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Math Review Ana Corona, DNP, FNP-C Nursing Professor July 2013 More presentations at: www.nurseana.com

Conversion Factors 1 Dram = 4 cc 1 Tbs = 15 cc 1 Tsp = 5 cc 1 Oz = 30 cc 1 gr = 60 mg 1 gm = 1,000 mg 1 mg = 1,000 ug (ug = micrograms) 1 hour = 60 minutes 1 kg = 2.2 pounds

Metric mcg – microgram mg – milligram gm – gram kg – kilogram ml – milliliter cc – cubic centimeter

Apothecary gr – grain (for weight) lb – pounds (for weight) m – minim (for volume) oz – ounce (for volume

Household tsp – teaspoon T or Tbs – tablespoon c – cup pt – pint qt – quart

Metric to Metric 1 kg = 1000 gm 1 gm = 1000 mg 1 mg = 1000 mcg 1 L = 1000 ml = 1000 cc 1 ml = 1000 mcl 1 ml = 1 cc

Household to Household 1 Tbs = 3 tsp 1 oz = 2 Tbs

Between Systems: gr 1 = 60 mg gr 5 = 300 mg gr 15 = 1000 mg = 1 g gr 1/150 = 0.4 mg 1 oz = 30 ml 1 dr = 4 ml 1 Tbs = 15 ml 1 tsp = 5 ml 1 min = 15 ml 1 min = 0.06 ml = 1 drop

Basic Formula Desired Dose x VOL. Dose on Hand = VOL. Desired Dose Dose on Hand or D x V = A H

Infusion Time Infusion Time = Total Volume to be Infused mL/hr being infused or Total Volume to Infuse ÷ gtt / min x 60 mi

Flow Rate Total Volume (mL) x Set Calibration (gtt/mL) Time (min) Flow Rate = mL/hr diveded by Division Factor Division Factor = 60 divided by calibration

1. Ordered ceclor 500 mg. Have ceclor 400 mg in 5 ml. How many ml will you give? Desired Dose order X Volume ml = Have on hand 1 Formula:D X V ml = H 1 ORDERED QUANTITY 500 mg  WANTED QUANTITY ____ ml  CONVERSION FACTOR 400 mg / 5 ml (Given in the problem)  SETUP 500 mg x 5 ml _______________ = ______ml 400 mg

 CROSS OUT the units which cancel out, leaving no units except the WANTED QUANTITY unit (In this case, you want the answer in ml).  500 mg x 5 ml _______________ = ______ml 400 mg

Do the Basic Math  Multiply the numbers across, then divide the number on top by the number on bottom. (500 x 5) 400 2500 (2500 divided by 400) 400  = 6.25 ml.

2. Ordered tylenol 10 grains. Have tylenol 160 mg in 1.6 ml. How many ml will you give?  ORDERED QUANTITY 10 gr  WANTED QUANTITY ____ ml  CONVERSION FACTORS 60 mg in 1 gr (we expect you to know this) and 160 mg in 1.6 ml (Given in the problem)  SETUP 10gr x 60 mg x 1.6 ml __________________ = ______ml 1 gr x 160 mg

 CROSS OUT the units which cancel out, leaving nothing but the WANTED QUANTITY 10 gr x 60 mg x 1.6 ml __________________ = ______ml 1 gr x 160 mg

Do The Basic Math  Multiply the numbers across, then divide the number on top by the number on bottom.  10 x 60 x 1.6 = ml  1 X 160  = 6 ml.

3. IV problem using the same method  You have an IV running at 21 gtts/min using macrodrip (15 gtt/ml) tubing.  You are going to switch the infusion over to an Abbott pump.  How many cc/hr will you set the pump at to keep the infusion running at the same rate?

