Bonnie and Jill's
Practical Approach to
Dosage Calculations

M & M THEORY OF MATH

The M & M theory of math is a way to reintroduce math to those who have not used their math skills recently. These are fun exercises designed to take the stress out of math for those who are math-aphobic and those who are just a little rusty. When you finish these exercises you will have accomplished four objectives:

1. You will have refreshed your math skills.
2. You will understand ratio, fraction, proportion, dimensional analysis.
3. You will be able to calculate basic medication problems.
4. You will be a little sweeter and a little less fearful of math.
5. Oops five? You will be able to calculate the pounds you gained analyzing all of these problems.

The first task is to open the M & M package and separate all of the different colors of M & Ms. For each problem please take the M & Ms and place them on a plain piece of white paper as you follow the exercise.
What a sweet way to learn math and medication administration.

M & M math relationships.

• What is an M & M ratio?
• What is an M & M fraction?
• What is an M & M proportion?

Get those M &Ms ready now. No eating until you complete the first problem. Ok! EAT ONE.

Two baby dots came to stand on top of each other. Some people think they look like a colon in ratios. We know they are baby dots in the M & M world. How are these baby dots used and what is a ratio anyway?

A ratio is a comparison of two numbers using division. A ratio can be written several different ways. Take three red M & Ms and place on your paper as in the example below, or place them on top of the example. Now place the baby dots one on top of the other. Take nine green M & Ms and place them on the opposite side from the baby dots. 3:9 You read this "3 to 9".

This shows a relationship between two numbers (e.g. the ratio of red M & Ms to green M & Ms). "3 red M & Ms to 9 green M & Ms." No more, no less-- just a relationship of numbers of M&Ms.

What is an M & M fraction? The M & M fraction has a lightning bolt to show the relationship of the numbers. For the more serious it is called a slash to separate the numerator (top number) and the denominator (down under number).

Take three M & Ms and place them on the paper. Place your lightning bolt next to the M & Ms. Place nine M & Ms to the right of the lightning bolt. Now you have a fraction, which is another relationship of numbers. Does it look familiar? Another way to state it would be three-ninths. 3/9 or "3 is to 9".

Fractions and ratios are basically the same. One has baby dots and the other has lightning bolts to show their relationship.

Use your M & Ms . 3 red M&Ms to 9 green M&Ms. M & M proportion. This demonstrates how equal things are in the community of M & M.

A proportion is a statement that 2 ratios or fractions are equal. This can also be demonstrated in several different ways and still mean the same thing. This is how the ratios or proportion of red and green M&Ms would be stated: 3 red M&Ms is to 9 green M&Ms" as "6 red M&Ms is to 18 green M&Ms."

Here again are the same proportions stated the same way: "3 red M&Ms to 9 green M&Ms" are equal to "6 red M&Ms to 18 green M&Ms". Or "3 is to 9 as 6 is to 18".

What is a typical proportion problem? How would it look? You need to find or determine the missing numbers of M&Ms.

To find the missing number, figure out what number you would multiply 9 by to get 18. Divide 18 by 9.

The answer is two.

Whatever number you use to multiply in the denominator (D=down=denominator), you must use for the numerator on top. What number multiplied by 2 would equal 6?

The answer is three 3.

The proportion equation would look like this:

Or you reduce the fraction (which is another way it may be stated).
An algebraic equation (Ok! Ok! Don't let the terms freak you out) we are still talking about the same thing.

X = ? where X/9 = 6/18
CROSS MULTIPLY: X x 18 = 6 x 9. 18 x X = 54
To make one X you divide both sides by 18.
18X divided by 18 = 1X and 54 divided by 18 = 3, so X = 3

PROBLEMS SOLVING FOR ? OR X RATIOS

Write each of the following statements as a proportion.

