Chapter 4_mcgee
- 1. Basic Math Review: Preparing for Medication Calculations Chapter 4 Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.
- 2. Preparing for Calculations: Basic Math Review Fractions Common way of showing a number divided into equal portions Numerator Denominator 2/3 2 is the numerator 3 is the denominator 2 is divided by 3 Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.2
- 3. Preparing for Calculations: Basic Math Review (Cont'd) Reducing fractions Find the smallest numbers that can represent the numerator and denominator without changing the fraction’s value. 5/25 = 1/5 Divide both numerator (5) and denominator (25) by 5. 5 divided by 5 = 1 25 divided by 5 = 5 Place the answer obtained from the numerator on top and place the answer obtained from the denominator on bottom. 1/5 Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.3
- 4. Preparing for Calculations: Basic Math Review (Cont'd) Reducing fractions Improper fraction Numerator larger than the denominator = 15/7 Reducing 15/7 = 2 1/7 Divide denominator (7) into numerator (15) = 2 with 1 remaining. Place the remaining number (1) over the denominator (7). Place whole number and fraction together = 2 1/7. Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.4
- 5. Preparing for Calculations: Basic Math Review (Cont'd) Reducing fractions Mixed fraction/mixed number A whole number plus a fraction = 3 1/2 Reducing 3 1/2= 7/2 Multiply the denominator (2) by the whole number (3) and add to the numerator (1) = 7 and place over the denominator (2) = 7/2. Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.5
- 6. Preparing for Calculations: Basic Math Review (Cont'd) Lowest common denominator Lowest number into which all denominators in problem can be evenly divided 3/4, 2/7 = 4, 7 will both go into 28 Then change each fraction to a fraction of the same value with the lowest common denominator. ¾ = divide the lowest common denominator (28) by the denominator (4) = 28/4 = 7 Multiply numerator (3) by the answer (7) = 3 x 7 = 21 Place this answer (21) over the lowest common denominator (28) = 21/28 Figure all the rest of the fractions in the problem 2/7 = 8/28 (28 divided by 7 = 4; then multiple 2 x 4) Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.6
- 7. Preparing for Calculations: Basic Math Review (Cont'd) Adding fractions First find the lowest common denominator. Convert fractions to equivalents. Add the numerators. Put the result over that lowest common denominator. Always remember to reduce your answer fraction to its lowest terms. Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.7
- 8. Preparing for Calculations: Basic Math Review (Cont'd) Subtracting fractions You must have the lowest common denominator for all fractions in the equation. Subtract the second numerator from the first. Place the result over the lowest common denominator. Reduce if possible. Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.8
- 9. Preparing for Calculations: Basic Math Review (Cont'd) Multiplying fractions The answer is called the product. This does not require conversion to the lowest common denominator. Multiply the numerators. Multiply the denominators. Place the product of the numerators over the product of the denominators. Reduce if needed. Canceling Process that can make multiplying fractions easier Reduces each pair of opposite numerators and denominators to their lowest terms Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.9
- 10. Preparing for Calculations: Basic Math Review (Cont'd) Dividing fractions The trick to dividing fractions correctly is inverting the divisor, or the second fraction in the equation. The phrase to remember is “invert and multiply.” Invert the divisor. Multiply the first fraction by the inverted divisor. Reduce as needed. Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.10
- 11. Ratio and Proportion Ratio Another way to represent a fraction: 1/2 = 1:2 Proportion Expression with two ratios separated by two colons: 1:2::3:4 Means 1:2::3:4; Means = 2 and 3 Extremes 1:2::3:4; Extremes = 1 and 4 One of the numbers (one of the means or one of the extremes) in proportion is unknown (x) Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.11
- 12. Ratio and Proportion (Cont'd) Method Multiply the means by each other. Multiply the extremes by each other. Put the product with the x on the left and the other product on the right for the new equation, separated by an equals (=) sign. Divide both sides of the equation by the number associated with x (also called isolating the x). Replace the x in the proportion with its derived value to make sure it is equivalent. Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.12
- 13. Conversions of Units of Measurement Metric system Most commonly used measurement in health care settings Uses decimals rather than fractions Must memorize Household measurements Apothecary measurements Old system To calculate conversions, can use the ratio and proportion method Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.13
- 14. Methods of Dosage Calculations Ratio and proportion method Set up the proportion. The prescription and unknown comprise the first ratio. The medication on hand is the second ratio. Multiply the means by each other. Multiply the extremes by each other. Place the product with the x on the left and the other product on the right for the new equation, separated by an equals (=) sign. Divide both sides of the equation by the number associated with x (also called isolating the x). Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.14
- 15. Methods of Dosage Calculations (Cont'd) Formula method Formula 1 for tablets/capsules: D/A Q = x “The desired, or ordered, dose (D) over the medication available (A) times the quantity (Q) of the available dose equals the amount to give, or x” Formula 2 for liquids: D/H V = x This formula is read as: “The desired dose (D) over the medication on hand (H) times the volume (V) of the available dose equals x” The units of the ordered dose and the on-hand or available dose must match before you try to calculate the dose; otherwise, you will make a critical calculation error. Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.15
- 16. Dimensional Analysis (Factor Labeling) Method This is useful for more complex calculations. It simplifies the process of converting between household and metric systems, as well as within the metric system. Dimensional analysis (DA) is an organized method. All factors are labeled, and the factors involved are related to each other. Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.16
- 17. Dimensional Analysis (Factor Labeling) Method (Cont'd) Method Step 1. Identify the beginning point of the calculation (usually the physician/prescriber’s order). Step 2. Identify the ending point (the label for the specific dosage you seek). Step 3. Include all other factors needed (conversion factors, strength/form of the medication that will be administered, patient weight, IV tubing drop factor, etc.) in your problem pathway. Note: Set up the problem so that “unwanted” labels are cancelled from the problem. Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.17
- 18. Basic Dosage Calculations Using Dimensional Analysis Basic calculations Step A: What did the prescriber order? Step B: What is the available form of the medication to be given/the label of the final answer? Step C: What is the strength (concentration) of the medication on hand? Step D: Conversion factor(s) needed May or may not have to use Step E: What is the problem pathway? Step F: Solve. Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.18
- 19. Basic Dosage Calculations Using Dimensional Analysis Question 1 Prescribed: Atropine 0.2 mg. The ampule is labeled gr 1/150 mL. How much should the nurse give? 1. 0.013 mL 2. 0.5 mL 3. 1 mL 4. 2 mL Copyright © 2014, 2009 by Mosby, Inc., an imprint of Elsevier Inc.19
- 20. ANSWER ANSWER AND RATIONALE: 2. 0.5 mL. First must change gr to mg. 60 mg = 1 gr, so 1/150 gr = 0.4 mg (60/150 = 0.4). Ratio and Proportion: 0.2:x::0.4:1; multiply the extremes (0.2 × 1 = 0.2); then multiply means (x × 0.4 = 0.4x); then divide both sides by 0.4 to isolate the x. 0.2/0.4 = 0.5 Formula: 0.2/0.4 × 1 mL = 0.5 mL Dimensional analysis: 0.2 mg x 1 gr x 1 mL = 0.2 = 0.5 mL 1 60 mg 1/150 gr 0.4 2009 by Mosby, Inc., an imprint of Elsevier Inc. 20