Summary of Math Presented in Gray, Calculate with Confidence Skills Ii

NURSING SKILLS – instructor sheet

SUMMARY OF MATH PRESENTED IN MORRIS’S CALCULATE WITH CONFIDENCE AND PRACTICE PROBLEMS

METHODS OF CONVERTING

1. Multiply or divide by the conversion factor (in metric system move the decimal point) – see conversion table on page 3

RULES: **smaller unit to larger unit – divide;

**larger unit to smaller unit – multiply

EXAMPLE #1: 10000 mg = X Gm?

10000 mg becomes 10.000 Gm (move decimal three spaces to left to divide)

OR USE RATIO/PROPORTION METHOD IF CAN’T REMEMBER IF NEED TO DIVIDE OR MULTIPLE TO CHANGE METRIC UNITS

10000mg = 1000mg RULE: Must have same units above the line

x 1 Gm and same units below the line eg mg

above and Gms below

(1000mg)(x) = (10000mg)(1 Gm)

1000mg x = 10000mg/GM

1000mg 1000mg

x = 10Gm RULE: MUST ASK SELF IF ANSWER IS

REASONABLE?

EXAMPLE #2: 5 Gm = X mg?

5 Gm becomes 5000 mg (move decimal three spaces to right to multiply)

OR USE RATIO/PROPORTION METHOD IF CAN’T REMEMBER IF NEED TO DIVIDE OR MULTIPLE TO CHANGE METRIC UNITS

1000mg = x mg REMEMBER ABOVE AND BELOW

1Gm 5Gm LINE RULE

(1000mg)(5Gm) = (1Gm)(x)

5000mg/Gm = 1Gm x

5000mg = x MUST ASK SELF IF ANSWER IS

REASONABLE?

2. Ratio-proportion method rule summary:

RULES:

· state known equivalents

· put the incomplete ratio on the other side of the equal sign, KEEPING THE SAME UNITS ABOVE THE LINE AND THE SAME UNITS BELOW THE LINE ON EACH SIDE OF THE = SIGN

· label all terms but ignore them while doing the math

· solve for X

PRACTICE: You do the following examples, using the ratio/proportion method

a. 8 mg = X g

1000mg = 8mg

1 Gm x

1000x = 8

x = 8

1000

x = .008 Gm

b. 12Gm = X mg

12Gm = 1 Gm

x 1000mg

x = (12)(1000)

x = 12000mg

DOSE CALCULATIONS (note: when different systems of measurement are involved, convert to the unit that is available(what you have on hand)before proceeding to calculate the dose)

1.Ratio – proportion method

EXAMPLE #1: Ordered: Lanoxin 0.75 mg;

Available supply: Lanoxin 0.25 mg tabs

RULE: SETTING UP THE PROBLEM:

What you Have OR Supply available = What you Want OR Doctor’s Order

0.25 mg = 0.75 mg Have or Supply = Want or Doc. order

1 tab X tabs

(0.25) X = (0.75)

(0.25) X = 0.75

(0.25) (0.25)

X = 3 tabs

HOUSEHOLD / APOTHECARY / METRIC
dram i / 4 or 5 ml (cc)
1 T (tbs) / 15 cc
gr 15 / 1 G (1000 mg)
Gr 1 / 60 mg
1oz / 30 ml (cc)
2.2 lb / 1 Kg (1000 g)

Other metric:

Kilo = 1000

Centi = one hundredth of (0.01)

Milli – one thousandth of (0.001)

Micro = one millionth of (0.000001)

1Gm = 1000mg

1kg = 1000Gms
Practice Math Calculations for Oral Medications

Answer Key: Practice Math Calculations for Oral Medications

1. Order: Prednisone 60 mg p.o. every day. Available: 20 mg tablets. How many tablet(s) would you give?

WANT = HAVE

60mg = 20mg

X 1 tablet

20x = 60

x = 3 tablets answer Logical?

2. Order: Lasix 0.06Gm p.o. every day. Available: 40 mg tablets. How many tablets would you give? How many Gm to mg? 1G = 1000mg

WANT = HAVE

0.06G = 1G Ratio

X 1000mg

(0.06G)(1000mg)= (x mg)(1G)

60.00mg = x

DOC.ORDER = SUPPLY

60mg 40mg

x = 1 tablet

40x = 60

x = 1.5 tablets answer Logical? (can the tablets be split?)

3. Your patient is unable to swallow pills. You need to crush the medication. Can you crush: tablets? Coated tablets? Slow release capsules?

Tablets: Yes – usually

Coated Tablets: Usually no!

Slow release capsules: No

4. Ordered: Proventil syrup 2mg/5ml. Give 3 ml p.o. TID. How many mg are you giving per dose?

SUPPLY = ORDER

2mg = x

5ml 3ml

(2)(3)= (5)(x)

6 = 5x

5 5

1.2 = x Answer: 1.2 mg/3ml Logical?