1. 4 is to 12 as 1 is to 3 ______________________________________________
   
   
2. 16 is to 40 as 2 is to 5 _____________________________________________
   
   
3. 35 is to 30 as 7 is to 6 _____________________________________________
   
   
4. 108 is to 24 as 9 is to 2 ____________________________________________
   
   
5. 77 is to 99 as 7 is to 9 _____________________________________________

Multiple choice

1. 4 is to 12 as 1 is to 3

   (a.) 1/12 = 4/3 (b.) 4:1 = 3/12 (c.) 4:12 = 1:3 (d.) 12/4 = 1/3

2. 16 is to 40 as 2 is to 5

   (a.) 16/40 = 2/5 (b.) 16/2 = 4/40 (c.) 16:5 = 2:40 (d.) 16:2 = 5:40

3. 35 is to 30 as 7 is to 6

   (a.) 35:30 = 7:6 (b.) 35:6 = 30:7 (c.) 35/6 = 30/7 (d.) 30 /35 = 7/6

4. 108 is to 24 as 9 is to 2

   (a.) 24/108 = 9/2 (b.) 24:108 = 9:2 (c.) 108/24 = 9/2 (d.) 24:108 = 2:9

5. 77 is to 99 as 7 is to 9

   (a.) 99:77 = 9:7 (b.) 77:99 = 7:9 (c.) 99/77 = 9/7 (d.) 77/99 = 9/7

REMINDER; The number that was used to determine the denominator should also be used to determine the numerator.

6. 4/8 = ?/16 ?= ______________________________

   (a.) 3 (b.) 8 (c.) 4 (d.) 2

7. 5/1 = 35/? ?= ______________________________

   (a.) 3 (b.) 5 (c.) 7 (d.) 35

8. 45/? = 5/9 ?= ______________________________

   (a.) 9 (b.) 81 (c.) 5 (d.) 56

9. ?/7 = 18/42 ?= _____________________________

   (a.) 3 (b.) 7 (c.) 6 (d.) 9

10. 7/12 = ?/108 ?= ____________________________

    (a.) 84 (b.) 9 (c.) 63 (d.) 56

11. 40/? = 4/12 ?=______________________________

    (a.) 10 (b.) 120 (c.) 100 (d.) 4

12. 18/35 = 108/? ?= ___________________________

    (a.) 18 (b.) 6 (c.) 10 (d.) 210

13. 51/25 = ?/1000 ?= __________________________

    (a.) 204 (b.) 20 (c.) 2040 (d.) 40

14. ?/76 = 66/228 ?= ___________________________

    (a.) 3 (b.) 198 (c.) 10 (d.) 6

15. 62/909 = ?/1818 ?= _________________________

    (a.) 124 (b.) 2 (c.) 20 (d.) 3

FREQUENTLY USED CONVERSIONS:

Note

Change mg to mcg by moving decimal 3 places to the right. (.1mg = 100 mcg) = multiply by 1000

Change mcg to mg by moving decimal 3 places to the left. (100 mcg = .1 mg) = divide by 1000

Change grams to mg by moving decimal 3 places to the right. (.25 g = 250mg) = multiply by 1000

Change mg to g by moving decimal 3 places to the left. (250mg = .25 g) = divide by 1000.

Note: "R" = the unknown rate of the drip. Solve for "R" just like you were solving for "X" in earlier exercises. "x" means multiply in the above formula.

To change from a LARGER unit to a smaller unit multiply by 10 for each unit decreased, or move the decimal point one space to the right for each unit changed.

DECI = one tenth (0.1)

CENTI = one hundredth (0.01)

MILLI = one thousandth (0.001)

MICRO = one millionth (0.000001)

EXAMPLE: Change deci (80) to centi. To move from deci to centi, you need to move 1 place. Count one place to the right.

E.g. 80 = 800

(deci) = (centi)

Answer = 800 cm

To move from a smaller unit to a LARGER unit move the decimal point from right to left.

E.g. 6000 milli = 60 deci

METRIC PROBLEMS:

1. 90 deci = _______ cm

   (a.) 900 (b.) 9 (c.) 9000 (d.) 0.9

2. 60 cm = _______ m

   (a.) 360 (b.) 0.360 (c.) 0.0360 (d.) 36

3. 4.16 M = _______ dm

   (a.) 416 (b.) 41.6 (c.) 0.416 (d.) 4160

4. 0.8 mm = _______ cm

   (a.) 0.08 (b.) 8 (c.) 80 (d.) 0.008

5. 2mm = _______ m

   (a.) 200 (b.) 0.02 (c.) 20 (d.) 0.002

VOLUME
A liter is the basic unit of volume.

