**Unformatted text preview: **Math for Nurses
Winston-Salem State University
Variety of calculation types
Varying levels of difficulty
Must (re)test every semester
Junior year: Original, Retake 1, Retake 2
Senior year: Original, Retake 1
Passing grade is defined as: ≥ 80%
Prerequisite for giving medications in a clinical
setting-if cannot pass in specificed retakes then
cannot attend clinical
USE ATI as a resource!!!!! 1 Table of Contents Introductory text . . . . . . . . . . . . . . . . . . . . . . . . 1
Problems solved in class . . . . . . . . . . . . . . . . . 19
Easily solved problems (outside class). . . . . . 66
More solved problems (outside class). . . . . . 68
Answers to More solved problems . . . . . . . . 93 2 Why are you learning to make
these calculations? It is physically impossible to stock every medication in every
possible dosage.
APRNs & physicians don’t know (or care) what is in your
medication inventory.
Nurse must ACCURATELY do the arithmetic to use what is in the
inventory and convert it to what the physician or APRN
ordered. 3 1 The nurse’s most important role in
medicating a patient The nurse is the patient’s last line of defense against receiving an
inappropriate medication. Right patient?
Right time? Right medication? Right route?
Right form? Right dose? Expiration date?
4 Arguments for/against using
dimensional analysis
For: Formulas are derived from dimensional analysis. If you
forget the formula, you have no rational backup. Guessing is
not rational! For: By canceling the excess labels before doing the
arithmetic, the problem setup is very likely to be correct.
(Avoids the generation of an inappropriate or nonsense
answer such as: mL2) Against: Dimensional analysis is more work than using
formulas.
5 Med-Math question types &
sample units of measure Intake/output
Counting (tablets, units of medication)
Mass (weight)
Volume (mL, Liter)
Rate (drops/min, mL/hr, mg/min, units/hr)
Time-based (what time will the IV bag empty?)
Reconstitution
IV rate changes 6 2 Time Abbreviations – Use of the
“q” abbreviation is discouraged,
but remains prevalent. q4h – every 4 hours
q8h – every 8 hours
q12h – every 12 hours
qd – every day (1 time/day)
bid – every 12 hours (two times a day)
tid – every 8 hours (three times a day) 7 Other Abbreviations
Mass (weight): microgam (mcg)
milligram (mg)
gram (g)
kilogram (Kg)
pounds (lbs, #)
Volume: milliliter (mL) = (cc) do not use “cc”
liter (L)
teaspoon (tsp)
ounce (oz)
tablespoon (tbs)
cup (C)
8 Other Abbreviations continued Time:
Count: hour (h, hr) minute (min) tablet (tab)
drop = gtt [Latin: gutta or guttae]
(singular plural) Unit [quantity of certain medications]
mEq [milliequivalents for electrolytes]
tablet 9 3 Rate definition
Rate = flow (These two words mean
the same thing)
How much medication AND how quickly?
Volume & Time (gtt/min, mL/hr)
Mass & Time (mg/min)
Counting & Time (tablets/dose, Units/hr) mL/hr is the default flow for IV
pumps
10 Graphic representation of grams,
milligrams and micrograms 11 Introduction to problem
solving Answer exactly what you are being asked to find.
Not what you think the question means.
Not what you think the question should ask. Determine the label for the answer.
NOTE: The answer label should be, but may not always be explicitly
stated in the problem.
Example: IV flow through a pump implies mL/hr. 12 4 Problem solving strategy
(1) Based upon the question, determine what
the answer’s label will be and place it to
the right of the previous lines. Then place
an equal sign (=) to the right of the label.
(2) The numerator of term immediately to the
right of the answer’s numerator label must
match the answer’s numerator label. You
may require a conversion factor such as
(1,000 mcg/1 mg) to force the correct
label in the 1st numerator.
13 Problem solving strategy
(3) If the question asks you to find (for example)
mL/hr, set up the following generic
statement. The intention is to cascade as
many labels as you need so that the labels
that do not appear in the answer are
arithmetically canceled. (x to x, y to y and z
to z; leaving mL per hr, as required in the
answer)
mL =
hr mL * x * y * z x y z hr 14 Problem solving strategy
Include medication order, medication source and
other factors to cancel labels that are not used in
the answer. (examples that may be relevant:
patient weight, drip set ratio, time factors and
conversions)
Notice that all parts of the formula contain PAIRS of
data. Examples: gtt/mL, mg/hr, mg/mL, g/L,
“something”/dose, mg/Kg/day By definition: a microdrip set = 60 ggt/mL
By definition: a macrodrip set = 10, 15 or 20
gtt/mL
15 5 Rounding Rules
*Always follow special directions in the question.
