Copyright © 2008 Thomson Delmar Learning Suffolk County Community College NUR 103 Fall 2008 Kathleen Burger, MSEd, MSN, RN, CNE Assistant Professor of Nursing MA207 Grant Campus

Copyright © 2008 Thomson Delmar Learning

Medication Errors 10-18% of hospital injuries are attributed to medication errors 44,000 to 98,000 people die in U.S. hospitals annually due to medication errors

Copyright © 2008 Thomson Delmar Learning Basic Mathematics Review Fractions & Decimals Textbook Assignment: Pickar, G. (2007). Dosage calculations: A ratio-proportion approach. (2 nd ed.) Chapter 1 Revised KBurger0808

Copyright © 2008 Thomson Delmar Learning Fractions Math Tip –Denominator begins with d and is down below the line in a fraction numerator denominator

Copyright © 2008 Thomson Delmar Learning Types of Fractions Proper –Value of numerator is less than value of denominator Example:

Copyright © 2008 Thomson Delmar Learning Types of Fractions Improper –The value of the improper fraction is greater than or equal to 1 Example:

Copyright © 2008 Thomson Delmar Learning Types of Fractions Mixed numbers –The value of the mixed number is always greater than 1 Example:

Copyright © 2008 Thomson Delmar Learning Types of Fractions Complex –The numerator and/or denominator are fractions 1/12 3/4 5 1/2 1/2 2 1/4

Copyright © 2008 Thomson Delmar Learning Comparing Fractions

Copyright © 2008 Thomson Delmar Learning Fractions When numerator and denominator are the same number the fraction is equivalent to the whole number 1 12 = 1 12

Copyright © 2008 Thomson Delmar Learning Reducing Fractions Divide both terms by the –Largest nonzero whole number that will divide both numerator and denominator evenly. Value remains the same Note: 3/5 is an equivalent fraction to 6/10

Copyright © 2008 Thomson Delmar Learning Tips for Reducing Fractions If the number is even it is divisible by 2 If the sum of the digits adds up to a number divisible by 3, the number is divisible by 3 If the last digit is 5 or 0, the number is divisible by 5

Copyright © 2008 Thomson Delmar Learning Enlarging Fractions Multiply both terms by –Same nonzero number Value remains the same Note: 2/24 is an equivalent fraction to 1/12

Copyright © 2008 Thomson Delmar Learning Converting Improper Fractions to Mixed Numbers Divide the numerator by the denominator Remainders should be written as a proper fraction in lowest terms 13 = 6 1/2 2

Copyright © 2008 Thomson Delmar Learning Converting Mixed Numbers to Improper Fractions Multiply the whole number by the denominator then add the numerator. Place that answer as numerator over the original fractions denominator 2 1/6 = [6X2+1] = 13 6

Copyright © 2008 Thomson Delmar Learning Adding or Subtracting Fractions Convert to equivalent fractions with least common denominators Add or subtract the numerators –Place that value in numerator Place least common denominator as denominator Convert answer to mixed number and/or reduce to lowest terms

Copyright © 2008 Thomson Delmar Learning Multiply and Divide Fractions To multiply –Cancel terms, multiply numerators, and multiply denominators To divide - Invert divisor, cancel terms, and multiply Convert results to a mixed number and/or reduce to lowest terms

Copyright © 2008 Thomson Delmar Learning Multiplication of Fractions X 16

Copyright © 2008 Thomson Delmar Learning Division of Fractions Dividend Divisor changed to Inverted Divisor Quotient

Copyright © 2008 Thomson Delmar Learning Simplification of Complex Fractions Complex fractions may be simplified by performing the indicated division 2/3 5/6 is the same as: 2 DIVIDED BY 5 3 6

Copyright © 2008 Thomson Delmar Learning Decimals X X X X X. X X X X hundreds tensones ten thousands thousands DECIMAL POINTWHOLE NUMBERS tenths hundredths thousandths ten thousandths DECIMAL FRACTIONS

Copyright © 2008 Thomson Delmar Learning Decimals = one thousandth 0.02 = two hundredths 0.7 = seven tenths

Copyright © 2008 Thomson Delmar Learning Comparing Decimals How to compare the following decimals 0.125, 0.05, and 0.2 to find largest decimal fraction Align decimal points and add zeros

Copyright © 2008 Thomson Delmar Learning Comparing Decimals

Copyright © 2008 Thomson Delmar Learning Decimal Values: Decimal Point and Zeros To avoid errors the JCAHO Official DO NOT USE LIST has the following rules for medication documentation –Always place a zero to the left of decimal point Called a leading zero [ 0.5 mg NOT.5 mg ] –Never place a zero at the of a decimal fraction Called a trailing zero [ 2.5 mg NOT 2.50 mg ] –www. JCAHO.orgwww. JCAHO.org

Copyright © 2008 Thomson Delmar Learning Add and Subtract Decimals To add or subtract decimals –Align decimal points and add zeros –Make all decimals of equal length –Eliminate unnecessary zeros in final answer

Copyright © 2008 Thomson Delmar Learning Multiply and Divide Decimals To multiply decimals –Place decimal point in product to left –As many decimal places as there are in the two decimals multiplied

Copyright © 2008 Thomson Delmar Learning Multiply and Divide Decimals To divide decimals –Move decimal point in divisor and dividend the correct number of decimal places to make divisor a whole number –Align it in the quotient

Copyright © 2008 Thomson Delmar Learning Multiply and Divide Decimals Multiply or divide by a multiplier of 10 –Move decimal point to right (to multiply) –Move to left (to divide) –Move number of decimal places as there are zeros in the multiplier of 10

Copyright © 2008 Thomson Delmar Learning Multiply and Divide Decimals

Copyright © 2008 Thomson Delmar Learning Converting Decimals & Fractions Express the decimal number as a whole number in the numerator of the fraction Express the denominator as the number 1 followed by as many zeros as there are places to the right of the decimal point Reduce to lowest terms 0.45 = 45/100 = 9/20 To convert a fraction to a decimal: Divide the numerator by the denominator

Copyright © 2008 Thomson Delmar Learning Rounding Decimals Underline the place to which you want to round Look at the value of the number to the right of this underlined place: If the number is 5 or greater – round up If the number is less than 5 – do not change Then drop all numbers to the right of the underlined value

Copyright © 2008 Thomson Delmar Learning Rounding Decimals Tenths Hundredths Thousandths Rounded to hundredths (two places)

Copyright © 2008 Thomson Delmar Learning Rounding Decimals Tenths Hundredths Rounded to tenths (one place)