Things to ponder…..

1. Things to ponder….. Should students interested in pursuing a career in health care be proficient in math? How does accuracy of mathematical calculations affect the quality of patient care? How will health care workers apply mathematical concepts?

2. Are mathematical calculations completed by humans or machines? Are either one free of error? What units of measurement are used in the health care field? How is data recorded in health care?

3. Medical professionals use math every day while providing health care for people around the world. • Write prescriptions • Administer medication • Draw up statistical graphs of epidemics • Figure out the success rates of treatments

4. Math requires the student to know systems of measurement (metric, household, apothecary) and how to convert within those systems of measurement. It is essential to understand drug weights and measures to accurately calculate medication dosages.

5. Basic mathematical calculations are used for: • Conversions • Charting • Graphing • Dosage calculations • Measurements

6. Roman numerals vs Arabic numerals The number system we use daily and are familiar with is Arabic numerals ( 0 – 9 or any combination of these digits). In medication, prescriptions, and other occasional uses, it is necessary to know Roman numerals. Roman numeral system uses letters to represent numeric values.

7. Roman Arabic I one 1 V five 5 X ten 10 L fifty 50 C one hundred 100 D five hundred 500 M one thousand 1000

8. Using Roman numerals… • Rule 1: • When two Roman numerals of the same or decreasing value are written beside each other, the values are added together. • Examples: • VI = 5 + 1 = 6 • XX = 10 + 10 = 20 • LX = 50 + 10 = 60

9. Rule 2 • When Roman numerals of increasing value are written beside each other, the smaller value is subtracted from the larger value. • Examples: • IV = 5 – 1 = 4 • XC = 100 – 10 = 90 • LX = 50 – 10 = 40

10. Rule 3 • No more than three roman numerals of the same value should be used in a row. Examples: To write the number 4, do not write IIII, instead write it as IV (5-1=4) To write the number 59, do not write LVIIII, instead write L for 50, then IX ( 10-1=9) which is written LIX.

11. Rule 4 • A line written over a Roman numeral changes its value to 1,000 times its original value. Examples: _ _ X = 10, 000 L = 50, 000

12. Convert Roman numerals to Arabic • Must be able to separate the Roman numerals into manageable units first. • The easiest way to do this is to make a distinction between the groups that need to be added together and the groups that require subtraction. • 1st – scan the Roman numerals looking for any groups where a smaller value is written before a larger value. These indicate subtraction. • 2nd – total the values from left to right.

13. Example 1: convert XCIV to an Arabic number • 1st – XC is a subtraction group (100-10= 90). • 2nd – IV is also a subtraction group (5-1=4) • Now total the values from left to right. • 90 + 4 = 4

14. Example 2: convert CDLXXVII to an Arabic number 1st – CD is a subtraction group (500-100=400) 2nd – Add 400+50+10+10+5+1+1= 477 Remember: before you begin conversion, it is necessary to know the values of the various Roman numerals so that you can recognize subtraction groups. Failure to recognize a small value written before a larger one will result n an incorrect answer.

15. Converting Arabic to Roman numerals Must be able to separate the Arabic numerals into manageable units first. The easiest way to do this is to make a distinction among the different place values in our number system (ones, tens, hundreds, etc.) Going from left to right, write each place value using Roman numerals. Be sure to follow the four rules for writing Roman numerals correctly.

16. Example 1: convert 1,768 to a Roman numeral Separate 1,768 Arabic Roman • 1000 M • 700 DCC • 60 LX • 8 VIII Write out the Roman numeral as one answer leaving no spaces between the different parts. Answer: MDCCLXVIII

17. Example 2: convert 479 to Roman numeral Separate 479 Arabic Roman 400 CD 70 LXX 9 IX Answer: CDLXXIX

18. Military time Military time works on the premise of a 24-hour day. The precise method of measuring time doesn't require the use of a.m. and p.m. designators to determine the time of day. Learning how to convert to military time begins with an understanding of how individuals express in different ways from the standard hour and minute method.

19. 1st - Think in terms of a 24-hour period of time. Military time begins at midnight with the figure of 00 hours indicating the start of a 24-hour day. Morning and evening designations aren't necessary when figuring time in 24-hour increments. 2nd - Recognize that each hour up to noon is exactly the same as regular time. The change occurs at the switch to regular time's p.m. designation. Military time denotes 1 p.m. as 1300 and each hour thereafter counts upward to 23.

