Medical Mathematics – Flashcards
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math anxiety
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become nervous when they hear the word "math." They tell themselves that they are not good at math and that they cannot understand mathematical concepts.
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Steps to over coming math anxiety:
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1. admit the fear and to be willing to do something about it. 2. replace negative thoughts with positive ones.
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Examples of mathematics in health care include:
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Calculating medical dosages Reading prescriptions Analyzing test results Weighing and measuring patients Taking temperatures Determining concentration levels Billing and record-keeping
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Numerical Systems
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an organized method of counting.
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most common numerical system
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Hindu-Arabic system. This system uses a set of 10 digits, 0 through 9, to create specific values.
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Roman Numerals
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a numerical system that was developed over 3,000 years ago. This system uses seven letters to express certain values.
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Roman Numerals:
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I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000
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Rules for Roman Numerals
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If a smaller numeral is placed in front of a larger numeral, the smaller numeral is subtracted from the larger numeral. IV = 5 - 1 = 4 IX = 10 - 1 = 9 XC = 100 - 10 = 90 If a smaller numeral is placed behind a larger numeral, the smaller numeral is added to the larger numeral. VI = 5 + 1 = 6 XI = 10 + 1 = 11 CXV = 100 + 10 + 5 = 115 If the same numeral is placed next to itself, the numerals are added together. II = 1 + 1 = 2 XXI = 10 + 10 + 1 = 21 MMV = 1000 + 1000 + 5 = 2005 The same numeral should not be placed next to itself more than three times. IIII does not equal 4. Instead, IV = 4. XXXX does not equal 40. Instead, XL = 40.
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Rules for Subtracting Roman Numerals
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Subtract only powers of 10, such as I (1), X (10), or C (100). Never subtract V (5), L (50), or D (500). VL does not equal 45. Instead, XLV = 40 + 5 = 45. LD does not equal 450. Instead, CDL = 400 + 50 = 450. Subtract only one number from another. IIX does not equal 8. Instead, VIII = 8. LIIV does not equal 53. Instead, LIII = 53. Do not subtract a number from another that is more than 10 times greater. IC does not equal 99. Instead, XCIX = 90 + 9 = 99. XD does not equal 490. Instead, CDXC = 400 + 90 = 490.
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How do you write 17 in Roman numerals?
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XVII
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How do you write 49 in Roman numerals?
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XLIX
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Numbers
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Numbers are the language of mathematics.
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Whole numbers
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the numbers used to count, beginning with 0, 1, 2, 3, and so on.
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Number parts
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may be expressed in one of the following forms: Fractions Decimals Percentages
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Fractions
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represents a part of a whole.
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A fraction is made of two parts:
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The numerator is the top number in the fraction. It shows the actual number of parts. The denominator is the bottom number in the fraction. It tells how many parts it takes to make a whole.
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reminders when working with fractions:
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When adding or subtracting, fractions must have the same denominator. To multiply, first multiply the numerators and then multiply the denominators. To divide, first flip the divisor fraction. Then multiply the numerators and multiply the denominators. After finishing a mathematic function, fractions should always be reduced to lowest terms.
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Decimals
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represents a fraction of a whole number whose denominator is a multiple of 10.
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place values of decimals
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located to the right of the decimal point on a number line. The first place value is tenths, then hundredths, thousandths, and so on.
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The following points are reminders when working with decimals:
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When adding and subtracting, the decimal points must be aligned. When multiplying, multiply the factors without aligning decimal points. Then, count the total number of digits to the right of the decimal points in the factors. Finally, place the decimal point so that the answer includes the number of decimal places that you counted in the factors. When dividing, first move the decimal point of the divisor to the right so that it becomes a whole number. Then, move the decimal point of the dividend the same number of spaces to the right. Divide as usual.
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Percentages
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express a whole or part of a whole. With percentages, the whole is always in terms of 100.
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The following points demonstrate how 20% may be converted.
