Microsoft word - math.doc

Revised 5/04 – Becky Gaffney, MSN 12/06 – Cedaliah Melton, MSN Melissa Powell, MSN Math proficiency is considered one of the critical skills necessary to meet one of the requirements of nursing. This proficiency is basic to safely administering medications and intravenous fluids. Enclosed is a booklet to guide you in mastering the mathematical competencies necessary for the accurate computation of medication dosages. This self-instructional booklet is designed to allow you to analyze the areas of mathematics that you may need to review. We encourage you to begin utilizing this booklet at the earliest possible date in your nursing program of study. There are multiple mathematical formulas that may be used to calculate dosages accurately. This booklet will instruct students to use the ratio and proportion method. Table of Contents
Math Requirements. 5 Math Learning Resources. 6 Systems of Measurement and Approximate Equivalents. 7 Common Pharmacologic Abbreviations. 9 PART A BASIC MATH REVIEW
1. Roman Numerals. 11
2. Fractions. 12
3. Decimals. 14
4. Practice Problems. 17
PART B MEASUREMENT SYSTEMS
1. Ratios and Proportions. 20
2. Metric System. 22
3. Practice Problems. 23
4. Household System. 23
5. Practice Problems. 23
PART C DOSAGE CALCULATIONS
1. Single-Step Calculation. 24
2. Multiple-Step Calculation. 26
3. Dosage by Weight. 29
PART D PRACTICE DOSAGE CALCULATION EXAMS
Criteria for Grading Dosage Calculation Exams. 32
Practice Exam #1. 32
Practice Exam #2. 37
PART E PEDIATRIC MEDICATIONS
Pediatric Medications. 41
Practice Exam #3. 43
PART F PARENTERAL MEDICATIONS
Directions for Calculating IV Flow Rates. 44
IV Formulas. 44
Practice Exam #4. 48

Practice Exam #5. 50
Practice Exam #6. 53
PART G ANSWERS
Basic Math Answers . 57
Practice Exam Answers. 59
PART H IV DRIP CALCULATIONS ADDENDUM

Calculation of Weight Based IV Drips . 67
Practice Exam #7. 68
One of the major objectives of nursing is that the student be able to administer medications safely. In order to meet this objective, the student must be able to meet the following math competencies. Translate Arabic numbers to Roman numerals. Translate Roman numerals to Arabic numbers. Add, subtract, multiply and divide whole numbers. Add, subtract, multiply and divide fractions. Add, subtract, multiply and divide decimals. Set up and solve ratio and proportion problems. Convert from one system of measure to another using: Solve drug problems involving non-parenteral and parental medications utilizing metric, apothecary, and household systems of measurement. Preparation for the math in nursing is a personal independent student activity. In order to facilitate this task it is suggested that the student utilize an organized approach. 1. Take the self-diagnostic math test. Allow 1 hour for self-test. Use an assessment sheet to pinpoint problem areas. Use the suggested resources to work on the problem areas. Retake the diagnostic test to determine the need for further help.
Students are encouraged to follow the above procedures. It will
organize their own learning efforts and also serve as a basis for
assistance from tutors or clinical instructors.
*NOTE: Part G – IV Drip Calculations contains material that will be
tested on after the first semester. Refer to this section beginning
in the second semester to solve practice problems.
This booklet, Fundamentals of Mathematics for Nursing. General math text - Sixth grade math books will include material on whole numbers, fractions, decimals, and ratio and proportion. Middle School math books will include material on solving for an unknown. These texts can be obtained from school or public libraries. College of Health Sciences -- Learning Resource Center (LRC) -- Rowlett 310 -- 622-3576 – has additional resources in the form of textbooks, computer programs and on-line access. There are three measurement systems commonly used in health care facilities: the metric, household, and apothecary system. In order to compare measured amounts in the systems, approximate equivalents have been developed. An example of an approximate equivalent is 1 teaspoon is approximately equal to 5 milliliters. Because the measures are not exactly equal, a conversion which takes more than one step will not produce as accurate a value as a conversion which takes only one step. For example, it is more accurate to convert from teaspoon to milliliters by using the conversion factor directly from teaspoons to milliliters than it is to go from teaspoons to ounces to milliliters. RULE: Always convert from one unit of measure to another by the shortest number of steps possible. Systems of Measurement and Approximate Equivalents The following conversion table will have to be memorized in order to accurately calculate dosage problems. Units and milliequivalents (meq) cannot be converted to units in other
systems. They have their value given and will never need to be converted.
1 unit = 1000 miliunits
*Cubic centimeters (cc’s) and milliliters (ml’s) are the same equivalents.
However, ml is the preferred usage.
Metric Weight 1 milligram (mg) = 1000 micrograms (mcg) 1 gram (g) = 1000 milligrams (mg) 1 kilogram (Kg) = 1000 grams (gm) Metric Weight to Volume 1 gram (gm) = 1 milliliter (ml) (approximately)
To transcribe medication orders and document drug administration
accurately, review the following commonly used abbreviations for drug
measurements, dosage forms, routes and times of administration, and
related terms. Remember that abbreviations often are subject to
misinterpretation especially if written carelessly or quickly. If an
abbreviation seems unusual or doesn’t make sense to you, given your
knowledge of the patient or the drug, always question the order,
clarify the terms, and clearly write out the correct term in your
revision and transcription.

