Within the proportion the two outside numbers are referred to as the extremes. The two inside numbers are referred to as the means.

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1 Basic Formulas Speaker: Jana Ogden This lecture will demonstrate the expectations for performing a variety of the more complex calculations. You are expected to refer to your text and complete the designated reading assignments to fully achieve the learning objectives of this unit. You will be expected to round correctly and you may use a calculator for all the calculations in this course, including your quizzes. We begin with the process of solving simple proportions. Many drug dose calculations are solved utilizing this calculation method. Let s look at an example of a proportion: 6 : 10 :: 3 : 5 You will see three sets of colons; two single and one double. Each number in the proportion represents a term. The first colon is between the first and second term; the third colon is between the third and fourth term. These two colons stand for the word is. The double colon separating the second and third term is present to separate the two ratios and stands for the word as. This proportion is read 6 is to 10 as 3 is to 5. Within the proportion the two outside numbers are referred to as the extremes. The two inside numbers are referred to as the means. 6 : 10 :: 3 : 5 10 and 3 represent the means (note these are the middle numbers) 6 and 5 represent the extremes (note these are the end numbers) You solve a simple proportion through multiplication of the means and the extremes; always multiplying the two means together and the two extremes together. Note the letter M in means could also be remembered as middle, and the E in extremes as end. Thinking of the middle and end may help you remember which two numbers will be multiplied together. 10 x 3 = 30 (product of the means) 6 x 5 = 30 (product of the extremes) You will be performing your calculations to find the value of a missing term. This will correlate to the amount of drug you intend to administer when you are calculating a drug dose. The missing value will be represented by an X. Here are instructions and example for solving for X: Example 2: Multiply the means (middle) together and multiply the extremes (ends) together, making sure you always multiply the X first. Page 1 of 8

2 4 : 5 :: 8 : X 4X = 5 x 8 4X = 40 X = 40/4 or 40 4 X = 10 o Place the product including the x on the left. o Place the product of the known terms on the right. o Divide the product of the known terms by the number next to x. o The quotient will be the value of x. Next, let s look at metric household equivalents. Household equivalents are not an accurate way to calculate medication dosages. Therefore conversion is necessary. To begin, commit the following measurements to memory: 1000 micrograms (mcg) = 1 milligram (mg) 1000 milligrams (mg) = 1 gram (g) 1000 milliliters (ml) = 1 liter (L) 5 milliliters (ml) = 1 teaspoon (tsp) 15 milliliters (ml) = 1 tablespoon (Tbsp) 30 milliliters (ml) = 1 ounce (oz) 240 milliliters (ml) = 1 standard measuring cup or 8 ounces 1 kilogram (kg) = 2.2 pounds (lb) When performing a conversion, you will use the proportion method. You begin by placing what you have memorized as the correct equivalent between the two units of measurement on the left side of the proportion (1000 ml : 1 liter). Set up the right side of the proportion making sure the units of measurement match the left side. In other words the unit of measurement must be written in the same place holder on both sides of the equation. Use the symbol x to represent the unknown quantity. Rewrite the proportion. Solve for x by multiplying the means and extremes. Write the answer as a decimal. Label the answer with the proper unit of measurement (ml, mcg, kg, etc.). 2.5 L equals how many ml 1000 ml : 1 L :: x ml : 2.5 L 1 x = 2500 x = 2500/1 x = 2500 SO 2.5 L = 2500 ml Example 2: Tip - You can skip the above step in simple conversions by moving the decimal point. Move the decimal 3 places left for larger units; 3 places right for smaller units 2.5L = ml Page 2 of 8