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To convert 20% to a decimal, drop the percent symbol and move the decimal point two places to the left. 20% is equal to 0.20. Because the zero in the hundredths place holds no value, this decimal can be written as 0.2. To convert 20% to a fraction, first determine the value of the whole. The whole in a percentage is always 100. Therefore, 100 is the denominator of the fraction. 20 is the numerator of the fraction because it tells how much of the pizza was eaten. So 20% is equal to 20/100. When reduced to lowest terms, 20/100 is written as 1/5.
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With percentages, the whole is always in terms of 100. (T or f)
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True
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How would 35% be written as a decimal?
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0.35
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Ratios
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shows a relationship between like values. Ratios ask the question, "How much of X is present when compared to Y?"
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Reducing Ratios
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ratios must also be reduced.
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Reducing Ratios example
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Suppose an emergency room has four unoccupied beds and eight occupied beds. The ratio of unoccupied beds to occupied beds is 4/8 (or 4 : 8). However, the ratio 4/8 is not written correctly because both the numerator and the denominator are divisible by 4. Therefore, the ratio of unoccupied beds to occupied beds should be written as 1/2 (or 1 : 2). In other words, for every one unoccupied bed, there are two occupied beds.
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Solution Strength
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Ratios are often used by health care workers to determine the strength, or concentration, of a solution
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A health care worker is told to mix a solution of ammonia and water in a ratio of 1 : 3. Which of the following demonstrates this ratio?
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1 gallon ammonia, 3 gallons water 10 cups ammonia, 30 cups water 3 liters ammonia, 9 liters water (All of the above)
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Proportions
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an equation that shows equality between two ratios.
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means
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In a proportion, the two middle terms.
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extremes
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The two outer terms.
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To determine if a proportion is equal, follow this rule:
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The product of the means is equal to the product of the extremes. In the proportion 2 : 3 :: 4 : 6, the means are 3 and 4. The extremes are 2 and 6. Because 3 × 4 = 12 and 2 × 6 = 12, the proportion is equal.
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Proportions are often used to solve for an unknown term. Suppose the proportion was written 2 : 3 :: X : 6. X is the unknown term. Follow these steps to solve for X:
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Multiply the means: 3 × X = 3X Multiply the extremes: 2 × 6 = 12 Set up the equation according to the rule: The product of the means is equal to the product of the extremes: 3X = 12 Solve for X by dividing both sides of the equation by the number in front of the X: 3X ÷ 3 = 12 ÷ 3 Identify the solution: X = 4
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Parallel Proportions
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To set up a proportion correctly, the equation must be arranged in the proper order. Consider the following model: A : B :: A : B
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Set Up Parallel Proportions
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Known: 9 tests in 4 hrs Unknown: 36 tests in X hours 9 Tests: 4 hrs : : 36 tests : X hrs Means: 4 x 36 = 144 Extremes: 9 x X = 9X Solve: 9X = 144 9X/9 = 144/9 X = 16 9 Tests : 4 Hrs : : 36 tests : 16 Hrs
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Which of the following proportions is parallel?
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20 mg : 1 tablet :: 100 mg : X tablets
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A doctor can complete 3 examinations in 2 hours. How many examinations can the doctor complete in 5 hours?
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7.5
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To create a dental mold, a dentist must add 45 milliliters of water to 100 grams of plaster. How much water should be added to 250 grams of plaster?
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112.5 ml of water
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You are asked to create a solution that is 3 parts water and 2 parts bleach. You have 4 liters of bleach. How much water should you add?
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6 liters of water
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Estimating
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figuring out an approximate answer, and then judging if the result of the actual calculation seems reasonable. Many estimates involve mental mathematics that allow health care workers to determine when an answer looks out of place.
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Health care workers can use several strategies when estimating:
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rounding and averaging.
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average
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a number that represents a set of numbers.
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What is a mathematical average?