DRUG AND SOLUTION MEASUREMENTS
oz.

DRUG DOSAGE FORMS
cap


ROUTES OF DRUG ADMINISTRATION
IM


TIMES OF DRUG ADMINISTRATION
ac


COMMON INTRAVENOUS FLUIDS
D5W – 5% Dextrose in water
D5NS – 5% Dextrose in normal saline
D5 ½NS – 5% Dexrose in ½ normal saline
L.R. – Lactated Ringers


BASIC MATH REVIEW
The following section serves as a review of basic math principles and allows students to identify any areas that will require further study. Students who find they need further development in basic math should refer to the table of math resources on page 5. Answers for practice problems are located in Part G, beginning on page 48. The basic form is to place the larger numerals to the left and add other numerals. There is an exception to the basic form. If smaller numeral precedes a larger numeral, the smaller should be subtracted from the larger. If there seems to be several ways of writing a number - use the shorter form. Only one smaller numeral is allowed to precede a larger numeral. . 11X = incorrect Numerals may be written as lower case letters and the number one may have a line and/or a dot over it. . . Numerator Denominator 2 = Proper fraction = numerator is smaller than denominator. 3 3 = Improper faction = numerator is larger than denominator. 2 1 1 = Mixed fraction = whole number and a fraction. 2 To change an improper fraction to a mixed number: a. Divide the numerator by the denominator. 13 = 2 3 To change a mixed number to an improper fraction: a. Multiply denominator by the whole number. 3 1 = 7 To reduce a fraction to its lowest denominator: a. Divide numerator and denominator by the greatest common divisor. b. The value of the fraction does not change. EXAMPLE: Reduce 12 60 12 divides evenly into both numerator and denominator 12 ) 12 = 1 12 = 1 60 ) 12 = 5 60 5 EXAMPLE: Reduce 9 12 3 divides evenly into both 9 ) 3 = 3 12 ) 3 = 4 9 = 3 12 4 EXAMPLE: Reduce 30 45 15 divides evenly into both 45 ) 15 = 3 30 = 2 45 3 You can multiply or divide when denominators are NOT alike. You CANNOT add or subtract unless the fractions have the same denominator. Addition of fractions: a. To multiply a fraction by a whole number, multiply numerator by the whole number and place product over denominator. To multiply a fraction by another fraction, multiply numerators and denominators. 6 4 24 8 Division of fractions: a. Invert terms of divisor. b. Then multiply. Decimal ________________ To the left Point To the right Reading from right to left, each place is 10 times larger in value. For example, 100 is 10 times larger than 10 and 1.0 is 10 times larger than 0.1. Changing decimals to fractions: a. a. three tenths b. 3 c.already reduced to lowest terms 10 EXAMPLE 2: 0.84 a. eighty-four hundredths b. 84 c. 21 100 25 Changing fractions to decimals: Divide the numerator by the denominator. .75 EXAMPLE 1: 3 4 *3.00 so 3 = 0.75 4 28 4 20 20 0 EXAMPLE 2: 8 40 *8.0 so 8 = 0.2 40 80 40 0 Addition and Subtraction of decimals: Use the decimal point as a guide and line up the numbers by their decimal place so that all the ones places are lined up under each other, all the tens places lined up and so on. ADDITION EXAMPLE 1: 7.4 ADDITION EXAMPLE 2: .003 +12.39 2.4 19.79 .15 + .02157 2.57457 SUBTRACTION EXAMPLE 1: 86.4 SUBTRACTION EXAMPLE 2: 6.079 - 3.817 - .85 82.583 5.229 Multiplication of decimals: a. Multiply the numbers as if they were whole numbers. Count the total number of decimal places to the right of the decimal point for each of the numbers. Use that total to count decimal places in the answer. a. 17.3 17.3 b. 17.3 has 1 decimal place past the decimal point. x 0.45 x 0.45 865 .45 has 2 decimal places past the decimal point 692 7785 = 7.785 c. Count 3 places for decimal in answer - 7.785 Division of decimals: To divide a decimal by a whole number, the decimal is placed directly above the decimal in the dividend. Quotient 1.37 Divisor *Dividend 5 *6.85 5 18 15 35 35 0 To divide a decimal by a decimal: Shift the decimal of the divisor enough places to make it a whole number. The decimal in the dividend is moved the same number of places as the divisor. Decimal point of quotient is placed directly above the new place of the decimal in the dividend. . 5. EXAMPLE 1: .6 *3.0 6 *30.0 V V 30 0 . 