Review of mathematical principles Jennifer Kean MSN,RN,CCRN

Arabic numerals Number system we are most familiar with Includes fractions, decimals, and whole numbers Examples include numbers 1,2,3 etc.

The roman system Each symbol represents a number I =1 V=5 X=10 L= 50 C=100 D=500 M=1000

Basic rules of roman numerals 1. Whenever a Roman numeral is repeated or a smaller Roman numeral follows a larger number, the values are added together For example: VIII (5+1+1+1=8) 2. Whenever a smaller Roman numeral appears before a larger Roman numeral, the smaller number is subtracted For example: IX (1 subtracted from 10=9)

Basic rules of roman numerals 3. The same numeral is never repeated more than three times in a sequence For example: I,II,II,IV 4. Whenever a smaller Roman numeral comes between two larger Roman numerals, subtract the smaller number from the numeral following it For example: XIX= 10+ (10-1)= 19

Examples VII represents 5+2=7 XII represents 10+2=12 XXV represents 20+5=25 XXXVII represents 30+5+2=37

Examples XL represents 50-10=40 CM represents 1000-100=900 CD represents 500-100=400 IV represents 5-1=4

Examples XIV represents 10+(5-1)=14 XXIV represents 20+(5-1)=24

Fractions One or more equal parts of a unit Part over whole, separated by a line 3 parts of 4= ¾ 3 is the top number, 4 is the bottom number The “numerator”, or top number, identifies how many parts of the whole are discussed The “denominator”, or bottom number, identifies how many equal parts are in the whole

Fractions Fractions may be raised to higher terms by multiplying the numerator and denominator by the same number ¾ x 3/3 = 9/12 Fractions can be reduced to lowest terms by dividing the numerator and denominator by the same number 9/12 divided by 3/3= ¾ A fraction is easiest to work with when it is expressed in its lowest terms

Adding fractions You must find the common denominator first Example: 1/3 +1/5 (multiply the 2 denominators) The common denominator is 15 1/3…(3 into 15 =5) so 1/3=5/15 1/5…(5 into 15= 3) so 1/5 =3/15 5/15 + 3/15 = 8/15 Are you able to reduce this fraction to its lowest terms?

Fractions Proper fraction: the numerator is smaller than the denominator For example: ¾ is a proper fraction (3 is less than 4) Improper fraction: the numerator is larger than the denominator For example: 8/6 is an improper fraction (8 is greater than 6) Mixed number: whole number is combined with a proper fraction For example: 1 2/3 is a mixed number

Question The number 9 5/8 is a (n): Proper fraction Improper fraction Mixed number Complex fraction

Fractions Multiplying fractions: multiply the numerators together and the denominators together For example: 2/4 x 3/9 = 2x3 (6)/ 4x9 (36) = 6/36 TIP: it is easier to reduce fractions to their lowest terms before multiplying Therefore, ½ x 1/3 = 1/6 6/36 reduced to lowest terms = 1/6

Fractions To divide two fractions, invert ( turn upside down) the fraction that is the divisor and then multiply For example: ¾ divided by ½= ¾ x 2/1 =3 x 2/4 or 6/4 6/4 can be reduced to 3/2 or 1 ½

Decimal fractions (less than 1) To the left of the decimal, numbers are whole numbers To the right of a decimal, numbers are fractions of a whole in denominations of 10 Tenths, hundredths, thousandths… the th is cueing you that the value is less than 10 Think money when you use decimals! To add or subtract decimals, line up the decimal points and do the math This is just like managing your checkbook (assuming you do so!)

Decimals All fractions can be converted to decimal fractions by dividing the numerator into the denominator For example: ¾ = 3 divided by 4 = 0.75 To add two decimal fractions, first line up the decimal points For example: 0.345 + 2.456 = 2.801 To subtract two decimal fractions, first line up the decimal points 1.6 – 0.567 = 1.033

Decimals Multiplying decimals 1.467 (3 decimal places) x 0.234 = 0. 343278 (6 decimal places in answer) Make sure the number of decimal places equals the number of decimal places in the two numbers added together

Decimals To divide two decimals, first move the decimal point in the divisor enough places to the right to make it a whole number 6 divided by 0.23 (the decimal point must be moved two places to the right to change 0.23 into “23”) 600 divided by 23 = 26.09 (rounded)

Ratios and percents A ratio is a way of expressing the relationship of one number to another or expressing a part of a whole number The relationship is reflected by separating the numbers with a colon (e.g., 2:1) Percent means parts per hundred; can be written as a fraction or a decimal

Proportions A way of expressing the relationship over two ratios The two ratios are separated by a double colon (::) which means “as” If three variables are known, the fourth can be determined When solving for “x”, the numerators must be the same measurement and the denominators the same measurement The numerators and denominators in the proportion must be written in the same units of measurement

Examples ½:: 3/6 or 1:2 :: 3:6 – these two expressions mean the same thing Some people work better with fractions Others work better with linear aspects Let’s see which you prefer

The Apothecary system Expressed in grains (gr), drams, minims, fluidrams, ounces, fluidounces 1 dram = 60 grains 1 fluidram = 60 minims 1 ounce = 480 grains 1 minim = 1 grain 1 pint = 16 fluidounces 1 quart = 2 pints 1 gallon = 4 quarts

Household measures 1 teaspoon = 60 drops (gtts) 1 tablespoon = 3 teaspoons 1 ounce = 2 tablespoons 1 glassful (cup) = 8 ounces 1 ounce = 6 teaspoons 1 ounce = 360 gtts

Approximate equivalents 1 ml = 15 or 16 minims = 15 gtts 4 ml = 1 dram = 60 gtt 15 ml = 4 drams = 1 tablespoon (T) 30 ml = 2 T 500 ml = 1 pint (pt) 1000 ml = 1 quart (qt)

Approximate equivalents 60 mg = 1 gr 1000 mg = 15 gr 4 g = 1 dram

IV fluids To determine gtts/minute: Need gtts/ml of given set Number of gtts/min = gtt/min= gtt/ml of given set ____________________ x total hourly volume 60 (number of minutes in 1 hour)

For example: Ampicillin 50 mg in 50 ml D5W/ hour Available set yields 10 gtt/ml Nurse must determine gtts/minute gtt/min= 10 500 --------- X 50 = ---------- = 8.33 60 60 Regulate the drip to 8 gtts/min

To determine ml/hr To give 1000 ml over 12 hours, divide 12 into 1000 You now know the ml/hr rate, so you can determine the gtts/minute rate

For example: To give 1000 ml over 8 hours: ------------ = 125 8 Give 125 ml/hr Usually, the nurse will be working with an IV pump which will determine the flow rates; however, on occasion it may still be necessary to calculate ml/hr or gtts/min, so it is important to know this information