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A number that represents a set of numbers
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A nursing student is budgeting for college. He spent $325.00 on books for the first semester, $460.00 on books for the second semester, and $395.00 for the third semester. How much should he budget for books for the fourth semester? Round to the nearest whole dollar.
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About $393
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Measurement Systems
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the English system, the metric system, and the apothecary system. Each system has its own units of measurement to designate length, volume, and weight.
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The English System
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Is not the most accurate system and is most commonly used in the U.S.
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English System: Length
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In the English system, length is measured in the following units: inch (in) foot (ft) yard (yd) mile (mi)
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English System: Weight
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ounce (oz) pound (lb) ton (tn)
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English System: Volume
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drop (gtt or gt) teaspoon (t or tsp) tablespoon (T or tbsp) ounce (oz) cup (c) pint (pt) quart (qt) gallon (gal)
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27 ounces to pounds and ounces
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1 pound and 11 ounces
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83 ounces to pounds and ounces
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5 pounds and 3 ounces
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3 teaspoons to drops
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180 drops
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10 quarts to gallons and quarts
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2 gallons and 2 quarts
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74 ounces to cups and ounces
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9 cups and 2 ounces
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Metric System
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is more accurate than the English system. In addition, many people find the metric system easier to use than the English system. Most countries outside of the United States use the metric system as the standard for measuring.
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Metric Units
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The metric system has three base units of measurement: Length is measured in meters (m). Weight is measured in grams (g). Volume is measured in liters (L).
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Larger and smaller units are created by adding a prefix. Each prefix represents a value that relates to the base unit. The values are based on multiples of 10.
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Kilo has a value of 1,000. Hecto has a value of 100. Deca has a value of 10. The base unit has a value of 1. Deci has a value of 0.1. Centi has a value of 0.01. Milli has a value of 0.001.
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Metric Relationships
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1 milliliter = 1 cubic centimeter = 1 gram In other words, the amount of liquid in 1 milliliter (mL) is equal to the amount of liquid that can be held in 1 cubic centimeter (cc). In addition, the amount of liquid in 1 milliliter or 1 cubic centimeter weighs 1 gram.
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Which way should you move the decimal point to convert from a larger unit to a smaller unit in the metric system?
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Right
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Apothecary System
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a system that was created in old England to measure weight and volume. It is primarily used by physicians and pharmacists to write medication dosages.
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What is the primary purpose of the apothecary system?
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Writing medical dosages
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Apothecary System: Weight
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In the apothecary system, weight is measured in the following units: grain (gr) dram (dr) ounce (oz) pound (lb)
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Apothecary System: Volume
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Volume is measured in the following units: minim (m) fluidram (fldr) fluidounce (floz) pint (pt) quart (qt) gallon (gal)
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Which of the following is a unit for measuring volume in the apothecary system?
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Fluidram
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In the apothecary system, what does ss stand for?
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1/2
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In the apothecary system, what symbols are used if the dosage is 1 or greater?
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Lower case Roman numerals
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200 grains to drams and grains
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3 drams and 20 grains
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1 pound and 7 ounces to ounces
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19 ounces
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13 drams to grains
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780 grains
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25 drams to ounces and drams
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3 ounces and 1 dram
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3 fluidrams to minims
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180 minims
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7 pints to quarts and pints
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3 quarts and 1 pint
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360 minims to fluidrams
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6 fluidrams
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15 ounces
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oz xv
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4 and ½ drams
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dr ivss
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20 minims
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m xx
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2/3 fluidram
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fldr 2/3
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Nomenclature
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Each system has its own method of naming measurement units.
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27 inches to centimeters
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67.5 cm
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2.5 meters to feet
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8.25 ft
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On a medication label, what is the NDC?
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The national code that identifies the drug
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What caution is written on all prescription medication labels?
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The medication should not be dispensed without a prescription.
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A patient is to receive 2.6 grams of medication. The medication is available in capsules of 325 milligrams. How many capsules should be given?
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8 capsules