17.2 EXAMPLE 2: 1.3 *22.36 13 *223.6 V V 13 93 91 26 26 Rounding off decimals: Decide how far the number is to be rounded, such as to the tenths place or the hundredths place. Mark that place by putting a line under it. If the digit to the right of that place is less than 5, drop that digit and any others to the right. If the digit to the right of the place to be rounded to is 5 or greater, increase the number in the place by 1 and drop the digits to the right. EXAMPLE 1: 7.423957 7.42 Rounded to nearest hundredth EXAMPLE 2: 87.852 87.9 Rounded to nearest tenth Rules for rounding off for nursing math tests: 1. At the end of each step round the answer to the nearest hundredths before proceeding to the next step. 2. If the final answer is less than one, the answer should be rounded off to hundredths, Example .6666 .67 3. If the final answer is greater than one, the answer should be 4. In IV problems, if the final answer is ml/hour or gtts/min,round to the nearest whole number. Therefore, you must round the final answer up if equal to or greater than .5 and round down if less than .5. See example, page 46. If the question states that the IV solution is administered by IV pump, the final answer must be rounded to the nearest hundredth.
ANSWERS: Page 57
1. 15 = 2 2. 13 = 6 3. 7 = 4 4. 11 = 3 5. 15 = 8 6. 37 = 5 7. 4 = 6 8. 3 = 9 9. 15 = 60 11. 5 + 2 = 9 5 12. 2 + 1 + 9 = 7 2 14 13. 1 - 1 = 2 3 14. 9 - 3 = 12 4 15. 6 - 2 = 7 3 16. 7 x 2 = ANSWERS: Page 57
Change fractions to decimals 1. 6 = 8 2. 5 = 10 3. 3 = 8 4. 2 = 3 Change decimals to fractions 5. 0.54 = 6. 0.154 = 7. 0.60 = 8. 0.2 = Add decimals 9. 1.64 + 0.6 = 10. 0.02 + 1.0 = 11. 2.63 + 0.01 = 12. 1.54 + 0.3 = Subtract decimals 13. 1.23 - 0.6 = 14. 0.02 - 0.01 = 15. 2.45 - 0.03 = 16. 0.45 - 0.02 = Multiply decimals 17. 0.23 x 1.63 = 18. 0.03 x 0.123 = 19. 1.45 x 1.63 = 20. 0.2 x 0.03 = Divide Round to hundredths
25. 0.4537 =
26. 0.00584 =
Round to tenths
27. 9.888 =
28. 50.09186 =
Round to tens
29. 5619.94 =
30. 79.13 =
ANSWERS: Page 58
MEASUREMENT SYSTEMS
The faculty is aware that ratio/proportional problems can be set up in several forms to solve the problem. We believe the fractional form is more conceptual in nature. The fractional form helps the student visualize what is ordered and is available to determine the correct amount of medication to administer. Students will be required to set up all dosage calculation problems in the fractional form. This method is demonstrated on the following pages: A ratio compares 2 quantities and can be written as a fraction, 3 to 4 or 3 . 4 4 quarters to 1 dollar is a ratio and can be written 4 or 4:1. 1 (Other familiar ratios are 60 minutes to 1 hour; 2 cups to 1 pint; 16 ounces to 1 pound). A proportion is 2 ratios equal to each other. 4 quarters = 8 quarters 1 dollar 2 dollars This proportion can be read 4 quarters are to 1 dollar as 8 quarters are to 2 dollars. In a proportion, the products of cross multiplication are equal. Using the proportion above: 4 = 8 4(2) = 1(8) 8 = 8 1 2 There are 4 basic steps to solving proportion problems: 1) Set up a known ratio. 2) Set up a proportion with known and desired units. Use x for the Be sure the units are the same horizontally. pounds pounds 3) Cross multiply. 4) Solve for x. To solve a proportion problem such as 3 lbs. = ? ounces: a) Set up a known ratio of pounds to ounces. b) Make a proportion using the known ratio on one side and the desired Be sure the units are the same horizontally, such as ounces on the top and pounds on the bottom of each ratio. Another name for a ratio with numerator and denominator of approximately the same value is a conversion factor. The ratios 4 quarters to 1 dollar and 2 pints to 1 quart are conversion factors. Systems of measure use conversion factors to change from one unit to another. The basic unit of weight in the metric system is the gram (G or gm.). The basic length is the meter (m) and the basic volume is the liter (l or L). Metric measurements uses the decimal system as the basis for its units. The prefix of the unit identifies its decimal location and value. micro (mc) = millionths milli (m) – thousandths centi (c)= hundredths deci (d) = tenths deka (da) = tens hecto (h) = hundreds Kilo (k) = thousands Decimal __________________ larger Point smaller The faculty desire that you use a ratio and proportion format to make conversions within the metric system. Conversion Examples 1. 1 G 0.5 G 1(x) = 1000 (0.5) x = 500 mg 2. 2000 mcg = _______ mg. 1000 mcg = 2000 mcg 1 mg x mg
ANSWERS: Page 58
This system of measure is not as accurate as the metric or apothecary systems. The units of volume include drop (gtts), teaspoon (tsp or t.), tablespoon (tbsp. or T) and ounces (oz.). 1 tsp = 60 gtts 1 tbsp. = 3 tsp. 1 oz. = 2 tbsp. Conversion example: 4 tsp. = X gtts 60 gtts = x gtt 1 tsp. 4 tsp. HOUSEHOLD CONVERSION PRACTICE #5 PROBLEMS 1.
ANSWERS: Page 58