3 Calculating intake is a responsibility of every nurse. Documentation will be made in the metric system. Let s assume a patient consumes the following: Coffee 8 Oz (240 ml) Juice 4 Oz (120 ml) Soup 6 Oz (180 ml) o Add total Oz = 18 o 18 X 30 = 540 ml total intake Nurses must also know the weight of a client in kilograms as medications may be ordered based on weight. Check out the example below: Standard equivalent lbs = 1 kg 35 kg = how many pounds (lbs)? o 35 X 2.2 = 77 lbs 110 lbs = how many kilograms (kg)? o 110 / 2.2 = 50 kg The next topic we will cover is drug calculations for oral and parenteral doses. Your calculations will continue following the proportion method. When calculating the dose you are to administer, check the units of measurement between what is ordered and what is supplied (grams, milligrams, micrograms). If units of measurement are the same, set up a proportion by placing the strength of the supplied drug on the left and the amount you intend to administer on the right. Physicians order = Give Lasix 60 mg po daily (supplied in 40 mg tablets) 40 mg : 1 tab :: 60 mg : x tabs If unit of measurement is different (order is in grams and supplied drug is in mg), convert ordered medication to supplied medication. This requires a two-step proportion. The first proportion is set up by placing what you know to be an equivalent measurement on the left and what you want to find for a unit of measurement on the right. The second proportion completes the calculation by placing the supplied drug on the left and unknown amount you plan to administer on the right. Example 2: Physician order reads: Keflex 0.5 grams po qid - The drug is supplied in 250 mg capsules Step 1 = Convert grams to milligrams (Remember start with the memorized known!) 1000 mg : 1 g :: x mg : 0.5 g 1x = 1000 x 0.5 x = g = 500 mg Page 3 of 8

4 Step 2 = Calculate oral dosage 250 mg : 1 capsule :: 500 mg : x capsules 250x = 1 x 500 x = 500/250 = 2 x = 2 capsules (you will administer 2 capsules) Tip - You can skip the first step if you convert using the 3 decimal placement movement method. Move the decimal 3 places left for larger units; right for smaller units. 0.5 g = 500. mg When a physician orders a medication, you will be reviewing the dosing information provided on a drug label. Here is an example and some additional things to consider. The dose you are administering will be in ml, or number of tablets, capsules, etc. You will always calculate the per dose amount unless otherwise specified. The supplied drug is the drug on hand; that information is on the drug label, in other words, what the pharmacy provides to you. The supplied drug always goes on the left. The physicians order always goes on the right (your physicians order contains the unknown; the amount you are expected to administer). Keep units of measurement in same place holder on the left as on the right. Physician orders Prozac 60 mg per NG daily at HS Let s look at how the pharmacy supplies the medication by reviewing the label below: The pharmacy sends 120 ml bottle of oral solution. All labels specify the per dose volume. On this label it states 20 mg is equal to 5 ml. This is a multidose bottle containing a total of 120 ml. Many students Page 4 of 8

5 attempt to use the amount of medication supplied in an entire container as the calculation for the supplied drug. Now you have all the information you need to solve the calculation: What did the pharmacy supply? 20 mg : 5 ml What did the physician order? 60 mg Set up proportion 20 mg : 5 ml :: 60 mg : x ml 20x = 5 x 60 = x = 300 x = 300/20 x = 15 ml (you will administer 15 ml via NG tube) Now, let s look at medications requiring reconstitution, doses measured in units, and weight based drugs. Be sure to carefully review the readings for specific information related to each type of calculation. Insulin is a medication dosed in units. Insulin must always be withdrawn from the insulin vial and administered using an insulin syringe. These syringes are marked as insulin syringes and are precalibrated in units/ml. Therefore no calculations exist, unless you are administering two different types of insulin together (NPH and regular, in the same syringe), then your only calculation is adding the ordered units together (see example). Be sure your vial and syringe correlate with the U-100 marking. This stands for 100 units of insulin per 1 ml of solution. Page 5 of 8