20. 3rd - Express minutes and seconds in exactly the same way as regular time. Military time uses 60 minutes in an hour and 60 seconds to a minute. The time of 4:35 in regular time could mean either morning or afternoon without the proper designation of a.m. or p.m. Military time shows 4:35 a.m. as 0435 and 4:35 p.m. as 1635. 4th - Write the correct military time notation properly. For example, use 0435:45 hours to express the time 4:35 and 45 seconds in regular time (4:35:45).

21. 5th - Recognize that 24 hour clocks may represent midnight as 0000 hour while others call midnight 2400 hours. 6th - Remember to always drop the colon to correctly format military time when writing. 7th - The proper language used for describing military time refers to hours in terms of hundreds. For example, 5 a.m. is referred to O-five hundred hours. Five p.m. is referred to as 17 hundreds hours (1700).

22. Examples: 1:00 pm will be 1300 2:00 pm will be 1400 3:30 pm will be 1530 4:09 pm will be 1609 11:20 pm will be 2320 12:00 am(midnight)will be 0000 or 2400 12:15 am will be 0015 not 2415 12:01 am will be 0001 not 2401

23. Percent Base • To find a certain part of a whole, to find what percent of the whole is being represented, or to find out what the whole number is to which you are comparing, you can work a percent-base problem. • The percent represents the part you are comparing and the base is the whole to which you are comparing

24. In a % base problem, there are 3 parts: • The percent • The base • The part (or percentage)

25. 16 x .25 = 4 16 is the base .25 is the % 4 is the part (whole) (changed to a decimal) (percentage) This problem indicates that 25% (.25) of 16 is 4. Multiplication is used in the problem with the multiplication and equal signs is an important part of being able to solve it.

26. It will be necessary to solve a percent-base problem looking for each of the three guidelines: Noticing the words “of” and “is” will help in setting up the problem and solving it. The word “what” indicates the missing answer. If the unknown answer is not alone on the left or right side of the equal sign, you must multiply to find the solution.

27. What is 15% of 200? 1. Put the problem into symbols and numbers. “what” = 15% x 200 2. Change the percent to decimal and solve. “what” = .15 x 200 3. Decide whether to multiply or divide (multiply because the unknown part is alone.) 200 x .15 30.00 Answer: 30 is 15% of 200

28. Forty is 20% of what number? 1. Put the problem into symbols and numbers. 40 = 20% x “what” 2. Change the percent to decimal and solve. 40 = .20 x “what” 3. Decide whether to multiply or divide. (divide because the unknown part is not alone) 40 divided by .20 = 200 Answer: 40 is 20% of 200

29. What percent of 80 is 24? 1. Put the problem into symbols and numbers. “what” % x 80 = 24 2. Change the percent to decimal and solve (we are looking for the percent…we can’t change it now, but we must once we find it) 3. Decide whether to multiply or divide (divide because the unknown part is not alone.) 24 divided by 80 = .3 4. Change .3 to a percent (.3 = 30%) Answer: 30% of 80 is 24

30. Proportion: Expresses the relationship between two ratios. It is written as two ratios with an equal sign between. Example: 3:4 = 1:5 The four numbers in the proportion have special names

31. 3:4 = 1:5 The two outer numbers in this case 3 and 5 are called the Extremes. The two inner numbers in this case 4 and 1 are called Means. In a true (equal) proportion, the product of the means should equal the product of the extremes. 3:4 = 1:5 Means Extremes 4x1=4 3x5=15 4 doesn’t equal 15 which means this is not a true proportion.

32. Solving Proportions If you know that a proportion is true (that the ratios are equal), you can solve for a missing part. This is very useful because it helps you solve problems based on another problem as your model.

33. For example: if you know a patient should get 1ounce of medicine for every 20 pounds of body weight, you can use a proportion to determine how much to give a 180 lb man. Example: you can compare ounces to pounds in two rations and set them equal. oz 1 oz = # of oz to give lb 20lb 180 lb

34. oz 1 oz = # of oz to give lb 20lb 180 lb Since this is a true proportion, the product of the means equals the product of the extremes. 1:20 = ?:180 Means = Extremes 20 x ?oz = 1 x 180 20 x ?oz = 180 20 20 oz = 9 A 180lb man needs 9oz of medicine.

