1. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Chapter 5 Mathematics Review and Introduction to Dosage Calculation

2. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Chapter 5 Lesson 5.1 2

3. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Objectives Identify the numerator and the denominator of a fraction. Identify a proper and an improper fraction. Change a whole number into a fraction. Change a mixed number into a fraction. Reduce a fraction to its lowest terms. Calculate the lowest common denominator of a series of fractions. Add two or more fractions and subtract two or more fractions. Multiply two fractions and divide two fractions. 3

4. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Why Do Nurses Need Math? Two of the six “rights” require calculation –Right dose –Right time DIMS test (“does it make sense?”) PINCH drugs –Potassium, insulin, narcotics, chemotherapy and cardiac drugs, and heparin or other anti-clotting drugs 4

5. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Talking About Numbers Figure 5-1. Comparison of part of a number to a whole number. 5

6. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Fractions Fractions are actually division problems –25/100 is the same as 25 ÷ 100 Top number is numerator Bottom number is denominator –Remember NU/DE! Whole numbers can be written as fractions –15 = 15/1 6

7. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Types of Fractions Proper fractions –½, ¾ Improper fractions –11/5, 7/2 Mixed number fractions –1½, 2¾ Reduced fractions –2/4 = ½, 3/9 = 1/3 7

8. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Comparing Fractions If all numerators are 1, smallest denominator = largest fraction If fractions have different numerators and denominators, determine lowest common denominator –Fraction with highest numerator will be the largest 8

9. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Comparing Fractions (cont’d) Figure 5-2. Fraction sizes. 9

10. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Adding and Subtracting Fractions Fractions with common denominators – Simply add/subtract numerators Fractions with different denominators –Convert fractions to lowest common denominator, then add/subtract numerators Reduce to lowest terms Subtraction rare in drug calculation 10

11. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Multiplying Fractions Reduce fractions, if possible Convert all mixed numbers to improper fractions Multiply all numerators –Product is new numerator Multiply all denominators –Product is new denominator Reduce! 11

12. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Dividing Fractions Invert (flip) the second fraction Multiply fractions –Multiply numerators –Multiply denominators Reduce If whole number is involved, change to improper fraction 12

13. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Chapter 5 Lesson 5.2 13

14. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Objectives Identify the divisor and the dividend of a decimal problem. Multiply two decimals and divide two decimals. Change a fraction into a decimal and a decimal into a fraction. Calculate a given percentage of a number. Compare the dose on hand (what you have) with the dose that has been prescribed (what you want). Calculate the number of tablets or amount of liquid drug needed to make the prescribed dose. Convert a set of fractions into a proportion. Solve for “X” (the unknown) in a math problem. 14

15. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Decimals Based on multiples of 10 A decimal divides a whole number and part of a number (fraction) –Whole number (.) tenths, hundredths, thousandths Always include a zero to the left of a decimal less than one Never put an extra zero to the right of a decimal! 15

16. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Adding and Subtracting Decimals Align decimal points Add or subtract as with whole numbers 16

17. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Multiplying Decimals Multiply as with whole numbers Count number of decimal spaces to the right of decimal points in the problem Starting at the far right of the answer, count same number of decimal spaces and place the decimal 17

18. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Dividing Decimals Divisor Dividend Quotient Parts: 18

19. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Dividing Decimals (cont’d) If divisor is whole number, keep decimal in quotient in the same place as dividend If divisor is decimal, convert to whole number Do to the divisor what is done to the dividend Check the math! Multiplying divisor by quotient should equal the dividend! 19

20. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Fractions and Decimals Fraction to decimal: –Divide numerator by denominator –Add 0 to left of decimal point if answer is less than 1 Decimal to fraction: –Keep numbers to left of decimal point as whole numbers –Drop decimal point and place numbers over the place value (e.g., 0.25 = 25/100) –Reduce to lowest terms (e.g., 0.25 = ¼) 20

21. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Rounding Parts of Numbers Liquid doses usually rounded to nearest tenth –Most syringes calibrated in tenths –Answers ending below 0.05 are rounded down –Answers equaling or ending above 0.05 are rounded up Tablets usually rounded to nearest whole –Exception – some tablets can be cut in half! 21

22. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Percents Express number as part of a hundred Used to calculate drug doses and strength of solutions –Example: 5% dextrose in water (D 5 W) 22

23. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Percents and Decimals Convert percent to decimal: –Drop % sign, multiply by 0.01 (or move decimal 2 places left) –Example: 9% = 0.09 Convert decimal to percent: –Add % sign, multiply by 100 (or move decimal 2 places right) –Example 0.05 = 5% 23

24. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Percents and Fractions Percent to fraction: –Convert percent to decimal –Convert decimal to fraction Fraction to percent: –Convert fraction to decimal –Multiply by 100 (or move decimal 2 places right) –Add % sign 24

25. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Percentage of a Number Convert percent to decimal Multiply Problem: 25% of 200 –Convert: 25% = 0.25 –Multiply: 200 × 0.25 = 50 Be careful with decimal points! 25

26. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Introduction to Dosage and Calculation Most drugs dispensed from pharmacy in correct dose Nurse is last check in the system Double-check decimal points and zeros! Label all numbers in calculations Plug numbers into formula, do the math Do the DIMS test! 26

27. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Oral Drugs Formula #1: Dry pill, tablets, etc. = Number of tablets to give Formula #2: Liquid medication × LIQUID = Amount of liquid to give 27

28. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Drugs Given by Injection Three types –Intramuscular (IM) –Subcutaneous –Intradermal (ID) Available in single- or multi-dose packaging Use formula #2, same as other liquid drugs 28

29. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Proportion Equal mathematical relationship between two sets of numbers –Example: ½ = 2/4 –Example: 3 boats/6 sails = 9 boats/18 sails Always label components Right side must be set up in same order as left (e.g., boats “as to” sails on each side) 29

30. Copyright © 2011 by Saunders, an imprint of Elsevier Inc. All rights reserved. Using Proportion to Solve for X Calculate dose using proportion –Order: Give 500 mg of primidone by mouth (orally) –On hand: Primidone 250 mg per 1 caplet –Question: How many caplets equal 500 mg? –Set up problem: 250 mg/1 caplet = 500 mg/ X caplets –Calculate: Cross-multiply and solve for X – 500/250 = X –Answer: 2 caplets 30