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# Rev. 0527 Basic Math Review Complete

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• ### Rev. 0527 Basic Math Review Complete

1. 1. Basic Math Review Tyra L. Ousley, RN, MSN
2. 2. I. PERCENTAGES <ul><li>Any quantity stated as the proportion per hundred; expressed with % sign meaning “for every hundred”. </li></ul>
3. 3. A. Convert a percent to a decimal <ul><li>RULES: </li></ul><ul><li>Delete the % sign </li></ul><ul><li>Divide the remaining number by 100, which is the same as moving the decimal point 2 places to the left. </li></ul><ul><li>Ex: 25% = 25/100 = 0.25 </li></ul><ul><li>50% = ___________ </li></ul><ul><li>75% = ___________ </li></ul><ul><li>67% = ___________ </li></ul>
4. 4. B. Convert a decimal to a percentage <ul><li>RULES: </li></ul><ul><li>Multiply the decimal number by 100 (move the decimal point 2 places to the right) and </li></ul><ul><li>Add % sign </li></ul><ul><li>Ex: 0.25 x 100 = 25% </li></ul><ul><li>0.50 = _______% </li></ul><ul><li>0.75 = _______% </li></ul><ul><li>0.67 = _______% </li></ul>
5. 5. C. Converting a common fraction to a percentage <ul><li>RULES </li></ul><ul><ul><li>Convert the fraction to a decimal by dividing the numerator by the denominator </li></ul></ul><ul><ul><ul><li>3/8 (0.375) </li></ul></ul></ul><ul><ul><li>Move the decimal point two places to the right, round off if necessary </li></ul></ul><ul><ul><ul><li>37.5 or 38 </li></ul></ul></ul><ul><ul><li>Add the % sign </li></ul></ul><ul><ul><ul><li>37.5% or 38% </li></ul></ul></ul>
6. 6. Examples <ul><li>4/5 </li></ul><ul><li>2/3 </li></ul><ul><li>7/8 </li></ul><ul><li>3/4 </li></ul>
7. 7. Convert a percent to a fraction <ul><li>RULES: </li></ul><ul><li>Delete the % sign </li></ul><ul><li>Write the remaining number as the numerator </li></ul><ul><li>Write the 100 as the denominator </li></ul><ul><li>Reduce the common fraction to the lowest term </li></ul><ul><li>Ex: 25% = __________ </li></ul><ul><li>50% = __________ </li></ul><ul><li>75% = __________ </li></ul>
8. 8. II. RATIOS AND FRACTIONS IN PROPORTIONS <ul><li>Numerical ways to compare items. </li></ul><ul><li>A proportion is a set of two equal ratios or fractions </li></ul>
9. 9. <ul><li>Ratios in proportions </li></ul><ul><li>Written with a double colon separating the ratios (Example: 3:1 :: 6:2 ) </li></ul><ul><li>The outer numbers (3&2) are the extremes. </li></ul><ul><li>The inner numbers (1&6) are the means </li></ul><ul><li>The product of the extremes must equal the product of the means </li></ul><ul><ul><li>Solve for X in this proportion </li></ul></ul><ul><ul><ul><li>3:1 :: 6:X </li></ul></ul></ul><ul><ul><ul><li>2.5 : 1.2 :: X : 3.2 </li></ul></ul></ul><ul><ul><ul><li>¼ : 2 :: 1/3 : X </li></ul></ul></ul>
10. 10. B. Fractions in proportions <ul><li>Cross products should be equal </li></ul><ul><ul><li>5 X </li></ul></ul><ul><ul><li>--- = --- </li></ul></ul><ul><ul><li>2 4 </li></ul></ul><ul><li>Rewrite the problem to multiply cross products </li></ul><ul><ul><li>2 x X = 5 x 4 </li></ul></ul><ul><li>Obtain the cross products </li></ul><ul><ul><li>2X = 20 </li></ul></ul><ul><li>Solve for X by dividing both sides by 2 </li></ul><ul><li>Find X (10) </li></ul>
11. 11. Example: <ul><li>X = 1 </li></ul><ul><li>55 2.2 </li></ul><ul><li>X = 0.5 </li></ul><ul><li>75 50 </li></ul><ul><li>80 = 60 </li></ul><ul><li>10 X </li></ul>
12. 12. Convert a fraction to a decimal <ul><li>RULE: To convert a fraction to a decimal, divide the numerator by the denominator. </li></ul><ul><li>Ex: 1/ 4 = _________ </li></ul><ul><li>2/5 = ____________ </li></ul><ul><li>4/10 = _____________ </li></ul>