Verify the rounding rules with your instructor. Typical rules follow:
WSSU Division of Nursing rules for rounding on drug calculations are to be included on all testing materials presented
to the students for evaluation and testing and in the course syllabus. Rules for rounding were developed based on
best practice evidence in current drug calculation texts and recommendations from the National Council of State
Boards of Nursing. In the event of any type of calculation that is not covered by this policy then faculty are directed to
include clear directions for rounding on the quiz, midterm, or final exam affected by this event.
Round drops to nearest WHOLE number
If you have 24.42 gtts/min, the answer will be 24 gtts/min
If you have 24.51 gtts/min, the answer will be 25 gtts/min Round weights (kg), infusion rates, and dosages (ml, mg, mcg, etc.) to the nearest TENTHS place
If you have 3.4445 ml, the answer will be 3.4 ml
If you have 3.4664 ml, the answer will be 3.5 ml
If you have 4.544 kg, the answer will be 4.5 kg
If you have 4.557 kg, the answer will be 4.6 kg
If you have 10.434 mg, the answer will be 10.4 mg
If you have 10.475 mg. the answer will be 10.5 mg
If you have 24.42 ml/hr, the answer will be 24.4 ml/hr
If you have 24.56 ml/hr, the answer will be 24.6 ml/hr 16 Problem with an explicit
answer
Order: 400 mg of med. Supply: 125 mg per 5 mL.
How many mL will you give?
5 mL
? mL = -----125 mg * 400 mg
--------1 an number over “1” makes the
numerator obvious & does not = 16 mL change the numerator’s value. 17 Problem with an implied
answer
Order: 400 mg of med. Supply: 125 mg per 5 mL.
5 mL * 400 mg
? mL = ---------------125 mg
1
= 16 mL
All further examples are typed on these slides as
follows:
mL = (5 mL/125 mg) * (400 mg/1)
= 16 mL
18 6 Class Problem mg/min Determine the mg/min required to administer when the flow
and solution concentration are given. The medication is
infusing at 32 mL/hr. The IV volume is 250 mL. The amount of
dissolved medication is 700 mg. If necessary, round answer to
1 decimal place. See next slide for important considerations. 19 Class Problem mg/min
Identify the pairs of data: 250 mL & 700 mg
1 hour and 32 mL Orient the pairs as required to satisfy the
answer’s label and cancel all other
labels.
Which conversion “tool” will you use to
change the hours to minutes?
20 Answer - mg/min
Determine the mg/min required to administer when the
flow and solution concentration are given. The
medication is infusing at 32 mL/hr. The IV volume is 250
mL. The amount of dissolved medication is 700 mg. mg/min=(700mg/250mL) * (32mL/hr) * (1 hr/60min)
= 1.49 Round up to 1.5 mg/min ___1____ . _4__ --9-- mg/min rounds to:
___1____ . _5__ - mg/min
21 7 Class Problem – mcg/min
Determine how many mcg/min are infusing if
the IV contains 240 mg of medication per 500
mL and is infusing at 16 mL/hr. If necessary,
round answer to 1 decimal place.
This problem does not have mcg in any of the
data; therefore, put a conversion “tool’ for
mcg and mg immediately to the right of the
equal sign (=). Then cascade and orient the
rest of the data so that labels not appearing in
the answer’s label are canceled.
22 Answer – mcg/min Determine how many mcg/min are infusing if the IV contains 240
mg of medication per 500 mL and is infusing at 16 mL/hr mcg/min = (1000mcg/mg) *(240mg/500mL) * (16mL/hr) *
(hr/60min)
= 218 mcg/min 23 Class Problem – mL/hr The provider has ordered 2 mcg/min. The nurse has 5 mg per 250
mL. The flow rate is _________________ mL/hr. If necessary,
round answer to 1 decimal place. 24 8 Answer – mL/hr The provider has ordered 2 mcg/min. The nurse has 5 mg per 250
mL. The flow rate is _________________ mL/hr mL/hr = (250mL/5mg) * (1 mg/1000mcg) * (2 mcg/min)*
(60min/1 hr)
= 6 mL/hr 25 Class Problem – mL/hr
The provider ordered a medication at the rate of 46
mcg/Kg/min. The client weighs 72.7 Kg. The
medication is supplied as 300 mg in 75 mL of
solution. The client should receive
______________mL/hr. If necessary, round answer to
1 decimal place.
