Chapter 4

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