DOSAGE CALCULATIONS
Medication may be ordered in a form or amount different from what is available. Proportion may be used to calculate the right dosage. Steps: a. Check to be sure units are the same horizontally. 60 mg of medication are ordered. Tablets are available which have 30 mg of medication in each of them. How many tablets are needed to give 60 mg? Set up the problem as a proportion. 30 mg are to 1 tablet as 60 mg are to X tablets. b) Remember to have the same units horizontally (mg to mg and 30 2 tablets = 60 mg = the amount of medication ordered EXAMPLE 2: Ordered: Available: 10 mEq/5 ml How many ml's needed? Units are matched therefore no need to convert (mEq to mEq and ml to ml) It may be necessary to convert from one unit to another first before solving a dosage problem. Steps: a) Substitute converted unit into the proportion. 240 mg are ordered. Medication is available in 2 grains/1 tablet. How many tablets should be given? The units are not alike so grains need to be converted to milligrams or milligrams to grains. It is usually more convenient to convert to the units of the tablet or liquid. Therefore in this problem convert milligrams to grains. Now substitute in the original proportion so the units now match. EXAMPLE 2: Ordered: 0.016 gm Available: 4 mg/1 ml How many ml should be given? a) Substitute converted units into proportion. Available: 300 mg/5 ml How many ml's should be given? a) Convert to like units (grains or grams or grams to grains) Substitute converted units into the proportion. Two tablespoons of a liquid every 2 hours for 12 hours. How many ml's of the drug will the client receive over the 12 hour period? Convert to like units. 15 ml = xml 1x = 30 Substitute converted units into the proportion. 30 ml = xml 2x = 360 2 hours 12 hours x = 180 ml The client will receive 180ml over a 12 hour period. EXAMPLE 5: A client is to receive 2 gm of a drug. The drug comes 500 mg/5 ml. Each vial contains 10 ml's. How many vials would you need? x mg 1000 mg 5 ml xml 1x = 1000(2) 500x = (5) 2000 1x = 2000 500x = 10,000 1 1 Available: 5 gm/20 ml How many ml's do you give to a 30 lb. child? The order first needs to be clarified to establish exactly what has been ordered. STEP 1: 1. Clarify the order (How much medicine is 25 mg/kg for a 30 lb. 25 mg = x mg Units don't match so they must be converted. (NOTE: Remember to round the Kg to hundredths place before c) Substitute converted units into the original proportion. STEP 2: Now, as in previous problems a proportion is set up with what is ordered and what medicine is on hand (available). a) Substitute converted units and solve for x. x = 6.8 = 1.364 ml (final answer rounded to 1.4 ml per rounding rules) Give 1.4 ml to 30 lb child ordered to have 25 mg/kg of body wt. A twenty-two pound infant is to receive 2 mg/kg of a drug. The drug is available in 10 mg/0.5 ml. How many ml's will be given? 22 lbs = 1 kg x mg 2 mg 1. 22 PRACTICE DOSAGE CALCULATION EXAMS
This is the format of the dosage calculation exams. Each practice exam should be completed in one hour. Criteria for Grading Dosage Calculation Exams 1. Each problem must be set up in the fractional format. 2. Must show fractional format for each step in multiple step 3. Must show units in formulas. 4. Must solve for x in each formula. 5. Always convert from one unit of measure to another by the shortest Rules for rounding off for nursing math tests: 1. At the end of each step round the answer to the nearest hundredths before proceeding to the next step. 2. If the final answer is less than one, the answer should be rounded 3. If the final answer is greater than one, the answer should be rounded to tenths, Example 1.812 1.8 4. In IV problems, if the final answer is ml/hour or gtts/min,round to the nearest whole number. Therefore, you must round the final up if equal to or greater than .5 and round down if less than .5. See example, page 46. If the question states that the IV solution is administered by IV pump, the final answer must be How many tablets should be given? ________ How many tablets should be given? ________ 4. How many tablets should be given? ________ How many tablets should be given? ________ How many tablets should be given? ________ How many tablets should be given? ________ How many tablets should be given? ________ How many tablets should be given? ________ How many tablets should be given? ________ Ordered: Two tablespoons of a liquid every 2 hours for 12 hours. How many ml's of the drug will the client receive over the 12 hour period? ________ A client weighing 110 lbs. is to receive a drug at the dosage of 2.5 mg/kg of body weight. How many mg of the drug will the client receive? ________ A client is to receive 0.2 ml/kg of a drug every 2 hours. The client weighs 110 lbs. How many ml's of drug will the client receive in 24 hours? ________ ANSWERS: Page 59