35. Proportions do not always contain just whole numbers as the means and extremes. Occasionally they may contain fractions, decimals, or more complicated expressions. These two can be solved by the unknown amount.

36. Example 1 Halterol is administered by the following formula: ½ tablet per blood lost. Josie recently lost three pints of blood. How much Halterol should be administered?

37. Tablets½ = unknown “x” Pints 1 3 ½ : 1 = x:3 Means = Extremes 1x = ½ (3) x = 1 ½ Josie needs 1 ½ tablets

38. Example 2 Solve the following: 5 : (x-2) = 10 : 6

39. Means = Extremes 10 (x – 2) = 5 x 6 (multiply everything in the parentheses by 10) 10x – 20 = 30 (add 20 to both sides) 10x – 20 + 20 = 30 +20 (-20 + 20 = 0) 10x = 50( divide both sides by 10) 10 10 Answer: x = 5

40. Remember: It is wise to check your answers when you have solved a proportion You should be able to replace the answer you found back into the original proportion, multiply the means and extremes, and the result will be a true proportion. If it is not, recheck your work.

41. Measurement The three main types of measurements: volume length mass English system and Metric system

42. English system • English system is the most common system used in the U.S. • Learn the abbreviations and equivalent measures. • To convert from one measurement to another, you must multiply or divide by different numbers for each different conversion. (Conversion Number)

43. Conversion numbers: Three basic group of conversion numbers: Volume - gallon, half gallon, quart, pint, cup, ounce, Tbsp, and tsp Length - mile, yard, foot, and inch Mass - pounds and ounces

44. When converting from a large unit to a smaller one, multiply by the conversion number. • When converting from a small unit to a larger one, divide by the conversion number. • Hint: you will need to memorize the conversion numbers for volume, length, and mass. • 1Tbsp = 3tsp 1oz = 2 Tbsp • 1ft = 12 inches 1 yd = 3 ft • 1lb = 16 oz

45. Metric System • Based on the number 10 • Learn the prefixes kilo (k) = 1,000 deci (d) 0.1 hecto (h) = 100 centi (c) 0.01 deka (dk) = 10 milli (m) 0.001 A prefix can never be used alone. It must have a base unit with it to indicate whether you are measuring length, volume, or mass.

46. Three basic units: • Gram (g) – measures mass or weight (solid) • Liter (l) – measures volume or liquid (fluid) • Meter (m) – measures length or distance *___*___*___One___*___*___* k(1000) h (100) dk (10) Basic Unit d (0.1) c (0.01) m (0.001) kl hl dkl Liter(l) dl cl ml kg hg dkg Gram(g) dg cg mg km hmdkm Meter(m) dm cm mm

47. Each unit can be multiplied by 10 to produce increasingly larger units or divided by 10 to produce smaller units. • Length – kilometer, hectometer, dekameter, meter, decimeter, centimeter, millimeter • Volume – kiloliter, hectoliter, dekaliter, liter, deciliter, centiliter, milliliter • Mass – kilogram, hectogram, dekagram, gram, decigram, centigram, milligram

48. Rule of thumb using metric system Because all of the measurements are related by the number ten, you convert measurements by the moving the decimal either to the left or right. Example: 6.9 liters (l) = ____ ml *___ *___ *___ * *___ *___ *____ k(1000) h (100) dk (10) Basic Unit d (0.1) c (0.01) m (0.001) kl hl dkl Liter(l) dl cl ml 6.9 liters 6900ml The decimal was moved 3 units to the right to go from liters(l) to milliliters(ml)

49. Converting Rules of thumb… • It is helpful to know the relationship of metric measurements to their English counterparts. • All units of measurement must be in the same system, that is, volume to volume, weight to weight, and length to length. • Label all units of measurement.

50. Be sure that the relationship between units is the same on both sides of the equation. • When changing English units to metric , multiply by the appropriate number. • When changing Metric to English divide by the appropriate number. • Hint: • English to Metric = multiply • Metric to English = divide