 2009 Delmar Cengage Learning

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 12 in/1 ft =144 in/x feet 144/12 = 12 feet • Look at figure 18 -9 © 2009 Delmar Cengage Learning

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 © 2009 Delmar Cengage Learning

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) © 2009 Delmar Cengage Learning

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 © 2009 Delmar Cengage Learning

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 © 2009 Delmar Cengage Learning

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 © 2009 Delmar Cengage Learning