The PDR states that the maximum dose is 0.3mg/kg in 3 divided doses. The child in the above example weighs 56 pounds. Is this a safe dose for the patient?

HAVE = WANT

How many kg is 56 lbs? 2.2 pound = 56 pounds

1kg = x

2.2x = 56

2.2 2.2

x = 25kg Logical?

What is the maximum dose for this child for the day?

25 kg x 0.3mg = 7.5 mg/day

What is the maximum dose divided into 3 doses?

7.5mg

3 = 2.5mg per dose

Your patient is receiving 1.2 mg per dose, which is below the maximum dose.

5. Order: Vicodin (2.5mg hydrocodone/500mg acetaminophen) i or ii tablets q 4-6 hrs prn pain. PDR states acetaminophen dose is not to exceed 4G/d.

Your patient had: 2 tabs at 0030, 1 tab at 0500, 2 tabs at 0930, 2 tabs 1440, and 1 tab at 1850. It is now 2250, your patient is in pain. How many tablets could you give the patient?

How many tablets can the pt have in a day?

(500mg per tablet and the limit is 4 G)

WANT = HAVE

4Gm = 1Gm

x mg 1000mg

(1)(x) = (1000)(4)

x = 4000mg

So your patient can have 4000mg of acetaminophen a day, which is how many tablets?

HAVE = WANT

500mg = 4000mg

1 tab = x tablets

500x = 4000

500 500

x = 8 tablets Logical?

If your patient can have 8 tablets in one day, how many tablets has your patient had so far?

8 tablets - Your patient has reached the limit.

6. Order: Keflex 250mg p.o. TID. The label on the bottle states: Keflex 125mg/5ml. Directions: Add 36ml of water to dry mixture in the bottle. Shake well. Will make 40cc of Keflex. How many cc per dose? About how many doses will the bottle contain? How many cc per dose?

SUPPLY = WANT

125mg = 250mg

5ml = x ml

(125)(x) =(5)(250)

125x = 1250

125 125

x = 10ml Answer = 10cc per dose Logical?

How many doses per bottle?

WANT = HAVE

40 cc = 10cc

x 1 dose

10x = 40

10 10

x = 4 doses per bottle Logical?

7. Order: Darvocet-N (propoxphene 65mg /acetaminophen 650mg) i or ii tablets q 4-6 hours prn pain. PDR states acetaminophen dose is not to exceed 4g/d. How many tablets could the patient have in a 24 hour period? How many mg in 4G?

WANT = SUPPLY/HAVE

1000mg = x

1G 4G

(1)(x) = (1000)(4)

x = 4000mg

So the patient could have 4000mg of acetaminophen per day. How many tablets is this?

WANT = SUPPLY/HAVE

4000mg = 650 mg

x 1tablet

650x = 4000

x = 4000

650

x = 6.1 tablets Answer = 6 tablets/day Logical?

EXAMPLE FOR PARENTERAL MEDICATION MATH CALCULATIONS

EXAMPLE #1: Ordered: heparin 1100 units / hour.

Have available 25000 units in 500 ml.

How many ml per hour would you run the IV?

HAVE = WANT

25000 units = 1100 units after checking same units above line and

500 ml X ml same units below line, remove units for

calculations

25000 = 1100

500 X

25000 X = (1100) x (500)

25000 X = 550,000

25000 25000

X = 22 ml Does this make logical sense?

Practice Math Calculations for Parenteral Medications

Answer Key: Math Calculations for Parenteral Medications

8. Order: Cyanocobalamin (Vitamin B12) 200mcg IM q month. Available: 100mcg/ml multi dose vial and 1000mcg/ml multi dose vial. Which one would you use? How many ml would you give?

Use: 100mcg/ml vial because wasting less medication

How much would you give?

WANT = HAVE

200mcg = 100mcg

x 1 ml

(100)x = 200

x = 200

100

x = 2ml You would give 2 cc. Logical?

9. Order: Heparin 15,000 units SQ now. Available: 20,000 u/ml. How many ml would you give?

ORDER = HAVE

15,000 u = 20,000 u

x 1 ml

15,000 = 20,000x

20,000 20,000

O.75 = x You would give 0.75cc. Logical?

10. Order: Penicillin G 30,000 u/kg q 12 hrs. Child weighs 8.8 lbs. How many units would you give? How many kg is the child? (2.2 lbs. per kg)

HAVE/RATIO = WANT

2.2 lbs = 8.8 lbs

1 kg x

2.2x = 8.8

x = 8.8

2.2

x = 4kg Logical?

How many units would you give?

HAVE = WANT

30,000u = x

1 kg = 4 kg

x = (30000) (4)

x = 120,000 u Logical?

Available vial reads:

Add diluent

9.6ml 100,000 u/ml

4.6ml 200,000 u/ml

1.6ml 500,000 u/ml

How much diluent would you use?