When using a 3-part component (e.g., mcg/Kg/min),
always use the 1st component in the numerator (mg)
and everything else in the denominator. For
example:
mg
Kg/min
26 Answer – mL/hr The provider ordered a medication at the rate of 46 mcg/Kg/min.
The client weighs 72.7 Kg. The medication is supplied as 300 mg
in 75 mL of solution. The client should receive
______________mL/hr mL/hr =
(75mL/300mg) * (1 mg/1000mcg) * (46mcg/Kg/1 min) * (72.7 Kg/1)
* (60min/1 hr)
= 50.163 rounds up to 50.2 mL/hr 27 9 Class Problem - tablets A medication comes out of the bottle as 2.5mg/tablet. Give
2.5mg tid. If necessary, round answer to 1 decimal place.
(1) How many tablets/dose?
(2) How many tablets daily? 28 Answer - tablets
A medication comes out of the bottle as 2.5mg/tablets.
Give 2.5mg tid.
(1) How many tablets/dose? (Each 1 dose = 2.5 mg.)
tabs/dose = (1 tab/2.5mg) * (2.5mg/1 dose)
= 1 tablet/dose (2) How many tablets daily? (tid = 3 doses/day)
tabs/day = (1 tab/2.5mg) * (2.5mg/dose) * (3doses/day)
= 3 tablet/day
29 Class Problem – mg/day The provider ordered 2 mg/Kg/day IV for a 16 pound infant. The
infant should receive _____________mg per day. If necessary,
round answer to 2 decimal places. 30 10 Answer – mg/day The provider ordered 2 mg/Kg/day IV for a 16 pound infant. The
infant should receive _____________mg per day. mg/day = (2mg/Kg/day) * (1 Kg/2.2 lbs) * (16
lbs/1)
=14.545 round up to 14.55 mg/day 31 Class Problem – determine the
label and solve the problem A medication is ordered for your patient at 80 mg/Kg/24 hours
every 8 hours. The child weighs 18 lbs. How many mg of
medication will you administer at each dose? If necessary,
round answer to 1 decimal place. 32 Answer – determine the label
and solve the problem A medication is ordered for your patient at 80 mg/Kg/24 hours
every 8 hours. The child weighs 18 lbs. How many mg of
medication will you administer at each dose? mg/dose= (80mg/Kg/24hrs) * (8hrs/dose) * (1 Kg/2.2
lbs) * (18 lbs/1)
= 218.182 rounds down to 218.2 mg/dose 33 11 Class Problem – gtt/min Calculate the drip rate of 1,000 mL of medication to infuse over
10 hours using an infusion set that delivers 15gtt/mL. How many
drops/min? If necessary, round answer to 1 decimal place. 34 Answer – gtt/min Calculate the drip rate of 1,000 mL of medication to infuse over
10 hours using an infusion set that delivers 15gtt/mL. gtt/min= (15gtt/mL) * (1,000 mL/10 hrs) * (1
hr/60 min)
= 25gtt/min 35 1 Liter bag of
medication 4 AM
5 AM
6 AM
7 AM Expectation What is observed 1,000 mL 1,000 mL 900 mL ? mL 800 mL ? mL 700 mL ? mL 600 mL ? mL 500 mL ? mL 400 mL 600 mL 8 AM
9 AM
10 AM 0 mL Drip chamber
7 tubing To the patient 36 12 Class Problem – Is the IV setup
working as expected? The IV above was started at 4 AM.
At 10 AM 600 mL remain in the bottle.
Is the IV running on time?
(Refer to previous slide for mL/hr) 37 Answer – Is the IV setup
working as expected?
The IV above was started at 4 AM.
At 10 AM 600 mL remain in the bottle.
Is the IV running on time?
(4 AM to 10 AM) = 6 hrs running time.
(1,000 mL/10 hrs) = 100 mL/hr.
(100 mL/hr * 6 hrs/1) = 600 mL should be used in 6 hours.
(1,000 mL – 600 mL) = 400 mL should still be in the bottle.
Therefore: bottle is emptying too slowly – NO: not on time.
Patient may have laid on the tubing and caused it to crimp.