Metric Problems-- Part 2:

6. 3.006 ml = _______ L

   (a.) 300.6 (b.) 30.6 (c.) 3.6 (d.) 0.003006

7. 6.17 cl = _______ ml

   (a.) 61.7 (b.) 617 (c.) 0.617 (d.) 0.0617

8. 0.9 L = _______ ml

   (a.) 90 (b.) 900 (c.) 0.90 (d.) 9

9. 1500ml = _______ L

   (a.) 150.0 (b.) 15 (c.) 1.5 (d.) 0.1500

10. 250 ml = _______ L

    (a.) 0.25 (b) 2.50 (c.) 0.0025 (d.) 2500

A Gram is a unit of weight abbreviated g or gm.
The same rule of large to small and small to large still applies.

1 milligram = 1000 micrograms (mcg)

1 kilogram = 1000grams or 2.2 lbs

Metric Problems-- Part 3 :

1. 6.4 mcg = _______ mg

   (a.) 6400 (b.) 64 (c.) 0.64 (d.) 0.0064

2. 1000mg = _______ g

   (a.) 1.0 (b.) 10 (c.) 100 (d.) 0.1

3. 0.8mg = _______ dg

   (a.) 0.008 (b.) 0.08 (c.) 8 (d.) 800

4. 35.6 mg = _______ g

   (a.) 356 (b.) 3.56 (c.) 0.356 (d.) 0.00356

5. 0.3 g = _______ cg

   (a.) 30 (b.) 3 (c.) 0.03 (d.) 0.003

6. 0.05 g = _______ mg

   (a.) 5 (b.) 0.05 (c). 500 (d.) 50

7. 93 cg = _______ mg

   (a.) 9.3 (b.) 0.93 (c.) 930 (d.) 9300

8. 100mcg = _______ mg

   (a.) 10 (b). 0.10 (c.) 1000 (d.) 0.0001

9. 2mg = _______ mcg

   (a.) 0.002 (b.) 20 (c.) 200 (d.) 2000

10. 1.0 mcg = _______ mg

    (a.) 100 (b.) 0.001 (c.) 10 (d.) 0.01

DRUG CONVERSION PROBLEMS

1. 300 mg = how many gr?

   (a.) 3 gr (b.) 3.5 gr (c.) 4 gr (d.) 5 gr

2. How many kg does a 250 lb. man weigh?

   (a.) 114 kg (b.) 11.4 kg (c.) 55.0 kg (d.) 5.5 kg

3. The order is Lasix 80 mg I.V. now. You have Lasix 100 mg in 10ml of NS. What volume would you give?

   (a.) 0.8 ml (b.) 8 ml (c.) 0.08 ml (d.) 80 ml

4. The order is Ceftriaxone 2 gm IVPB stat. You have Ceftriaxone 1000mg in 2cc NS. How many cc's will the patient receive?

   (a.) 2cc (b.) 3cc (c.) 4cc (d.) 6cc

5. The order is for Erythromycin 5 gm po on call to the O.R. You have a bottle of Eryc. 500 mg per tablet. How many tablets should be administered?

   (a.) 10 tabs (b.) 12 tabs (c.) 12.5 tabs (d.) 14 tabs

6. A baby weighs 5.2 kg. The weight in grams is:

   (a.) 5.2 gm (b.) 5.02 gm (c.) 5,200 gm (d.) 520 gm

7. The number of mg of Imipenem remaining in a 5 gm vial after 250 mg are removed is:

   (a.) 47 mg (b.) 4,750 mg (c.) 4 gm (d.) 750 mg

8. The order is for 4 T. of MOM now. How many tsp is this?

   (a.) 8 tsp (b.) 8.5 tsp (c.) 10 tsp (d.) 12 tsp

9. Your patient who is on a clear liquid diet must drink 480 ml of water for lunch. How many cups is this?

   (a.) 2 cups (b.) 2.5 cups (c.) 3 cups (d.) 3.5 cups

10. The order is for 0.05 mg Synthroid po q a.m. You have Synthroid 0.025 mg/tablet. How many tablets should you give?

    (a.) 1 tab (b.) 2 tabs (c.) 2.5 tabs (d.) 3 tabs

Drug Conversion Problems-- Part 2

11. The order reads Asa gr X po now. You have Asa 325 mg per tablet. How many tablets should you give?

    (a.) 1 tab (b.) 1.5 tabs (c.) 2 tabs (d.) 2.5 tabs

12. The order reads Phenobarbital gr 1/4; take gr 1/2 t.i.d. How many mg of Phenobarbital should the patient receive?

    (a.) 300 mg (b.) 0.3 mg (c.) 3,000 mg (d.) 30 mg

13. The order reads Digoxin 62.5 mcg in elixir po QD. The elixir label reads 0.05 mg/ml. How many ml's of Digoxin should the patient take every day?