Criteria for Grading Dosage Calculation Exams 1. Each problem must be set up in the fractional format. 2. Must show fractional format for each step in multiple step 3. Must show units in formulas. 4. Must solve for x in each formula. 5. Always convert from one unit of measure to another by the shortest Rules for rounding off for nursing math tests: 1. At the end of each step round the answer to the nearest hundredths before proceeding to the next step. 2. If the final answer is less than one, the answer should be rounded 3. If the final answer is greater than one, the answer should be rounded to tenths, Example 1.812 1.8 4. In IV problems, if the final answer is ml/hour or gtts/min,round to the nearest whole number. Therefore, you must round the final up if equal to or greater than .5 and round down if less than .5. See example, page 46. If the question states that the IV solution is administered by IV pump, the final answer must be How many tablets should be given? ________ Ordered: 0.25 mg Available: 0.05 mg/ml How many ml's will the client receive? ________ How many tablets should be given? ________ How many tablets should be given? ________ How many tablets should be given? ________ How many tablets should be given? ________ How many tablespoons should be given? ________ How many tablets should be given? ________ How many tablets should be given? ________ How many teaspoons should be given? ________ A client receives 30 ml of a drug every 4 hours for 24 hours. How many ounces will the client receive in 24 hrs? ________ A 66 lb. child is to receive a drug 2.5 mg/kg body weight. How many mg's will the child receive? ________ 20. A sixty-six pound child is to receive 0.4 meq/kg of a drug. The drug is available in 2 meq/4 ml. How many ml's will be given? ________
ANSWERS: Page 63