Since you need 120,000Units, select 4.6 ml to make 200,000 u/ml.

(smaller injection and wasting less medication)

How much (ml) medication would you give?

HAVE = WANT

200,000 u = 120,000 u

1 ml x ml

200,000x = 120,000

200,000 200,000

x = 0.6cc

Give 0.6 cc of medication Logical?

11. Order: Rocephin 1 gram IM now. Rocephin I gram vial reads: Add 2.7cc of sterile water or lidocaine to yield 3 cc of solution. How many ml of medication would you give?

Yield 3cc of solution means 1 gram of Rocephin in 3cc.

WANT = HAVE

1G = 1 G

x = 3 cc

x = 3 cc Give 3cc Logical?

12. Order: Rocephin 1.5 grams IM now. Available: Rocephin 2 gram vial and the label reads: Add 2.7cc of sterile water to yield 3 cc of solution. How many cc would you give?

HAVE = WANT

2 g = 1.5 g

3cc x

2 x = (1.5)(3)

2 x = 4.5

2x = 4.5

2 2

x = 2.25 Give 2.25 or 2.3 cc of Rocephin. Logical?

13. Order: Demerol 50 mg IM and Vistaril 25 mg IM now. Available: Vistaril 50mg/ml

and Demerol 50mg/ml. You know: They can be mixed. The Demerol comes in a

tubex syringe and the Vistaril is a multi dose vial.

How many ml of Vistaril would you give?

HAVE = WANT

50mg = 25mg

1 ml x

50x = 25

50 50

x = 0.5 Give 0.5 ml of Vistaril Logical?

How many ml of Demerol will you give? HAVE = WANT

50mg = 50mg

1 ml x

x = 1ml of Demerol Logical?

How many ml of medication will you give?

Demerol 1 ml

Vistaril 0.5ml

Total volume: 1.5 ml

Is the volume a safe amount to give?

Yes, for IM you can give 1-3 cc in all sites except the Deltoid

IV Calculations

Terminology/Misc information:

Drop factor – number of drops (gtts) per ml. Administration sets are labeled.

Macro drop tubing – Large drops. Come in 10, 15, 20 gtts per 1 ml

Microdrip tubing – Small drops. Comes in 60 gtts per 1 ml

Standard IV bags come in 50cc, 100cc, 250cc, 500cc, 1000cc

Rate – flow of IV over 1 hour. (Usually written ____ ml or cc/hr)

Description of word problems:

1L D5W.45 NS with 1 amp MVI (multivitamin) infuse over 8 hours.

2 grams Rocephin in 100 cc NS @ 200 cc/hr

Calculating Hourly Rate or Infusion Rate (ml/hr)

Example: Scenario: You need to set the rate on an IV pump—always use cc/hr

Order: Infuse D5W 1000 cc over 8 hours.

Answer Volume 1000cc

Infusion time 8 hours = 125cc/hr

Practice – Find infusion rate when setting rate on an IV pump

1. Infuse 0.25% NS 500cc over 6 hours.

500ml = x

6hr

83.3ml/hr = x Logical?

2. Infuse D5W 1000cc over 12 hours.

1000cc = x

12hr

83.3cc/hr = x Logical?

Calculating Drip Rate or gtts/min using the shortcut chart

1. Figure out the infusion rate

2. Knowing the size of the administration set and the hourly rate, use the chart below to figure out the gtts/min.

If drop factor is

Then divide hourly fluid infusion amount by___ to get gtts/mins

10 gtts = 1 ml / 6
15 gtts = 1 ml / 4
20 gtts = 1 ml / 3
60 gtts = 1 ml / 1

(Notice that you can multiple the number in the first column by the number in the second column and always get 60!)

Example:

Scenario: You don’t have an IV pump and you need to figure out the drip rate. You have to count the number of gtts per minute to set the rate.

Order: Infuse D5W 1000 cc over 8 hours. Administration set 20 gtts/ml.

Answer

1. Figure out the infusion rate.

Volume 1000cc

Infusion time 8 hours = 125cc/hr

2. Now figure out the gtts/min. Use the chart above.

125cc/hr

3 = 41.6 = 42 gtts /min

Practice – gtts per min when not using a pump

3. Infuse 0.45% NS 1000cc over 12 hours. Administration set 20 gtts/ml.

Step one- find infusion rate:

1000cc =83 cc/hr

12hrs

Step two – find the gtts/minute using:

83 cc/hr = 27.6 or 28 gtts/min

4. Infuse D5W 1000cc with 1 amp MVI over 8 hours. Administration set 15gtts/ml.

Step one – find infusion rate:

1000cc = 125 cc/hr

8 hrs

Step two – find the gtts/minute

125cc/hr =31.2 or 31 gtts/min

CALCULATING IV DRIP RATES

1. FORMULA: Volume to be infused X drop factor = gtts/min