MODULE 1: MATH BASICS

Transcription

1 MATH FUNDAMENTALS

2 MODULE 1: MATH BASICS In the medical world, the most beneficial drug can be rendered worthless or dangerous if the veterinarian or animal health technician does not accurately calculate the dose. Many medical professionals can testify, it is not enough to have a superficial understanding of dosage calculation, because superficial knowledge often fails in the crisis situation of an emergency The key to becoming competent in these situations is through routine practice of the concepts we will discuss in these modules.

3 MODULE 1: MATH BASICS Adding/Subtracting with decimal numbers Solve for these questions =? =? =? =? =? =?

4 MODULE 1: MATH BASICS Adding/Subtracting with decimal numbers Answers = = = = = = Make sure that all the decimals line up. Ex

5 MODULE 1: MATH BASICS Multiplying/Dividing with decimal numbers Solve for these questions 5 x 2.5 =? 3.0 x 8.35 =? x =? 1.5 / 2.5 =? 2.5 / 1.5 =? 35 / 0.5 =?

6 MODULE 1: MATH BASICS Multiplying/Dividing with decimal numbers Answers 5 x 2.5 = x 8.35 = x = / 2.5 = / 1.5 = / 0.5 = 70

7 MODULE 1: MATH BASICS Convert the following percentages to decimal numbers. Ex. 25% = 25 = % =? 100% =? 6% =? 0.8% =?

8 MODULE 1: MATH BASICS Convert the following percentages to decimal numbers. 79% = % = 1 6% = % = All percentages should be divided by 100 to produce the same value as a decimal

9 MODULE 1: MATH BASICS Convert the following decimal numbers to percentages. Ex. 0.5 = 0.5 x 100 = 50% 0.45 =? 1.00 =? =? =? =?

10 MODULE 1: MATH BASICS Convert the following decimal numbers to percentages = 45% 1.00 = 100% = 10.3% = 27.1% = 65.13%

11 MODULE 2: SCIENTIFIC NOTATION Look at these four numbers below quickly To reduce the confusion when using very large and very small numbers, decimal numbers are expressed in scientific notation. Scientific notation expresses numerical values as some number multiplied to the power of 10

12 MODULE 2: SCIENTIFIC NOTATION Examples of Positive Scientific Notation 10 = 1 x = 1 x = 2 x = 2.5 x = 2.53 x 10 2 Examples of Negative Scientific Notation 0.2 = 2 x = 2.5 x = 4 x = 4.6 x 10-3

13 MODULE 2: CONVERSIONS Conversions are a key focus in Animal Health Technology. Students must understand how to convert from milligrams to grams, grams to kilograms or kilograms to pounds. These conversions play a key role in calculating drug doses which we will discuss later

14 MODULE 2: CONVERSIONS Converting Celsius to Fahrenheit or Celsius to Kelvin is a component of the mathematics and chemistry courses in Animal Health Technology. Examples 25 C = F 99 F = C 28 C = K 95 F = K

15 ANSWERS Examples 25 C = 77 F 99 F = C 28 C = 82.4 K 95 F = 35 K

16 MODULE 2: CONVERSIONS Converting Pounds (lbs) to Kilograms (kg) is a very common calculation in veterinary medicine. We as people typically know our body weight in pounds but all drugs require an animals weight in kilograms in order to give the correct amount of medical drug. Here is how to convert pounds to kilograms 1kg = 2.2lbs Ex. 15lbs = kg 15lbs / 2.2 = 6.82kg (divide by 2.2 when trying to find kg) Ex. 12kg = lbs 12kg x 2.2 = 26.4lbs (multiply by 2.2 when trying to find lbs)

17 MODULE 2: CONVERSIONS Volumes All units have a scientific notation that correspond to it The standard unit for liquids in Animal Health Technology is the liter Scientific Notation = 10 0 Other units of volume Deciliters = 10-1 Milliliters = 10-3 Microliter = 10-6 Weights All weights that we convert have grams or pounds in their name The standard unit for solids in Animal Health Technology is the gram Scientific Notation = 10 0 Other units of weight Kilogram = 10 3 Milligram = 10-3 Microgram = 10-6