PEDIATRIC MEDICATIONS
Steps: 1. Convert pounds to kilograms. 2. If weight is in ounces, convert ounces to nearest hundredth of a 3. Since 16 oz. = 1 lb., change oz. to part of a pound by dividing by 16. Carry arithmetic out to three places and round off. 4. Then, convert total pounds to kilograms to nearest hundredths. Example I: O: Lasix 15 mg. po BID A: 2 mg/kg The infant weighs 16 lbs. 10 oz. How many mg will you give? Single dose? Bid? .625 = 0.63 lb. Child’s wt. is 16.63 lbs. Example II: O: 115 mg/ml tid A: 30 mg/kg/day in divided doses Infant weighs 25 lbs. 4 oz. How many mg will nurse give in 1 day? 4 oz. = 1 or 0.25 = 0.250 1. A 20 pound, 8 ounce child is to receive Cosmegen 20 mcg/kg of body weight. How many micrograms should the child receive? 2. Ordered: Phenergan 1 mg/kg of body weight. How many mgs should 3. Ordered: 30 meq per kg. Client weighs 8 lb. 8 oz. How many meq How many ml’s should you give to a 8 lb. 4 oz infant? 5. Ordered: 40 meq per kg of body wt. Your client weighs 8 lbs. 6 ANSWERS: Page 63