13. 13. Convert decimal to a fraction <ul><li>Decimal fractions are fractions with a denominator of 10, 100, 1000 or any multiple or power of 10. </li></ul><ul><li>Ex: 0.1 = _________ </li></ul><ul><li>0.01 = _______ </li></ul><ul><li>0.001 = ___________ </li></ul>
14. 14. SYSTEMS OF DRUG MEASUREMENT <ul><li>I. METRIC SYSTEM </li></ul><ul><ul><li>Basic units of measurement: </li></ul></ul><ul><ul><ul><li>Meter (m) – unit of length </li></ul></ul></ul><ul><ul><ul><li>Liter (L) – unit of volume </li></ul></ul></ul><ul><ul><ul><li>Gram (G, GM, Gm) – unit of weight </li></ul></ul></ul>
15. 15. METRIC SYSTEM WEIGHT ABBREV CONVERSION FACTOR Gram g 1g=1000 mg milligram mg 1 mg=1000 mcg =0.001 g microgram mcg 1 mcg=0.001 mg = 0.000001 g kilogram kg 1 kg=1000 g
16. 16. Metric Conversions <ul><li>To convert a smaller unit to a larger one, move the decimal point to the left or divide by the appropriate multiple of 10 </li></ul><ul><ul><li>Example: milligrams to grams </li></ul></ul><ul><ul><li>1000 milligrams / 1000 = 1 </li></ul></ul><ul><li>To convert a larger unit to a smaller one, move the decimal point to the right or multiply by the appropriate multiple of 10 </li></ul><ul><ul><li>Example: gram to milligrams </li></ul></ul><ul><ul><li>1 gram x 1000 = 1000 mg </li></ul></ul>
17. 17. <ul><li>Larger to smaller unit MULTIPLY (L-S-M) </li></ul><ul><li>Smaller to larger unit DIVIDE (S-L-D) </li></ul><ul><li>Identify conversion factors </li></ul><ul><li>Convert 2 grams to equivalent milligrams </li></ul><ul><ul><li>Equivalent conversion= 1g=1000mg </li></ul></ul><ul><ul><li>2 g = 2 x 1000=2000 mg- by multiplication OR </li></ul></ul><ul><ul><li>2.000 = 2000 mg(moving decimal 3 places to right) </li></ul></ul>
18. 18. II. HOUSEHOLD SYSTEM <ul><li>Usually used at home </li></ul><ul><ul><li>Drop gtt (standard measure varies) </li></ul></ul><ul><ul><li>Teaspoon t (tsp) 1 t = 60 gtt </li></ul></ul><ul><ul><li>Tablespoon T(tbs) 1 T = 3 t </li></ul></ul><ul><ul><li>Ounce(fluid) oz 2 T = 1 oz </li></ul></ul><ul><ul><li>Ounce(wt) oz 1 lb = 16 oz </li></ul></ul><ul><ul><li>Cup cup 1 cup = 8 oz </li></ul></ul><ul><ul><li>Pint pt 1 pt = 2 cups </li></ul></ul><ul><ul><li>Quart qt 1 qt = 4 cups = 2 pints </li></ul></ul><ul><ul><li>Gallon gal 1 gal = 4 qt </li></ul></ul>
19. 19. III. Apothecaries’ System <ul><li>Uses Roman numerals </li></ul><ul><li>Unit of measurement is placed before the Roman numeral (Example: 5 grains is written as grains v ) </li></ul><ul><li>Basic units of measurement </li></ul><ul><ul><li>Minim: for liquid volume </li></ul></ul><ul><ul><li>Grain (gr): for solid weight </li></ul></ul>
20. 20. IV. Avoirdupois System <ul><li>Used for ordering and purchasing some pharmaceutical products and for weighing patients in clinical settings </li></ul><ul><li>Units of weight include grains, ounces, pounds </li></ul>
21. 21. V. Unit System <ul><li>USP – United States Pharmacopeia Units </li></ul><ul><li>IU – International Units </li></ul><ul><li>Common drugs in units </li></ul><ul><ul><li>Insulin </li></ul></ul><ul><ul><li>Heparin </li></ul></ul>
22. 22. VI. Milliequivalent System <ul><li>Most electrolytes are measured in mEq </li></ul><ul><ul><li>Example: Potassium Chloride </li></ul></ul>
23. 23. APPROXIMATE EQUIVALENTS <ul><li>1 g = gr(grains) xv = 1 ml = 1 cc </li></ul><ul><li>gr 1 = 60 mg </li></ul><ul><li>1 t = 5 ml </li></ul><ul><li>1 T = 3 t = 15 ml = ½ oz </li></ul><ul><li>1 oz = 30 ml = 6 t </li></ul><ul><li>1 L = qt I = oz 32 = pt ii = 4 c </li></ul><ul><li>pt I = = 500ml = oz 16 = 2 cups </li></ul><ul><li>1 cup = 240 ml = oz 8 </li></ul><ul><li>1 kg = 2.2 lbs </li></ul><ul><li>1 inch = 2.54 cm </li></ul>
24. 24. Conversions for Other Clinical Applications: Time and Temperature Chapter 5
25. 25. Time is an essential part of the drug order
26. 26. What are some issues related to using the traditional time method?