 GIVEN QUANTITY 21 gtts/min  WANTED QUANTITY ____ ml/hr (cc and ml are equivalent)  CONVERSION FACTORS 60 min/ hr (you know this) and 15 gtt/ml (Given in the problem)  SETUP 21 gtts x 60 min x 1 ml __________________ = ______ml/hr 1 min x 1 hr x 15 gtts

 CROSS OUT the units which cancel out, leaving nothing but the WANTED QUANTITY 21 gtts x 60 min x 1 ml __________________ = ml/hr 1 min x 1 hr x 15 gtts

Do The Basic Math  Multiply the numbers across, then divide the number on top by the number on bottom.  (21 x 60 x 1) divided by ( 1 x 1 x 15) = 84 ml/hr.

Question 1-4 1.1/4 ounce = _________ cc. 2.How many cc in 3.75 Tbls 3.Ordered tylenol 600 mg. Have tylenol 250 mg in ½ tsp. How many cc will you give? 4.Ordered ceclor 550 mg. Have ceclor 400 mg in 5 ml. How many mL will you give?

Answer to Question 1 Dimensional Analysis Method Answer Units = cc Conversion Factor = 30cc/oz 1/4 oz 30 cc _____ X ____ =7.5cc 1 oz Old Fashion Method There are 30 cc in one ounce. Multiply The number of oz x 30cc to obtain the correct answer. 1/4oz x 30 cc = 7.5 cc

Answer to Question 2 Dimensional Analysis Method Answer Units = cc Conversion Factor = 15 cc/1 TBLS 3.75 TBLS. 15 cc _______ X ______ = 56 cc 1 TBLS.

Answer to Question 2 Old Fashion Method First convert the half teaspoon to cc Then use the standard formula (dose ordered/dose available x the number of cc). There are 5 cc in one teaspoon 5cc x 1/2 tsp = 2. 5 cc. Now use the standard formula: 600 mg/250 mg x 2. 5 cc = 6 cc.

Answer to question 3 Dimensional Analysis Method Answer Units = cc Conversion Factors = 250 mg/ 1/2 tsp AND 5 cc/1 tsp 600 mg 1/2 tsp 5 cc ______ X _______ X ______ = 6 cc 250 mg 1 tsp

Answer to question 3 Old Fashion Method First convert the half teaspoon to cc Then use the standard formula (dose ordered/dose available x the number of cc). There are 5 cc in one teaspoon 5cc x 1/2 tsp = 2. 5 cc. Now use the standard formula: 600 mg/250 mg x 2. 5 cc = 6 cc.

Answer to question 4 Dimensional Analysis Method Answer Units = mL Conversion Factor = 400 mg/ 5mL 550 mg 5 mL ______ X ________ = 6.875 mL 400 mg

Answer to Question 4 Old Fashion Method Just use the standard ordered/available x ml formula 550/400 x 5 ml = 6. 875 ml.

Rounding  How do you give 6.875cc? Mathematically, this number rounds to 6.9 ml. However, in the clinical setting, you would need to give this in a 10 ml syringe which has marks every 0.2 ml.  You would therefore have to draw up either 6. 8 ml or 7 ml. I would give 6. 8 ml, rather than "round" 6.87 ml clear up to 7 ml, to avoid any possible overdose.

Question 5 5.Ordered tylenol 15 grains. Have tylenol 160 mg in 1.6 mL. How many mL of tylenol will you give?

Answer for question 5 Dimensional Analysis Method Answer Units = mL Conversion Factors = 160 mg/ 1.6 mL tsp AND 60 mg/1 gr 15 gr 60 mg 1.6 mL _____X _____ X _______ = 9 mL 1 gr 160 mg

Answer for question 5  Old Fashion Method First convert the 15 grains into mg. There are 60 mg in one grain, so 15 x 60 = 900 mg.  Now use the standard formula. 900mg/160 mg x 1.6 mL = 9 mL.

Question 6  Ordered Demerol 80 mg and Vistaril 50 mg IM. You have Demerol in 1 mL ampules with 100 mg/ml.  Vistaril is in a 10 mL multi- dose vial labeled 50 mg/ml. What is the total volume to be given?

First, why do I care about total volume?  These medications are ordered together to treat pain and nausea.  They can be given mixed in the same syringe, to avoid giving the patient separate IM injections.  In order to correctly draw up the two medications in one syringe, you need to know how many cc of each medication you will give, and the total volume you will end up with in the syringe.