PARENTERAL MEDICATIONS
A. To find flow rate stated in ml’s per hour (if not given in the Divide the total volume of the solution in ml by the total number of hours to run. Example: 1000 ml IV solution ordered to infuse over 8 hours. This number (ml/hr) is used to calculate drops per minute.
*When answer does not come out evenly, round off to the nearest whole number. If 5 & greater round up. Below 5, round down. Example: 1000 ml solution to infuse over 6 hours. B. To find flow rate stated in drops per minute: Drop factor is the number of drops it takes to equal 1 ml with a specific type of IV tubing. The drop factor is stated on the tubing package. 60 minutes/hr is a constant in this formula Example: The drop factor is a 15 gtts/ml and the flow rate is 120ml/hr x 15 gtts/ml = 1800 = 30 gtts/min Example: The drop factor is 20 gtts/ml and the flow rate is 100 100ml/hr x 20 gtts/ml = 2000 = 33 gtts/min *Remember, when answer does not come out even, round off to nearest whole number. 1000x = 500 x = 0.5 mg/ml D. How much drug in hour? 500 mg Keflin = x mg 10 hr 1 hr 10x = 500 x = 50 mg/hr Example: 1000 ml = 10 hr 9 AM + 10 = 7 PM, end time With IV fluids - round off to the nearest whole number. With 5 or greater round up, less than 5 round down. Example: D5W with 20 meq Kcl per liter to infuse at 50 ml/hour. To prepare this solution, the nurse uses the stock preparation of Kcl (10 meq/5 ml) to add to the liter of D5W to make the concentration ordered. The drop factor is 60 gtts/ml. How many gtts/min will IV run? 50 ml/hr x 60 (drop factor) = 50 gtts/min
How much fluid will client receive in 24 hours? How many meq of Kcl will client receive in one hour? 1000 ml 50 ml (amount of solution received in one hour)
4. Ordered:
5. Ordered: D51/2NS to infuse 2 liters over 16 hours. How many At the end of each step round the answer to the nearest hundredths before proceeding to the next step. If the final answer is less than one, the answer should be rounded off to hundredths, Example .6666 .67 If the final answer is greater than one, the answer should be rounded to tenths, Example 1.812 1.8 In IV problems, if the answer is in ml/hr or gtts/min, round to the nearest whole number. Therefore, you must round the final answer up if equal to or greater than .5 and round down if less than .5. See example, page 46. If the question states that the IV solution is administered by IV pump, the final answer must be rounded to the nearest hundredth. ALL WORK MUST BE SHOWN!
The answer must be clearly identified by placing answer on the blank line or circled on the worksheet by the question. How many drops per minute? _______________________ 500 ml of LR with 20 meq Kcl over 8 hours (15 gtts/ml) How many drops per minute? _______________________ How many tablets will you give? ________________________ How many ml’s will you give? ___________________________ How many ml’s will you give? ___________________________ How many ml’s will you give? ___________________________ How many ml’s will you give? ____________________________ How many tablets will you give? ___________________________ How many ml’s will you give? ______________________________ How many ml’s do you give? ____________________________ ANSWERS: Page 66
At the end of each step round the answer to the nearest hundredths before proceeding to the next step. If the final answer is less than one, the answer should be rounded off to hundredths, Example .6666 .67 If the final answer is greater than one, the answer should be rounded to tenths, Example 1.812 1.8 In IV problems, if the answer is in ml/hr or gtts/min, round to the nearest whole number. Therefore, you must round the final answer up if equal to or greater than .5 and round down if less than .5. See example, page 46. If the question states that the IV solution is administered by IV pump, the final answer must be rounded to the nearest hundredth. ALL WORK MUST BE SHOWN!
The answer must be clearly identified by placing answer on the blank line or circled on the worksheet by the question. Order: 1000 ml of D5W to infuse over 12 hours (20 gtts/ml) How many ml per hour? ____________________ How many drops per minute? ____________________ Order: 1000 ml of D5NS to infuse at 125 ml/hr (60 gtts/ml) How many drops per minute? ____________________ Order: 100 ml D5W with 2 gm Keflin to infuse in 1 hour (15 gtts/ml) How many drops per minute? ____________________ How many mg of Keflin in 1 ml? ____________________ Order: 500 ml LR to infuse over 10 hours (60 gtts/ml) How many ml per hour? ____________________ How many drops per minute? ____________________ Order: 500 ml D5W with 500 mg Aminophyllin to infuse at 150 ml/hr (20 How many drops per minute? ____________________ Order: 1000 ml LR to infuse over 10 hours (60 gtts/ml) How many ml per hour? ____________________ How many drops per minute? ____________________ Order: 250 ml NS to infuse at 50 ml/hour - started at 9 a.m. (60 How many drops per minute? ____________________ At what time of day will the NS have infused? ___________ How many ml’s will you give? ____________________ How many tablets will you give? ____________________ How many ml’s will you give? ____________________ How many ml’s will you give? ____________________ How many ml’s will you give? ____________________ How many tablets will you give? ____________________ How many ml’s will you give? ____________________ Order: 30 mg/kg po (Client weighs 110 lbs.) How many capsule(s) will you give? ____________________
ANSWERS: Page 67
At the end of each step round the answer to the nearest hundredths before proceeding to the next step. If the final answer is less than one, the answer should be rounded off to hundredths, Example .6666 .67 If the final answer is greater than one, the answer should be rounded to tenths, Example 1.812 1.8 In IV problems, if the answer is in ml/hr or gtts/min, round to the nearest whole number. Therefore, you must round the final answer up if equal to or greater than .5 and round down if less than .5. See example, page 46. If the question states that the IV solution is administered by IV pump, the final answer must be rounded to the nearest hundredth. ALL WORK MUST BE SHOWN!
The answer must be clearly identified by placing answer on the blank line or circled on the worksheet by the question. Order: IV of D5W to infuse at 140 ml/hr (20 gtts/ml) Order: 1000 ml of D5LR with 20 units Pitocin over 10 hours (15 How many drops per minute? ____________________ How many ml’s will you give? ____________________ How many tablet(s) will you give? ____________________ How many ml’s will you give? ____________________ How many ml’s will you give? ____________________ How many ml’s will you give? ____________________ How many tablet(s) will you give? ____________________ How many ml’s will you give? ____________________ How many ml’s will you give? ____________________ Order: IV of NS to infuse at 90 ml/hr (12 gtts/ml) How many drops per minute? ____________________ Order: 1000 ml of LR to infuse over 5 hours (20 gtts/ml) How many drops per minute? ____________________ How many ml’s will you give? ____________________ How many tablet(s) will you give? ____________________ How many ml’s will you give? ____________________ How many ml’s will you give? ____________________ How many ml’s will you give? ____________________ How many tablet(s) will you give? ____________________ How many ml’s will you give? ____________________ Order: 15 mg/kg IM (Client weighs 154 lbs.) How many ml’s will you give? ____________________
ANSWERS: Page 67