27. 27. 24-Hour Clock
28. 28. Traditional and 24-Hour Clock AM Int’l. Time PM Int’l Time 12:00 midnight 2400 12:00 noon 1200 1:00 0100 1:00 1300 2:00 0200 2:00 1400 3:00 0300 3:00 1500 4:00 0400 4:00 1600 5:00 0500 5:00 1700 6:00 0600 6:00 1800 7:00 0700 7:00 1900 8:00 0800 8:00 2000 9:00 0900 9:00 2100 10:00 1000 10:00 2200 11:00 1100 11:00 2300
29. 29. What Time Is It? <ul><ul><li>3:15 p.m. </li></ul></ul><ul><ul><li>4:45 a.m. </li></ul></ul><ul><ul><li>5:30 p.m. </li></ul></ul><ul><ul><li>10:10 p.m. </li></ul></ul><ul><ul><li>12:35 a.m. </li></ul></ul><ul><ul><li>0017 </li></ul></ul><ul><ul><li>1010 </li></ul></ul><ul><ul><li>1730 </li></ul></ul><ul><ul><li>2310 </li></ul></ul><ul><ul><li>0635 </li></ul></ul>
30. 30. What Is Wrong? <ul><li>Give two Tylenol at 9:00 </li></ul><ul><li>Blood pressure to be taken at 2510 </li></ul><ul><li>Insulin given at 23:10 p.m. </li></ul>
31. 31. Celsius and Fahrenheit Scales <ul><li>Convert between Fahrenheit and Celsius temperatures: </li></ul>
32. 32. Celsius and Fahrenheit Scales
33. 33. IMPORTANT FORMULAS <ul><li>TEMPERATURE CONVERSIONS </li></ul><ul><ul><li>Celsius °F-32 </li></ul></ul><ul><ul><ul><ul><ul><li>°C = ----------- OR 5/9 ( °F – 32) </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>1.8 </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>Example: 101 °F </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li> (101 – 32) </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>------------ OR 5/9 (101 – 32) </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>1.8 </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>= 69 /1.8 OR (5 x 69)/9 </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>= 38.3 °C </li></ul></ul></ul></ul></ul>
34. 34. TEMPERATURE CONVERSION <ul><li>FAHRENHEIT </li></ul><ul><ul><li>° F = 1.8 °C + 32 OR 9/5 °C + 32 </li></ul></ul><ul><ul><li>Example: 38.3 °C </li></ul></ul><ul><ul><li>1.8 x 38.3 + 32 OR (9 x 38.3) </li></ul></ul><ul><ul><li>------------ + 32 </li></ul></ul><ul><ul><li>5 </li></ul></ul><ul><ul><li>= 100.9 °F </li></ul></ul>
35. 35. Calculate the Temperatures <ul><li>40˚ Fahrenheit </li></ul><ul><li>75˚ Fahrenheit </li></ul><ul><li>18˚ Celsius </li></ul><ul><li>65˚ Celsius </li></ul>
36. 36. ORAL DOSAGE FORMS Steps: <ul><li>1. Ensure that all measurements are in the same system of measurement and the same size unit of measurement. If not, convert. </li></ul><ul><li>2. Calculate using this formula </li></ul><ul><li>D = desired amount or order </li></ul><ul><li>H = available or have on hand </li></ul><ul><li>Q = quantity </li></ul><ul><li> </li></ul>D H = Amount to be given X Q
37. 37. Oral Dosage Forms: Liquid Preparations <ul><li>Steps: </li></ul><ul><li>Ensure that all measurements are in the same system of measurement and the same size unit of measurement. If not, convert. </li></ul><ul><li>Calculate using this formula </li></ul><ul><li>D </li></ul>H X Q = Amount to be given
38. 38. Converting between measurement systems <ul><li>Example: grains to milligrams </li></ul><ul><li>Order: Aspirin gr v </li></ul><ul><li>Available : Aspirin in mg. </li></ul><ul><li>Set up the first ratio with the conversion factor </li></ul><ul><li>1 gr : 60 mg </li></ul><ul><li>Set up the second ratio with the unknown quantity in the appropriate position </li></ul><ul><li>5 gr : X </li></ul><ul><li>Use these ratios in proportion </li></ul><ul><li> 1 gr:60 mg :: 5 gr: X </li></ul><ul><li>Solve for X (unknown) based on the principle that the product of the means equals the product of the extremes </li></ul><ul><li>1 gr x X = 60 mg x 5 gr </li></ul><ul><li>X = 300 mg </li></ul>
