copyright © 2011 by saunders, an imprint of elsevier inc. all rights reserved. chapter 5...
TRANSCRIPT
Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved.
Chapter 5Chapter 5
Mathematics Review and Introduction to Dosage
Calculation
Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved.
Chapter 5Chapter 5
Lesson 5.1
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Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved.
Objectives
• Identify the numerator and the denominator of a fraction.
• Identify a proper and an improper fraction.• Change a whole number into a fraction.• Change a mixed number into a fraction.• Reduce a fraction to its lowest terms.• Calculate the lowest common denominator of a
series of fractions.• Add two or more fractions and subtract two or
more fractions.• Multiply two fractions and divide two fractions.
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Why Do Nurses Need Math?
• Two of the six “rights” require calculation– Right dose– Right time
• DIMS test (“does it make sense?”)
• PINCH drugs– Potassium, insulin, narcotics, chemotherapy
and cardiac drugs, and heparin or other anti-clotting drugs
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Talking About Numbers
Figure 5-1. Comparison of part of a number to a whole number.
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Fractions
• Fractions are actually division problems – 25/100 is the same as 25 ÷ 100
• Top number is numerator
• Bottom number is denominator– Remember NU/DE!
• Whole numbers can be written as fractions– 15 = 15/1
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Types of Fractions
• Proper fractions – ½, ¾
• Improper fractions– 11/5, 7/2
• Mixed number fractions– 1½, 2¾
• Reduced fractions– 2/4 = ½, 3/9 = 1/3
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Comparing Fractions
• If all numerators are 1, smallest denominator = largest fraction
• If fractions have different numerators and denominators, determine lowest common denominator– Fraction with highest numerator will be the
largest
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Comparing Fractions (cont’d)
Figure 5-2. Fraction sizes.
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Adding and Subtracting Fractions
• Fractions with common denominators– Simply add/subtract numerators
• Fractions with different denominators– Convert fractions to lowest common
denominator, then add/subtract numerators
• Reduce to lowest terms
• Subtraction rare in drug calculation
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Multiplying Fractions
• Reduce fractions, if possible
• Convert all mixed numbers to improper fractions
• Multiply all numerators – Product is new numerator
• Multiply all denominators– Product is new denominator
• Reduce!
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Dividing Fractions
• Invert (flip) the second fraction
• Multiply fractions– Multiply numerators– Multiply denominators
• Reduce
• If whole number is involved, change to improper fraction
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Chapter 5Chapter 5
Lesson 5.2
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Objectives
• Identify the divisor and the dividend of a decimal problem.
• Multiply two decimals and divide two decimals.• Change a fraction into a decimal and a decimal
into a fraction.• Calculate a given percentage of a number.• Compare the dose on hand (what you have) with
the dose that has been prescribed (what you want).
• Calculate the number of tablets or amount of liquid drug needed to make the prescribed dose.
• Convert a set of fractions into a proportion.• Solve for “X” (the unknown) in a math problem.
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Decimals
• Based on multiples of 10
• A decimal divides a whole number and part of a number (fraction)– Whole number (.) tenths, hundredths,
thousandths
• Always include a zero to the left of a decimal less than one
• Never put an extra zero to the right of a decimal!
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Adding and Subtracting Decimals
• Align decimal points
• Add or subtract as with whole numbers
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Multiplying Decimals
• Multiply as with whole numbers
• Count number of decimal spaces to the right of decimal points in the problem
• Starting at the far right of the answer, count same number of decimal spaces and place the decimal
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Dividing Decimals
8.216.432Divisor
Dividend
Quotient
Parts:
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Dividing Decimals (cont’d)
• If divisor is whole number, keep decimal in quotient in the same place as dividend
• If divisor is decimal, convert to whole number
• Do to the divisor what is done to the dividend
• Check the math! Multiplying divisor by quotient should equal the dividend!
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Fractions and Decimals
• Fraction to decimal:– Divide numerator by denominator– Add 0 to left of decimal point if answer is less
than 1
• Decimal to fraction:– Keep numbers to left of decimal point as
whole numbers– Drop decimal point and place numbers over
the place value (e.g., 0.25 = 25/100)– Reduce to lowest terms (e.g., 0.25 = ¼)
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Rounding Parts of Numbers
• Liquid doses usually rounded to nearest tenth– Most syringes calibrated in tenths– Answers ending below 0.05 are rounded
down– Answers equaling or ending above 0.05 are
rounded up
• Tablets usually rounded to nearest whole– Exception – some tablets can be cut in half!
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Percents
• Express number as part of a hundred
• Used to calculate drug doses and strength of solutions– Example: 5% dextrose in water (D5W)
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Percents and Decimals
• Convert percent to decimal:– Drop % sign, multiply by 0.01 (or move
decimal 2 places left)– Example: 9% = 0.09
• Convert decimal to percent:– Add % sign, multiply by 100 (or move decimal
2 places right)– Example 0.05 = 5%
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Percents and Fractions
• Percent to fraction:– Convert percent to decimal– Convert decimal to fraction
• Fraction to percent:– Convert fraction to decimal– Multiply by 100 (or move decimal 2 places
right)– Add % sign
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Percentage of a Number
• Convert percent to decimal
• Multiply
• Problem: 25% of 200– Convert: 25% = 0.25– Multiply: 200 × 0.25 = 50
• Be careful with decimal points!
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Introduction to Dosage and Calculation
• Most drugs dispensed from pharmacy in correct dose
• Nurse is last check in the system
• Double-check decimal points and zeros!
• Label all numbers in calculations
• Plug numbers into formula, do the math
• Do the DIMS test!
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Oral Drugs
• Formula #1: Dry pill, tablets, etc.
= Number of tablets to give
• Formula #2: Liquid medication
× LIQUID = Amount of liquid to give
HAVE
WANT
HAVE
WANT
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Drugs Given by Injection
• Three types– Intramuscular (IM)– Subcutaneous – Intradermal (ID)
• Available in single- or multi-dose packaging
• Use formula #2, same as other liquid drugs
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Proportion
• Equal mathematical relationship between two sets of numbers– Example: ½ = 2/4– Example: 3 boats/6 sails = 9 boats/18 sails
• Always label components
• Right side must be set up in same order as left (e.g., boats “as to” sails on each side)
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Using Proportion to Solve for X
• Calculate dose using proportion– Order: Give 500 mg of primidone by mouth
(orally)– On hand: Primidone 250 mg per 1 caplet– Question: How many caplets equal 500 mg?– Set up problem: 250 mg/1 caplet = 500 mg/
X caplets– Calculate: Cross-multiply and solve for
X – 500/250 = X– Answer: 2 caplets
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