There are other possible reasons for the delayed emptying. 38 Conversion factors to
memorize 1 oz = 30 mL 8 oz = 1 cup = 240 mL ======================
16 oz = 1 pint = 32 oz = 1 quart =
128 oz = 1 gallon = 500 mL
1,000 mL = 1 liter
4,000 mL 39 13 Class Problem – Intake &
Output
12 hour I/O for patient Smith on 4/7/2008: 4 oz cranberry juice
175 mL urine
1/2 cup oatmeal
2 slices of toast
120 mL yellow vomit
8 oz black
coffee
1/2 cup flavored gelatin 100 mL diarrhea
a tuna fish sandwich
3 oz cream of mushroom soup 6 oz 1% milk
230 mL urine
16 oz water
1 pint ice cream
2 tsp liquid medication
1 tbs liquid medication
IV @ 150mL for 3 hrs
1 cup applesauce What is the intake? ______________
What is the output? ______________
Net gain or net loss of fluid? _______
40 Answer - Intake
4 oz cranberry juice
4 oz * 30 mL/oz
= 120 mL
8 oz black coffee
8 oz * 30 mL/oz
= 240 mL
1/2 cup flavored gelatin
4 oz * 30 mL/oz
= 120 mL
3 oz cream of mushroom soup 3 oz * 30 mL/oz
= 90 mL
6 oz 1% milk
6 oz * 30 mL/oz
= 180 mL
16 oz water
1 pint
= 500 mL
1 pint ice cream
1 pint
= 500 mL
2 tsp liquid medication
2 tsp * 5 mL/tsp
= 10 mL
1 tbs liquid medication
1 tbs * 15 mL/tbs = 15 mL
IV @ 150 mL for 3 hrs
150 mL/hr * 3 hr = 450 mL
1 cup applesauce
1 cup * 16 oz/cup = 240 mL Answer: - ---------------------------------------- 2,465 mL
41 Answer - Output & Net gain
or loss
175 mL urine
120 mL yellow vomit
230 mL urine
100 mL diarrhea
625 mL Output Input = 2,465 mL Output = 625 mL Net gain = 1,840 mL
More fluid was retained
than was excreted; therefore,
patient has a net gain.
42 14 Class Problem mL/hr
with distracters
This problem contains distracters. Determine
what the answer label is. Then look to see
which components of the question will satisfy
the requirements for the answer’s label. Ignore
everything else. If necessary, round answer to 1
decimal place.
An IV of 1,000 mL medication contains 60 mEq
of an electrolyte and is set to infuse at 27 drops
per minute. The tubing delivers 10gtts/cc. How
many mL/hr are you administering?
43 Answer - mL/hr
with distracters
An IV of 1,000mL medication contains 60 mEq of an electrolyte and
is set to infuse at 27 drops per minute. The tubing delivers
10gtts/cc. How many mL/hr are you administering?
Be in the habit of rewriting drops to gtt and cc to mL.
Remember to find pairs of data that may work for you.
27 gtt/min
10 gtt/mL mL/hr 1,000 mL/mEq
Correct answer: mL/hr = (1 ml/10 gtt) * (27 gtt/1 min) * (60 min/1
hr)
= 162mL/hr
Why is this wrong? mL/hr = (1,000 ml/60 mEq) *
(27 gtt/1 min) * (60 min/1 hr)
44 Class Problem – Time-based
Unless otherwise specified, and if necessary,
round answer to 1 decimal place. 900 mL of medication is ordered to infuse at
80 mL per hour.
(1) Assuming that there are no interruptions,
how long will it take to empty the bag?
(2) If the IV line is started at 2:47 PM, what
time will the bag run dry? 45 15 Answer - Calculate the hours 1) Assuming that there are no interruptions, how long will it take to
empty the bag?
Hours = (1 hr/80 mL) * ( 900 mL/1) = 11.25 hours
This answer is expressed in hours and it
means
11 and ¼ hours.
It is NOT 11 hours and 25 minutes!
46 Answer - Calculate the
minutes minutes = (60 min/1 hr) * (0.25 hr/1)
= 15 minutes 47 Answer – total run time
expressed in hours & minutes (1) Assuming that there are no interruptions, how
long will it take to empty the bag? The bag will empty in 11 hours and 15 min. 48 16 Answer - Time bag will
theoretically empty (2) If the IV line is started at 2:47 PM, what time will the bag run
dry? (from previous page)
2 PM + 11 hours -------> 1 AM
47 minutes + 15 minutes = 62 minutes
1 AM + 62 minutes ------> 2:02 AM 49 Class Problem – Reconstitution Reconstitution problems ask the nurse to dissolve a drug (typically
a powder) whose quantity is usually expressed in grams or
milligrams in: a specific quantity of a liquid (usually measured in milliliters).
Frequently, the liquid is normal saline (0.9% NS) or D5W.