Answer to question 6 Dimensional Analysis Method Answer Units = mL Conversion Factors = 100 mg/ 1 mL (Demerol) AND 50 mg/mL (Vistaril) Demerol 80 mg 1 mL _____________ X _____ = 0.8 mL 100 mg Vistaril 50 mg 1 mL ___________ X _______ = 1 mL 50 mg 0.8 mL + 1 mL = 1.8 mL

Answer to question 6 Old Fashion Method (Ordered over Available) Demerol 80mg/100mg x 1mL = 0.8 mL Vistaril 50 mg/50mg x 1 mL = 1mL 0.8mL + 1mL = 1.8 mL

Question 7  Ordered Penicillin 75,000 units. Have 10 mL vial labeled Penicillin 100,000 units/ 5 mL  How many mL will you give?

Answer to question 7 Dimensional Analysis Method Answer Units = mL Conversion Factor = 100,000u/5 mL 75,000 u 5 mL ________ X ________ = 3.75 mL (Round to 3.8 mL) 100,000 u

Answer to question 7 Old Fashion Method  75,000 u/100,000 u x 5 ml = 3.75 cc.  However, the closest you can measure in a 5 cc syringe will be 3.7 and 3.8, so you may round up to 3.8 ml.

Note: be careful with multidose vials.  The label will state both how much is in the vial AND the dose concentration. YOU NEED TO KNOW THE DOSE CONCENTRATION.  This problem states that the vial holds 10 ml of fluid, but the dose concentration is 100,000 units/ 5ml.  This is the information you need to solve the problem.

Question 8  At the end of your 8 hour shift, you are calculating I&O for your patient.  When you received report from the previous shift it was stated that this patient had 375 cc remaining in her IV for you to count.

 During your shift the patient ate one egg and a slice of toast for breakfast and had a hamburger, french fries and 4 oz. of tea for lunch.  She also drank two cartons of milk at 8 oz. each and had 150cc of pop. The client then became nauseated and vomited 150 cc.

 She also starting having stomach cramps and passed two liquid stools.  After vomiting, she has only eaten and retained one 90 cc orange popsickle.  She voided clear yellow urine three times during your shift: 250 cc, 365 cc, and 200 cc.

 You hung a new 1000 cc bag of IV fluid which now has 650 cc in it.  The patient also received Keflex 250 mg IVPB in 50 cc of N/S one time during your shift.

Question  What is this patient's I&O for your shift?

How to Calculate the Intake  Oral Intake - the patient drank 4 oz of tea (120 cc), two 8 oz cartons of milk (2 x 240 cc = 480 cc), 150 cc of pop, and ate one 90 cc popsickle.  This is all of her total oral intake, which comes to 840 cc.

 IV fluid - the patient had 375 cc up in her IV when you started this shift.  Sometime during your shift all of that 375 cc went into the patient.  You then hung a new bag with 1000 cc in it.  As you are getting ready to do I&O for your shift you note that only 650 cc are remaining in that bag you hung.

 This means that 1000 - 650 = 350 cc of IV fluid from that bag went into your patient during your shift, so you count 375 cc + 350 cc = 725 cc IV fluid in your intake. The remaining 650 cc in the bag is left for the next shift to count.

 IVPB - (IV piggybacks or IV meds) Your patient had one 50 cc IVPB so add this 50 cc to the patient's intake.  Total Intake is the sum of her oral intake (840cc) added to her IV fluid (725 cc) plus her IV med (50 cc) 1615 cc total intake

How to Calculate the Output  For output, you add up the amount of emesis (150 cc) plus the amount of urine (250cc + 365 cc+ 200 cc).  If the patient had an N/G connected to suction, you would count the N/G drainage as output also.

 Total Output is the sum of her emesis (150 cc) added to her urine (815cc) + an unknown amount in liquid stool  Total Output is recorded as 965+ cc You should get lots of practice with this type of problem during your clinicals.

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