math basics for the health care professional copyright © 2014, 2009 by pearson education, inc. all...

Math BasicsMath Basicsfor the Health Care Professionalfor the Health Care Professional

Copyright © 2014, 2009 by Pearson Education, Inc.All Rights Reserved

FOURTH EDITION

UNIT

The Basics of Intravenous Fluid Administration

13

Math Basics for the Health Care Professional, Fourth EditionMichele Benjamin Lesmeister

Student Learning OutcomesStudent Learning Outcomes

1. Calculate intravenous flow rate, time, and volume

2. Calculate amount infused versus amount remaining to be infused

3. Use the language that is used for intravenous infusion


Intravenous: OverviewIntravenous: Overview

• Intravenous (IV) infusions Placed directly into bloodstream Have very quick effect Used when meds needed immediately Used to deliver large doses

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Intravenous: OverviewIntravenous: Overview

• Uses of IV solutions Provide therapy Maintain/replace fluids Keep vein open

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AbbreviationsAbbreviations

• Common abbreviations used Intravenous (IV) Piggy-back (PB) Drop/drops (gtt/gtts) Hour (hr) Minutes (min) Drops per minute (gtts/min) Drops per milliliter (gtts/mL) Milliliters per hour (mL/hr)

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AbbreviationsAbbreviations

• Common abbreviations used Water (H20, W)

5% dextrose water (D5W)

10% dextrose water (D10W) Normal Saline (0.9%) (NS) ½ normal saline, 0.45% (½ NS) Ringer’s lactate solution (RL) Lactated Ringer’s solution (LR)

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IV Infusion SetsIV Infusion Sets

• Infusion set parts Sealed plastic bag or

bottle Drip chamber Tubing

• Macrodrip (10, 15, or 20 gtts/mL)

• Microdrip (60 gtts/mL)

Needle or catheter Clamp

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Infusion RateInfusion Rate

• Drug order contains Type of fluid, amount of fluid, # of hours

to infuseDRIP RATES

Microdrip administration 60 drops per milliliter

Standard administration(macrodrip administration)

10, 15, 20 drops per milliliter

Blood administration 10 drops per milliliter

Drop factor: # of drops in 1 mLMacrodrip: ≥ 125 mL/hourMicrodrip : ≤ 50 mL/hour

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Infusion Flow RatesInfusion Flow Rates

• Flow rates Rate (the flow rate) = volume / time

OR

Example: Infuse 3000 mL of D5W IV over next 24 hrs.• V/t = R (formula)• 3000 mL ÷ 24 hr = R• 125 ml/hr = R

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Rate (flow rate)=

Volume

Time R

V

t

3000mL

24hrR

125mL / hr R


Calculating IV Infusion RatesCalculating IV Infusion Rates

• Three pieces of information Amount to be infused Time in minutes Administration set drop factor

• Formula:

SHORTCUT: To convert hours to minutes quickly, replace the [hours] with [hours × 60 minutes] in

the formula.

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amt of fluid in mL

total time in mindrop factor = drops/min


Calculate: by FormulaCalculate: by Formula

• Problem To administer 500 mL of IV fluid over

12 hours using a microdrip administration set, how many drops/min would the nurse administer?

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Calculate: by FormulaCalculate: by Formula

• Problem

Hint: Microdrip has a drop factor = 60 drops/min.

FORMULA

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amt of fluid in mL

total time in mindrop factor = drops/min

500 mL

12 hr60 drop factor = drops/min

500 mL

12 60 min 60 drop factor = drops/min

500

12 = drops/min

41.6666 = drops/min

42 = drops/min


Calculate: Dimensional AnalysisCalculate: Dimensional Analysis

• Problem To administer 500 mL of IV fluid over

12 hours using a microdrip administration set, how many drops/min would the nurse administer?

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Calculate: Dimensional AnalysisCalculate: Dimensional Analysis

• Problem

Hint: Microdrip has adrop factor = 60

drops/min.