Conceptually, this is identical to dissolving 1 teaspoon of table salt
in 1 cup of hot water. 50 Class Problem –
Reconstitution Order: 350 mg of the drug to be given q8h IV. How many mL will
you give per dose? Supply: The drug is available in 500 mg containers. The label tells
the nurse to dissolve the powder in 25 mL of normal saline (NS). 51 17 Class Problem –
Reconstitution
Which pairs of data do you find in the problem?
350 mg every 8 hours. (every 8 hours means: 1
dose.)
500 mg of the powder is dissolved in 25 mL of NS.
What is the answer’s label for your calculation?
How many mL/dose?
Can you isolate all of the components that are required to
solve this problem? (YES, of course you can do this!)
52 Answer – Reconstitution mL/dose = (25 mL/500 mg) * (350 mg/dose)
= 17.5 mL/dose 53 Class Problem –
Reconstitution Order: 250 mg of the drug to be given q8h IV. How many mL will
you give per dose?
Supply: The drug is available in 1g containers. The label tells the
nurse to dissolve the powder in 50 mL of normal saline (NS).
The disconnect is between the grams and the milligrams, so use
the appropriate conversion “tool.” 54 18 Answer – Reconstitution mL/dose = (50 mL/1 g) * (1 g/1000 mg) *
(250 mg/dose)
= 12.5 mL/dose 55 Class Problem –
Reconstitution Order: 20 mg/Kg of the drug to be given q8h IV. Patient weighs
50 pounds. How many mL will you give per dose? Supply: The drug is available in 500 mg containers. The label tells
the nurse to dissolve the powder in 5 mL of normal saline (NS).
With which data pair is the “dose” a factor? Why? 56 Answer – Reconstitution mL/dose = (5 mL/500 mg) * (20 mg/1 Kg/1
dose) *
(1 Kg/2.2 lbs) * (50 lbs/1)
= 4.545 rounds up to 4.55
mL/dose
Dose is only related mg/Kg. Any other pair does not make any
sense. 57 19 Class Problem –
Reconstitution
Order: 700,000 Units given IM. How many mL will you
give?
Supply: The drug is available in 5,000,000 Unit
containers. The label tells the nurse to reconstitute
(dissolve) the powder in 3.2 mL of normal saline (NS)
to yield 1,000,000 Units/mL.
This problem contains a distracting pair. To
determine what the distracting pair is, you must
understand the sequence of the problem’s
operation. See picture on next slide.
58 Reconstitution Graphic
5 million
Units in
3.2 mL 1 million
Units/1 mL The patient Which medication source DIRECTLY affects the patient? 59 Answer – Reconstitution
The distracters are the 5 million Units and 3.2 mL. Your reconstituted supply is now 1 million Units/mL.
The 5 million units dissolved in the 3.2mL is how you
arrived at the 1 million Units/mL. Now they are
irrelevant = distractors.
mL = (1 mL/1,00,000 Units) *
(7.000,000 Units/1)
= 0.7 mL 60 20 Class Problem –
Reconstitution Order: 500 mg IV every 4 hours. Supply: The drug is available in 1 gram containers. The label
tells the nurse to reconstitute (dissolve) the powder in 10 mL of
0.9% NS. THEN further dilute this mixture in 50 mL of NS. Infuse it
over 30 minutes. The drip set is 10gtt/mL. 61 Class Problem – Reconstitution
Refer to the previous graphic and make a similar
picture for this problem. Step-A: How many mL will you use of the 10 mL
in which you dissolve the 500 mg of powder?
Step-B: How many mL/hr will you give the patient?
Step-C: How many drops/min? 62 Answer – Reconstitution
This is a multi-step (3) problem. (A) Determine how many mL after mixing the powder (Step-1). mL = (10 mL/1 gram) * (1 gram/1,000 mg) *
500 mg/1)
= 5 mL 63 21 Answer – Reconstitution (B) Determine how many mL/hr after diluting the mixture (Step-2). mL/hr = (55 mL/30 min) * (60 min/1 hr)
= 110 mL/hr Your picture should tell you why we use 55 mL, not 50 mL. 64 Answer – Reconstitution (C) Determine how many gtt/min: gtt/min = (10 gtt/1 mL) * (110 mL/1 hr) *
(1 hr/60 min)
= 18.3 rounds down to 18 gtt/min 65 Easily solved problems
with answers – [in brackets]
Supply: 5 mg/mL.
Supply: 10 mg tablets. Order: 50 mg.
Order: 30 mg. Supply: 250 mg/5 mL. Order: 1.5 g.
Supply: 50 mg tablets.
Sup...

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- Spring '17
- Dr. Donna
- Decimal, ml