    (a.) 1.25 ml (b.) 1.5 ml (c.) 1.8 ml (d.) 2.0 ml

14. The order is for 60 meq of KCL po QD. The only solution on hand contains 20 meq/ml. How many T should you give the patient?

    (a.) 2 T (b.) 3 T (c.) 3.5 T (d.) 4 T

15. Convert 4 gm to grains.

    (a.) 40 gr (b.) 50 gr (c.) 60 gr (d.) 70 gr

16. A prescriber has ordered 12.5 mg of Capoten po. What is the equivalent quantity in mcg?

    (a.) 11,000 mcg (b.) 11,500 mcg (c.) 12,000 mcg (d.) 12,500 mcg

17. The doctor has ordered Neostigmine gr X IM q4h prn. What is the dose of this drug in gm's?

    (a.) 0.6 gm (b.) 1.6 gm (c.) 0.06 gm (d.) 16 gm

18. Jennifer weighs 103 lbs 8 oz. What is her weight in kg?

    (a.) 42 kg (b.) 47 kg (c.) 49 kg (d.) 51 kg

19. The order is for Cleocin 0.6 gm sq. What is the equivalent dose in mg?

    (a.) 450 mg (b.) 475 mg (c.) 500 mg (d.) 600 mg

20. KCL 20 mEq q.i.d. is prescribed. KCL elixir is available as 6.7 mEq/5ml. You will give _____ ml or _____ ounce(s) four times a day.

    (a.) 5 ml, 1/2 oz. (b.) 10 ml, 1 oz. (c.) 15 ml, 1/2 oz. (d.) 30 ml, 1 oz.

INTRAVENOUS (IV) THERAPY

• Drop factors are printed on infusion packages.
  
• The number of drops an IV set delivers in one ml. is called the drop factor.
  
• Marcrodrip = 10gtt/ml, 15gtt/ml, 20gtt/ml
  
• Microdrip = 60gtt/ml

10 drops = 1 ml

• A controller regulates drop rate by gravity
  
• An infusion pump exerts pressure agaist the tubing & fluid at a preselected rate.

Calculating flow rates:

The Nurse is responsible for regulating flow rates:

• Calculate ml/hr
• Calculate the gtt/min that need to enter the drip chamber to deliver a set ml/hr.

The drip rate (125 gtt/min) is the same as the flow rate (ml/hr).

REMEMBER: You can check the rate of flow of IV solutions by counting the number of drips in 15 seconds and then multiplying that number by 4 to determine the number of drops in a minute (gtt/min).

SAMPLE IV PROBLEMS

1. Order: 1000ml D5NS IV q8hr. The IV infusion set's drop factor is 15gtt/ml.

   (a.) 28.5gtt/min (b.) 31.25gtt/min (c.) 33.0gtt/min (d.) 34.5gtt/min

2. Administer 250ml of 0.45%NS over 5 hrs. The drop factor is 60gtt/ml.

   (a.) 50gtt/min (b.) 54gtt/min (c.) 58gtt/min (d.) 60gtt/min

3. Infuse 500ml of 0.9%NS over 6 hrs. The drop factor is 20gtt/ml.

   (a.) 26gtt/min (b.) 24gtt/min (c.) 28gtt/min (d.) 30gtt/min

4. Infuse 1000ml of LR over 10 hours. The drop factor is 15gtt/ml.

   (a.) 25gtt/min (b.) 26gtt/min (c.) 27gtt/min (d.) 28gtt/min

5. Deliver 1000ml of D5W 1/2NS +20meq KCL over 4 hrs. How much fluid would the nurse administer each hour?

   (a.) 260ml/hr. (b.) 275ml/hr. (c.) 300ml/hr. (d.) 250ml/hr.

6. Administer 100ml of Albumin over 2 hrs. The drop factor 15gtt/ml.

   (a.) 11gtt/min (b.) 13gtt/min (c.) 15gtt/min (d.) 17gtt/min

7. Administer 1000ml of LR at 50ml/hr. The total infusion time would be _____ hrs.

   (a.) 20 hrs. (b.) 25 hrs. (c.) 30 hrs. (d.) 35 hrs.

