Chapter 3 Pharmacology Math Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc.

Objective 1 Describe military time as it compares to civilian time.

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 1  Military time uses a 24-hour scale without a.m or p.m. designations.  It is similar to civilian time from midnight until noon.  After noon, it increases in 1-hour increments from 12.

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 1  To convert military time to civilian time after noon, subtract 12.  1900 hours becomes 7 p.m.  To convert civilian time to military time after noon, add 12.  1 p.m. becomes 1300 hours.

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 1  Military time is pronounced differently than civilian time.  5 a.m. in civilian time is 0500 military time and pronounced “Oh-five-hundred.”  4:46 p.m. is 1646 military time and pronounced “sixteen forty six hours.”

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 2  Understanding Fractions - A fraction is a number that represents one or more equal parts of a whole. - A fraction is a number that represents one or more equal parts of a whole. - It can be written as a/b or, where b is - It can be written as a/b or, where b is never equal to zero never equal to zero - a is the numerator and b is the denominator a b

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 2  Addition and subtraction of fractions - To add (or subtract) a fraction whose - To add (or subtract) a fraction whose denominators are the same, just add (or subtract) the numerators and keep the same denominator denominators are the same, just add (or subtract) the numerators and keep the same denominator 2/5 + 1/5 = 3/5 2/5 + 1/5 = 3/5

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 2  To add (or subtract) fractions which have different denominators: - Convert the fractions to equivalent fractions with the lowest common denominator - Convert the fractions to equivalent fractions with the lowest common denominator 1/2 + 1/3 = ? 1/2 + 1/3 = ? 1/2= 3/6 and 1/3 = 2/6 1/2= 3/6 and 1/3 = 2/6 - Now add: 3/6 + 2/6 = 5/6 - Now add: 3/6 + 2/6 = 5/6

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 2 To add (or subtract) mixed numbers  Convert the mixed numbers to equivalent improper fractions  Find the lowest common denominator  Add (or subtract) as usual  Note: ALWAYS REDUCE TO LOWEST TERMS

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 2  4 2/ /6 = ?  14/3 + 7/6 = ?  28/6 + 7/6 = 35/6 = 5 5/6

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 2  Multiplication and division of fractions - To multiply two fractions, multiply the numerators together and then multiply the denominators together. - To multiply two fractions, multiply the numerators together and then multiply the denominators together. - The result is the new fraction - The result is the new fraction - Reduce to lowest terms - Reduce to lowest terms

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 2  2/3 x 1/4 = ? 2 x 1 = 2 = 1 2 x 1 = 2 = 1 3 x x

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 3  Understanding Decimals - Decimal numbers are written by placing digits into place value columns that are separated by a decimal point - Decimal numbers are written by placing digits into place value columns that are separated by a decimal point -Place value columns are read in sequence from left to right as multiples of decreasing powers of 10 -Place value columns are read in sequence from left to right as multiples of decreasing powers of 10

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 3 Hundreds tens ones decimal point point652. To the left of the decimal point represents numbers greater than 1

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 3 decimal tenths hundredths thousandths point.345 To the right of the decimal point represents numbers less than 1

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 3  Addition and Subtraction of decimals - Line up the decimal points and carry out the appropriate calculations - Line up the decimal points and carry out the appropriate calculations * * *Note: Adding the zero does not change the value of the number 5.04, yet helps with subtraction

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 3  Multiplication and division of decimals - To multiply, carry out the operation, then add the number of decimal places from the right of the original two numbers. This is the total number of decimal places in the answer - To multiply, carry out the operation, then add the number of decimal places from the right of the original two numbers. This is the total number of decimal places in the answer x 2.1 = x 2.1 = Two places + one place = three places in the answer - Two places + one place = three places in the answer

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 3  To divide, carry out the operation align the decimal point of the answer directly over the dividend (see text).  If the divisor is a decimal, convert it to a whole number first. Remember to move the decimal point of the divisor and that of the dividend the same number of places to the right so as not to change the value of your problem (see text).