Roman Numerals #1
1. 16
2. 21
3. XXIX
4. XIX
5. III
Fractions #2
Decimals #3
Metric Systems #4
Household System #5
Practice Exam #1 Answers
2 hr 24 hr 2x = 10 x 24 2x = 240 2 2 x = 120 ml q 24 hrs Practice Exam #2 Answers
These practice problems should assist the student to identify strengths and weaknesses in math skills. There are appropriate resources in the Learning Resource Center to assist with identified weakness. Refer to page 6 in this booklet. Answers to Practice Exam #3 (Pediatric Problems)
x = 9.32 Kg
x = 20.45 kg
x = 20.45 = 20.5 mg of phenergan
x = 3.86 kg
x = 115.8 meq
x = 3.82kg
x = 152.8 meq
Answers to Practice Exam #4 (IV Problems)
1. 33
Answers to Practice Exam #5
Answers to Practice Exam #6
Part H IV DRIP CALCULATIONS Calculation of Weight Based IV Drips Drugs can be administered to clients in continuous IV drips. The medication bag/syringe is labeled with the concentration of medication in the solution (i.e. units/ml, mcg/ml, meq/ml). The medication order will be used to determine the setup of the problem. Ratio and proportions can be set up to solve these problems, and depending upon the complexity of the order several steps may be needed. The following examples will show you the basis for solving these problems. Example Order: Fentanyl 5 mg/hr. The bag is labeled 250 mg in 500 ml of solution. How fast will the IV need to be infused to give the correct dose? 1. The IV rate will be as an hourly rate, so no conversion needs to be made for time. If the order was written with a different time, you would need to calculate the mg/hr. (use ratio and proportion) 2. Put the problem in ratio and proportion. B. The order may be written as unit of measurement/ Kg of weight/ hour. Example Order: Heparin 100 units/Kg/hr. The label on the solution reads 10,000 units/50 ml. The patient weighs 70 Kg. How fast should the solution run to give the correct dosage? First you need the total dosage/hr. Dose (units/hr) x weight in Kg equals the hourly dose. If the weight is in lbs, that must be converted to Kg first. Now put the dose in ratio and proportion with the concentration. 7,000 units = 10,000 units 10,000x = 50 (7,000) x= 350,000 x= 35 ml/hr x ml 50 ml C. When the order is written as unit of measurement/Kg of wt/minute. Example Order: Dopamine 20 mcg/Kg/minute. The bag is labeled Dopamine 100 mg/50 ml. The patient weighs 88 lbs. How fast will the IV run to give the dose? 1. First because the weight is in lbs, you must convert lbs. to Kg. (88 lbs = 40 Kg) Find the hourly dose. Because it is written in mcg/K/min you must multiply by 60 minutes to get the hourly dose. 20mcg x 40 Kg x 60 minutes = 48,000 mcg/hr Note that the concentration is in mg/ml not mcg, so you must convert to obtain like units of measure. Lastly set the problem up in ratio and proportion. 100,000 mcg = 48,000 mcg/hr 100,000x = 2,400,000 x = 24 ml / hr IV rate 50 ml 1. Order: Morphine 5 mg/hr. The syringe is labeled 100 mg/ 100 ml. How fast will the IV run to deliver the correct dosage? ___________________ 2. Order: Heparin 50 units/Kg/hr. The solution is labeled 1000 units/ ml. The patient weighs 10 Kg. What is the correct rate? __________ 3. Order: Dobutamine 10 mcg/Kg/min. The bag is labeled 1 mg/ ml. The patient weighs 23 Kg. What is the correct rate? ____________________ 4. Order: Pitocin 5 miliunits/minute. The bag is labeled 10 units/liter. What is the 5. Order: Ritodrine 0.05 mg/min. The bag is labeled 0.15 gm/500 ml. The patient weighs 198 lbs. What is the correct rate in ml/hrs?__________ 50 units x 10 Kg x 60 min = 30,000 units/hr a. 10 mcg x 23 kg x 60 min = 13,800 mcg/hr NOTE: You must have like units of 1mg = 1000 mcg a. 5 miliunits x 60 min = 300 mililunits/hr

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