6 If the physician orders 5 units of insulin, using the above syringe and insulin vial, you will fill the syringe to the 5 unit mark. If the physician orders 5 units of regular insulin, and 15 units of NPH insulin, you will fill the syringe to the 20 unit mark ( = 20). WARNING: Insulin is considered a high alert medication requiring verification of accuracy by another nurse. Regular insulin and the intermediate acting insulin NPH are the only two insulins mixed in the same syringe. Regular insulin is the only insulin given intravenously. The nurse s role in reconstituting medications will vary facility to facility. When a medication is unstable over long periods of time in its liquid form, it is supplied by the manufacturer in a powdered form. A specified diluent; usually sterile H 2 O or 0.9% normal saline, is combined into the powdered medication for mixing. Be sure to read information and directions on drug labels carefully. Identify the type of diluent, amount of diluent, and route of administration. Note the drug strength or concentration after reconstitution. Note the length of time that medication is usable after reconstitution. Note the directions for storage of reconstituted medication. You will place your initials, date and time of preparation, and date and time of expiration on the drug label after reconstituting, when the medication is a multidose vial. Multidose vials contain the total dose and amount within the entire vial, as well as the diluent instructions; often giving three diluent methods. The nurse will select a concentration closest to the drug dose ordered. Do not confuse the amount within the entire vial with the per dose equivalent. Your label will tell you the drug concentration per unit of measurement in the instructions for reconstituting. ml of diluent to be added Units per ml after concentration 18.2 ml 250, ml 500, ml 1,000,000 Page 6 of 8

7 Let s look at a physician s order Physician orders = penicillin 250,000 units IM now. The pharmacy supplies this medication in powder form requiring reconstitution. The above direction gives you a choice of potential drug concentrations. You will be selecting the amount closest to your drug order; in this instance you have the option of selecting the actual dose ordered; this will not always be the case. For this order you will reconstitute with 18.2 ml of sterile H 2 O to yield a concentration of 250,000 units/ml; your exact dose. When the concentration you want is not precisely available, you will reconstitute to yield a concentration that is closest to the dose ordered. Some medications will only give you one choice for the reconstitution added, yielding only one concentration. Some drugs are given based on the client s weight. The steps for weight based calculations are provided in the following example: Physician orders Lovenox 1 mg per kg Drug is supplied as Lovenox 100 mg/ml Dosage is given based on the client s weight in kilograms (kg) Client s weight is 132 lbs Convert patient s weight into kilograms: 132/2.2 = 60 (client s weight is 60 kg) Since the physician ordered 1 mg per kg, you will administer 60 mg (1mg x 60kg) You now must calculate the ml of medication you will administer to the client Calculate this dose using the proportion method 100 mg : 1 ml :: 60 mg : x ml 100x = 1 X x = 60 x = 60 / 100 = 0.6 x = 0.6 ml (You will administer 0.6 ml of Lovenox to this client) Now we will look at the two formulas necessary to administer fluids intravenously (IV). A physician orders the type of solution, amount to be given, and total time the fluid is to be administered over. Gravity infusions are calculated as drops per minute. You will use this formula when you are hanging an intravenous solution by gravity; there will not be a pump to program. You will be using the roller clamp on the IV tubing to adjust your flow as you watch drops drip into the drip chamber of the IV tubing. Refer to your text for more details on microdrip and macrodrip IV tubing. The drop factor is always provided on the package of the IV tubing. Page 7 of 8

8 Each simulated intravenous math calculation that is to be calculated in drops per minute will provide you with the tubing drop factor. This figure is a necessary part of your formula. Volume to be administered Divided by time in minutes x the tubing drop factor = drops per minute Physicians order is for 500 ml of 0.9% normal saline to be given over 1 hour. Your tubing drop factor is 10. Calculate the drops per minute. 500 / 60 x 10 = 83.3 or 83 drops per minute Pump infusions of IV solution are programmed in ml per hour. The nurse programs the IV pump with the exact flow rate based on the number obtained from the IV formula after calculation. Example 2: Volume to be administered Divided by time in hours = ml per hour Infuse 750 ml of lactated Ringer s solution (LR) over 12 hours. How many milliliters per hour should the IV pump be programmed to deliver? 750/12 = 62.5 or 63 ml per hour Special note when using a pump to administer any volume less than 1 hour, you will use a decimal equivalent. Example 3: Infuse 250 ml over ½ hour 250/0.5 = 500 ml per hour Lori Bailey and Indian Hills Community College Page 8 of 8

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