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 4 The order of operations:  Parentheses  Exponents  Multiplication  Division  Addition  Subtraction  “Please Excuse My Dear Aunt Sally”

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 5  Understanding percentages - Percents are special fractions which mean “per every hundred” - Percents are special fractions which mean “per every hundred” - The denominator is always understood to be The denominator is always understood to be It can be shown by the symbol % - It can be shown by the symbol % - To write a percentage as a fraction, drop the % and place the number value as the numerator, such as 25% = 25/100 which = 1/4 - To write a percentage as a fraction, drop the % and place the number value as the numerator, such as 25% = 25/100 which = 1/4

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 6 Understanding how to use these operations in order to convert between fractions, decimals, and percents

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 6  To convert fractions to decimals, divide the numerator by the denominator, as 1/4= 1.00 divided by 4 = 0.25 so 1/4 =0.25  To convert decimals to fractions, the decimal number expressed becomes the numerator and the decimal place becomes the denominator, as 0.95 = 95/100

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 6  To find the percent of a number, change the percent to a decimal or fraction, replace the “of” with a times (x) and multiply, as 10% of 100 = 0.10 x 100 = 10 10% of 100 = 0.10 x 100 = 10

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 7  Understanding ratios and proportions - Ratio is a comparison of two numbers - Ratio is a comparison of two numbers a & b expressed as a:b, a/b or a a & b expressed as a:b, a/b or a b - Proportion is a statement of equality between ratios as a:b = c:d, a/b = c/d or a c - Proportion is a statement of equality between ratios as a:b = c:d, a/b = c/d or a c b = d b = d

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 7  Proportions can be used to solve for an unknown term when the other three terms are known. Let x = the unknown and remember that the product of the means equals the product of the extremes  2:3 = X:9 3×X = 2×9 3X = 18 X = 6 X = 6

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 8  Temperature conversions - Celsius (centigrade scale) - Celsius (centigrade scale) - Fahrenheit scale - Fahrenheit scale C = 5/9 (F-32) C = 5/9 (F-32) F = 9/5 C + 32 F = 9/5 C + 32

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 9  Measurement systems - The metric system - The metric system *International system of measurement *International system of measurement *Allows ways to calculate small drug *Allows ways to calculate small drug dosages dosages *In multiples of ten *In multiples of ten *Length = the meter *Length = the meter *Volume = the liter *Volume = the liter *Weight = the gram *Weight = the gram

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 9 The metric system prefixes  micro  milli.001  centi.01  deci.1  unit 1  deka 10  hecto 100  kilo 1000

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 9 Measurement systems  Apothecary system  Used for writing medication orders in ancient Greece and Rome, Europe of the Middle Ages  Based upon everyday items as a grain  Seldom used today

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 9 Measurement systems  Household system  Used in over-the-counter medications and recipes  Less accurate than the metric so not used in the surgical setting  More familiar to the public, so can be used to compare amounts to those in the metric

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 10 Conversions in the metric system  Length 1 m = ? cm 1 m = ? cm Note the prefixes: One centimeter is two decimal places to the right of the unit (meter), so move two places to the right for the answer 1 m = 100 cm Note the prefixes: One centimeter is two decimal places to the right of the unit (meter), so move two places to the right for the answer 1 m = 100 cm 1 cm = ? mm (1 place to the right) 1 cm = ? mm (1 place to the right) 1 cm = 10 mm 1 cm = 10 mm

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 10 Conversions in the metric system  Volume 1L = ? mL 1L = ? mL Note the prefixes: milli (Liter) is three decimal places to the right of the unit, so move three spaces to the right for the answer 1L = 1000 mL Note the prefixes: milli (Liter) is three decimal places to the right of the unit, so move three spaces to the right for the answer 1L = 1000 mL 5000 mL = ? L (three spaces to the left) 5000 mL = 5L

Elsevier items and derived items © 2006 by Saunders, an imprint of Elsevier Inc. Objective 10 Conversions in the metric system  Weight 1 kg = ? g 1 kg = ? g note the prefixes, kilo is three spaces to the left of the unit, so move three spaces to the left 1kg = 1000 g 1 g = ? mg (three spaces to the right) 1 g = 1000 mg 1 g = 1000 mg