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
x
1 Gm
RULE:
Must have same units above the line
and same units below the line eg mg
above and Gms below
(1000mg)(x) = (10000mg)(1 Gm)
1000mg x
1000mg
x
=
=
EXAMPLE #2:
10000mg/GM
1000mg
10Gm
RULE: MUST ASK SELF IF ANSWER IS
REASONABLE?
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
1Gm
= x mg
5Gm
REMEMBER ABOVE AND BELOW
LINE RULE
(1000mg)(5Gm) = (1Gm)(x)
5000mg/Gm = 1Gm x
5000mg = x
MUST ASK SELF IF ANSWER IS
REASONABLE?
1
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
2
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
1 tab
X tabs
Have or Supply = Want or Doc. order
(0.25) X = (0.75)
(0.25) X = 0.75
(0.25)
(0.25)
X = 3 tabs
HOUSEHOLD
APOTHECARY
dram i
1 T (tbs)
gr 15
Gr 1
1oz
2.2 lb
METRIC
4 or 5 ml (cc)
15 cc
1 G (1000 mg)
60 mg
30 ml (cc)
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
3
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
X
=
1G
1000mg
Ratio
(0.06G)(1000mg)= (x mg)(1G)
60.00mg = x
DOC.ORDER
60mg
x
40x
=
x
=
= SUPPLY
40mg
= 1 tablet
60
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
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
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
2.2x
= 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
5
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
500x
500
x
= 4000
500
= 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
125mg
5ml
(125)(x)
125x
125x
125
x
= WANT
= 250mg
= x ml
=(5)(250)
= 1250
= 1250
125
= 10ml
Answer = 10cc per dose
Logical?
How many doses per bottle?
WANT = HAVE
40 cc = 10cc
x
1 dose
10x = 40
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
6
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
500 ml
X ml
after checking same units above line and
same units below line, remove units for
calculations
25000 = 1100
500
X
25000 X = (1100) x (500)
25000 X = 550,000
25000 X = 550,000
25000
25000
X = 22 ml
Does this make logical sense?
7
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
x
x
= 200
= 200
100
= 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
15,000
20,000
=
20,000x
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
2.2 lbs
1 kg
=
=
2.2x
x
=
=
x
=
WANT
8.8 lbs
x
8.8
8.8
2.2
4kg
Logical?
8
How many units would you give?
HAVE
30,000u
1 kg
=
=
=
WANT
x
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
200,000x
=
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
=
1G
x
=
3 cc
x
= 3 cc
Give 3cc
Logical?
9
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
2x =
(1.5)(3)
2x
= 4.5
2x
2
x
=
=
4.5
2
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
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
10
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.
Volume
to infuse
Description
Infusion
Rate/hr
Total Infusion
Time
of fluid /
2 grams Rocephin in 100 cc NS @ 200 cc/hr
medication
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
Infusion time
1000cc
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?
11
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
3
12
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
4
CALCULATING IV DRIP RATES
1. FORMULA: Volume to be infused X drop factor = gtts/min
Time in minutes
EXAMPLE #1:
Ordered: 100 ml/hour; drop factor = 10 gtt / ml. At what rate do you set the IV for
gravity flow to drip?
(100 ml) x (10 drops/ml factor)
60 minutes
= X (gtts/min)
100 x (10)
60
1000
60
or
100
6
17 gtt/min = X
EXAMPLE #2:
Ordered: Rocephin 50 ml/over 30 minutes; drop factor = 20 gtt/ml. At what drip rate
should the IV be set for gravity flow?
50ml x 20 gtts/ml factor
30 min
=X
(50) x (20) = X
30
1000 = X
30
33.3 gtts/min = X
13
Calculating the Amount of Drug in a Specific Amount of Solution
Example:
Order: 0.45%NS 500cc with 80 U of Regular Insulin added. Give 8 U per hour. What
is the infusion rate?
Answer
500cc
80U
80x
80x
x
x
= x
8U
= (8)(500)
= 4000
= 4000
80
= 50cc/hr
Practice Calculating the Amount of Drug in a Specific Amount of Solution
5. 0.45% NS 500cc with 120 U Regular Insulin added. Give 10 U/hr. What is the
infusion rate?
120U = 10U
500ml
x
120x = 5000
120x
120
x
= 5000
120
= 41.6 or 42ml/hr
6. Order: Heparin 600 U/hr. When the bag arrives from the Pharmacy, the label reads:
D5W 1000ml with 20,000 U Heparin added. What is the infusion time?
20000U = 600U
1000ml
x
20000x = (600)(1000)
20000x = 600,000
20000x
20000
x
=
=
600,000
20000
30cc/hr
14
7. You want to know how many units of Heparin a client is receiving. The label on the
bag reads: D5W 500 ml mixed with 2,000 U of Heparin. The infusion rate is 15ml/hr.
500ml = 15ml
2000U
x
500x
500x
= (15)(2000)
= 30,000
500x
500
= 30,000
500
x
= 60U of Heparin per hour
15