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z drops/min =

z drops/min = 500 mL

12 hr


12 hr

1 hr

60 min


12 hr

1 hr

60 min

60 drops

1 mL

z drops/min = 500

1241.6666 42


Solving a (Complex) ProblemSolving a (Complex) Problem

• Problem: The doctor has prescribed 750 mg of Ampicillin in 125 mL NS to infuse over 45 min. What is the mL per hour infusion rate?

• First, change minutes to hours.

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1 hr

60 min

x hr

45 min

1 45 45

45 60 0.75 hr

45 min = 0.75 hr


Solving our Problem (continued)Solving our Problem (continued)

• Problem: The doctor has prescribed 750 mg of Ampicillin in 125 mL NS to infuse over 45 min (0.75 hr). What is the mL per hour infusion rate?

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R

V

t R

125 mL

0.75 hr

R 166.666

mL

hr

R 167

mL

hr


Solving: Dimensional AnalysisSolving: Dimensional Analysis

• Problem: The doctor has prescribed 750 mg of Ampicillin in 125 mL NS to infuse over 45 min. What is the mL per hour infusion rate?

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?mL/hr

?mL/hr 125 mL

45 min

?mL/hr 125 mL

45 min

60 min

1 hr

?mL/hr 7500

45

?mL/hr 166.66mL

hr167

mL

hr


Handy Helpers for Missing InfoHandy Helpers for Missing Info

• Solve for either of the three missing items: V, R, t

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R

V

t t

V

R V R t


Example: Missing Example: Missing ““tt”” in Rx in Rx

• Problem: The doctor orders D5 ½ NS 1000 mL at 175 mL/hr. (Note: We’re missing “t”.)

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t V

R

t 1000 mL

175 mL/hrt 1000 175

t 5.71428 hrs

t 5.71 hrs

t 5.71 hrs to infuse 1000 mL


Converting Decimal to hrs/minsConverting Decimal to hrs/mins

• Problem: The doctor orders D5 ½ NS 1000 mL at 175 mL/hr (t = 5.71 hours

• Convert the decimal 5.71 hrs to hours and minutes.• Separate the whole number from the

decimal number.• 5 hours and 0.71 hrs

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• Convert the decimal 5.71 hrs to hours and minutes• Multiply the decimal number 0.71 × 60

min = 42.6 minutes• Round to the nearest minute: 43

minutes• Place the hours and minutes back

together.• 5 hours 43 minutes

• The final answer is 5 hours 43 minutes

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Solving: Dimensional AnalysisSolving: Dimensional Analysis

• Problem: The doctor orders D5 ½ NS 1000 mL at 175 mL/hr. (Note: We’re missing “t”.)

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t hours =

t hours = 1000 mL

1

t hours = 1000 mL

1

1 hr

175 mL

t hours = 1000

1755.71428 5.71



• Problem: The doctor orders D5 ½ NS 1000 mL at 175 mL/hr (t = 5.71 hours

• Convert the decimal 5.71 hrs to hours and minutes.• Separate the whole number from the

decimal number.• 5 hours and 0.71 hrs

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• Convert the decimal 5.71 hrs to hours and minutes• Multiply the decimal number 0.71 × 60

min = 42.6 minutes• Round to the nearest minute: 43

minutes• Place the hours and minutes back

together.• 5 hours 43 minutes

• The final answer is 5 hours 43 minutes

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Example: Missing Example: Missing ““VV ”” in Rx in Rx

• Problem: What is the total volume infused in 5 hours if the infusion rate is 65 mL/hr? Solve using the formula.

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V t R

V 5 hrs 65 mL/hr

V 325 mL


Example: Missing Example: Missing ““VV ”” in Rx in Rx

• Problem: What is the total volume infused in 5 hours if the infusion rate is 65 mL/hr? Solve using dimensional analysis.

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V mL =

V mL = 5 hrs

1

V mL = 5 hrs

1

65 mL

1 hr

V mL = 5 65

1 1325


Calculate infused Calculate infused versus remaining to be infusedversus remaining to be infused

• Infuse 2000 milliliters at 125 milliliters per hour. Infuse for _____________.

• Ordered: 1800 milliliters 0.45% NS at 75 milliliters per hour. What is the total time of infusion? _______________

• Ordered: 750 milliliters RL at 83 milliliters per hour. What is the total time of infusion? _______________

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