18 LET S REVIEW THE UNITS WE USE IN SCIENCE (SI UNITS AND CONVERSIONS)

19 MODULE 2: CONVERSIONS The calculation always follows the same format Unknown values scientific notation known values scientific notation Ex Micrograms (µg) = milligrams (mg) Micrograms = -6 Milligrams = -3 (-3) (-6) = 3 Answer 10000µg = 10mg (see, three decimal places to the left) A positive value means you move the decimal point that many places to the left If the value was negative you would move the decimal point that many places to the right

20 MODULE 2: CONVERSIONS Therefore when you are asked a question like this Convert: 100.0ml = L ml = 10-3 and L = 10 0 (0) (-3) = 3 You want to know the unknown which is liters so you move the decimal three places to the left because the value is positive. Answer = 0.1L Examples Convert: 0.01g = mg mg = 10-3 and g = 10 0 (-3) (0) = -3 You want to know the unknown which is milligrams so you move the decimal three places to the right because the value is negative. Answer = 10mg

21 MODULE 3: PERCENTAGES In module 1, we learned how to convert percentages from decimal numbers and vice versa. Now we will look at examples of percentages problems commonly seen in the medical field. How many mg (milligrams) is 20% of a 100mg dose? How much of the 200 mg solution is left if 40% is removed? What percentage of 100mg is 20mg? What percentage of 250mg is 100mg? Each of these questions asks something slightly different. The technician s responsibility is to understand what is being asked of them and how they line up their numbers to achieve the correct answer.

22 MODULE 3: PERCENTAGES How many mg (milligrams) is 20% of a 100mg dose? In this question we begin by converting our percentage to a decimal number. 20% = 20/100 = 0.2 Next take the decimal number and multiply it by the value you started with. 0.2 x 100mg = 20mg 20% of a 100mg dose is 20mg

23 MODULE 3: PERCENTAGES How much of the 200 mg solution is left if 40% is removed? This question begins the same as the last, by converting the percentage to a decimal. 40% = 40/100 = 0.4 Multiply this value by the value you started with. 0.4 x 200 = 80mg Now 80mg is 40% of 200mg but we want to know the value if 40% was removed so we calculate as follows mg 80mg = 120mg 120mg is the value that is remaining when 40% of 200mg is removed.

24 MODULE 3: PERCENTAGES What percentage of 100mg is 20mg? This question involves the student having to find the percent. The question is one that has a fractional component. A direct way to answer these questions is to set up a fraction, convert it to a decimal and then convert that decimal into a percentage. Fraction 20mg = mg Then take 0.2 and convert to a percent 0.2 x 100 = 20% By following these three steps you find that 20mg is 20% of 100mg.

25 MODULE 3: PERCENTAGES What percentage of 250mg is 100mg? Fraction 100mg = mg Then take 0.4 and convert to a percent 0.4 x 100 = 40% By following these three steps you find that 100mg is 40% of 250mg.

26 MODULE 4: DRUG DOSE CALCULATIONS Calculating an amount of drug to give a patient involves three steps and you require three important facts 1. The patient s weight 2. The dosage of the drug How much drug you can give per kg or lb of body weight Ex 22mg/kg (for every kilogram of bodyweight the animal should get 22mg of that medical drug) 3. The concentration of the drug How much weight of a drug is in each unit Ex 100mg/ml (for every ml of drug you draw up you are giving 100mg of that medical drug) The important part is that all the units must be the same when calculating a drug dose. The following questions and those in the Practice Questions powerpoint will provide you with different ways a question can be asked.

27 MODULE 4: DRUG DOSE CALCULATIONS Example 1 You have a dog that weighs 10kg and you need to draw up a drug that has a concentration of 10mg/kg and has a concentration of 50mg/ml. How much will you draw up? Step 1: If 10mg are in one kg how many mg are in 10kg x 10kg Step 2: Now you have the amount of mg you need to give (100mg) so what value will you draw up into your syringe. The concentration is 50mg per ml and you need 100mg. Therefore the answer is you would give 2ml of this drug 100mg x 10mg = 1kg = 50mg 1ml = 100mg = 2ml