39. 39. Pounds to kilograms <ul><li>A patient weighs 217 pounds. Convert to kg to compute the amount of medication to be given </li></ul><ul><ul><li>1 kg : 2.2 lb </li></ul></ul><ul><ul><li>X kg : 217 lbs </li></ul></ul><ul><ul><li>1 kg : 2.2 lb :: x kg : 217 lb </li></ul></ul><ul><ul><li>2.2 lb X = 1 X 217 lb </li></ul></ul><ul><ul><li>X = 217/2/2 </li></ul></ul><ul><ul><li>X = 98.6 kg </li></ul></ul>
40. 40. Examples <ul><li>The physician writes an order for secobarbital 0.2 gm every 6 hours prn for sleep. Each secobarbital capsule is labeled 100 mg. The nurse should administer______ capsules per dose. </li></ul>
41. 41. Examples <ul><li>The physician orders 500 mg of amoxicillin by mouth to be given every 6 hours. Available are 250 mg of amoxicillin capsules. The nurse should administer _________ capsule(s) for each dose. </li></ul>
42. 42. Examples <ul><li>The physician writes an order for acetaminophen 240 mg po for an elderly adult. You have on hand 80 mg acetaminophen oral liquid in 0.8 ml. The nurse should administer _________ ml per dose. </li></ul>
43. 43. Examples <ul><li>The physician orders amoxicillin 250 mg po. The pharmacy supplies amoxicillin suspension 250 mg/5 ml. in a 50 ml. bottle. The nurse should instruct the client to take _________ ml per dose. </li></ul>
44. 44. Practice Questions: <ul><li>A physician’s order reads 2 Tbs milk of magnesia. How many milliliters will the nurse administer? </li></ul><ul><li>The Physician’s order reads Tylenol supp. Gr x every 4 hrs p.r.n. for temp. > 101 F. The package label states that each suppository contains 10 grains of Tylenol. How many suppositories should the nurse administer? </li></ul><ul><li>The order states Lithium Carbonate gr x p.o. tid. The drug is labeled Lithium Carbonate 300 milligrams/capsule. How many capsules should the nurse give? </li></ul>
45. 45. <ul><li>The order for Coumadin is 5 mg. It is available in 2.5 mg tablets. How many tablets should be given? </li></ul><ul><li>The physician’s order is Ferrous Sulfate 300 mg p.o. tid X 1 week. How many tablets in total should be dispensed for the patient? </li></ul>
46. 46. Calculation for individualized drug dosing <ul><li>Based on actual body weight </li></ul><ul><li>Used to individualize medication administration for children and adults </li></ul>
47. 47. Steps <ul><li>Convert pounds(lbs) to kilograms (kg) </li></ul><ul><li>Determine the drug dose per body weight by multiplying drug dose X body weight X frequency </li></ul><ul><li>Choose one of the four methods of drug calculation for the amount of drug to be given </li></ul><ul><ul><li>Basic formula </li></ul></ul><ul><ul><li>Ratio proportion </li></ul></ul><ul><ul><li>Fraction equation </li></ul></ul><ul><ul><li>Dimensional analysis </li></ul></ul>
48. 48. <ul><li>The physician orders morphine sulfate 1.8 mg IM stat. </li></ul><ul><li>The child weighs 79 lbs. </li></ul><ul><li>Is the dose safe? </li></ul>Verifying Safe Dosages
49. 49. Verifying Safe Dosages <ul><li>Convert 1 lb to kg </li></ul>
50. 50. Verifying Safe Dosages <ul><li>Calculate mg/kg as recommended by a drug resource </li></ul><ul><ul><li>Resource indicates the usual IM/SC dosage may be initiated at 0.05 mg/kg/dose </li></ul></ul><ul><li>The dose is safe </li></ul>
51. 51. <ul><li>Kee, pp. 98 -109 </li></ul>
52. 52. REFERENCES <ul><li>Broyles, B. (2003) Dosage Calculation Practice for Nurses. Canada: Delmar </li></ul><ul><li>Erickson, B. ( 1991). Nurse’s Clinical Guide Dosage Calculations. Pennsylvania: Springhouse Corporation </li></ul><ul><li>Kee, J and Marshall, S.(2004). Clinical Calculations. 5 th Edition. Missouri: Elsevier </li></ul><ul><li>Pickar, G. ( 2008). Dosage Calculations. 8 th Edition. Canada: Delmar </li></ul>
53. 53. ANY QUESTIONS ????