copyright © 2011 by saunders, an imprint of elsevier inc. all rights reserved. chapter 5...

Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved.

Chapter 5Chapter 5

Mathematics Review and Introduction to Dosage

Calculation


Chapter 5Chapter 5

Lesson 5.1

2


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.

3


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

4


Talking About Numbers

Figure 5-1. Comparison of part of a number to a whole number.

5


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

7


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

8


Comparing Fractions (cont’d)

Figure 5-2. Fraction sizes.

9


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

10


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!

11


Dividing Fractions

• Invert (flip) the second fraction

• Multiply fractions– Multiply numerators– Multiply denominators

• Reduce

• If whole number is involved, change to improper fraction

12


Chapter 5Chapter 5

Lesson 5.2

13


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.

14


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!

15


Adding and Subtracting Decimals

• Align decimal points

• Add or subtract as with whole numbers

16


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

17


Dividing Decimals

8.216.432Divisor

Dividend

Quotient

Parts:

18


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!

19


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)

20


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!

21


Percents

• Express number as part of a hundred

• Used to calculate drug doses and strength of solutions– Example: 5% dextrose in water (D5W)

22


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%

23


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

27


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

28


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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copyright © 2011 by saunders, an imprint of elsevier inc. all rights reserved. chapter 5...

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