8. Give 350mg Aminophylline / 150ml D5W IV over 1 hr. The drop factor is 15gtt/ml. How many gtts/min would you give?

   (a.) 36gtt/min (b.) 38gtt/min (c.) 39gtt/min (d.) 40gtt/min

9. Infuse 30ml of 0.9%NS I.V. q 1 hr. continuously. The drop factor is 60gtt/ml. How many gtt/min will deliver 30ml/hr?

   (a.) 15gtt/min (b.) 20gtt/min (c.) 25gtt/min (d.) 30gtt/min

10. The order reads: 1000ml LR I.V. Infuse from 0600-1400. The drop factor is 20gtt/ml. The flow rate is?

    (a.) 38gtt/min (b.) 42gtt/min (c.) 44gtt/min (d.) 46gtt/min

Sample I.V. Problems-- Part 2

1. Heparin 25,000units/1000ml D5W to infuse at 30ml/hr. What is the hourly dosage of Heparin?

   (a.) 650u/hr (b.) 700u/hr (c.) 750u/hr (d.) 800u/hr

2. The order reads: Heparin drip at 1000u/hr. You have D5W 1000ml with Heparin 20,000u added. The drop factor is 15gtt/ml. The Heparin is infused by pump. What is the flow rate?

   (a.) 50ml/hr (b.) 54ml/hr (c.) 58ml/hr (d.) 60ml/hr

3. Administer Heparin 600u/hr I.V. You have D5W 500ml with 25,000u Heparin added. The drop factor is 60gtt/min. Calculate the flow rate.

   (a.) 9gtt/min (b.) 10gtt/min (c.) 11gtt/min (d.) 12gtt/min

4. The order reads: Lidocaine drip at 2mg/min. You have D5W 500ml with 2 g of Lidocaine added. What is the flow rate in ml/hr?

   (a.) 15ml/hr (b.) 30ml/hr (c.) 45ml/hr (d.) 60ml/hr

5. If a patient has a Dopamine drip of 800mg in 500ml of D5W, the concentration is:

   (a.) 1.6mg/ml (b.) 0.16mg/ml (c.) 160mg/ml (d.) 16mg/ml

6. A patient has an IV of D5W 500ml. The flow rate is 19 drops per minute. If the drop factor is 60gtt/ml, how many hours will it take for this infusion to finish?

   (a.) 23.3 hrs. (b.) 26.3 hrs. (c.) 28.3 hrs (d.) 30.3 hrs.

7. The order reads: Insulin drip at 7 units/hr. You have NS 50ml with 50 units of regular insulin added. The insulin is infused by pump. What is the flow rate in ml/hr?

   (a.) 4ml/hr (b.) 5ml/hr (c.) 6ml/hr (d.) 7ml/hr

8. The order reads: Insulin drip at 11units/hr. The label reads NS 100ml with 75 units of regular insulin added. The insulin is infused by pump. Calculate the flow rate.

   (a.) 5ml/hr (b.) 10ml/hr (c.) 15ml/hr (d.) 20ml/hr

9. The order reads: Insulin drip at 5 units/hr. The pharmacy brings 50 units of regular insulin in 100ml of NS. The insulin is infused by pump. Calculate the flow rate.

   (a.) 10ml/hr (b.) 15ml/hr (c.) 20ml/hr (d.) 30ml/hr

10. The order reads: Insulin drip at 8 units/hr. You have 100 units of regular insulin in 100ml of NS. The insulin is infused by pump. Calculate the flow rate.

    (a.) 5ml/hr (b.) 6ml/hr (c.) 7ml/hr (d.) 8ml/hr

Ambrose, M. L. & Wittig, P. (1998). Dosage calculations made incredibly easy. Springhouse, PA : Springhouse.

Boyer, M. J. (1994). Math for nurses. A pocket guide to dosage calculation and drug preparation. (3rd ed.). Philadelphia, PA: J.B. Lippincott.

Daniels, J. M. & Smith, L.M. (1999). Clinical Calculations: A unified approach. (4th ed.). Albany, N.Y. : Delmar Publishers.

Janney, C. & Flahive, J. (1996). Calculation of drug dosages. (5th ed.). Penn Valley, CA: TJ Designs.

McDuffie, M.T. (1994). Quick calc: Med dosage calculations. Redwood City, CA: Addison-Wesley.

Olsen, J.L., Ablon, L.J. & Giangrasso, A. P. (1995). Medical dosage calculations. (6th ed.). Redwood City, CA: Addison-Wesley.

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