3.
Example: <ul><li>xxx = 30 or 10 plus 10 plus 10 </li></ul><ul><li>DC = 600 or 500 plus 100 </li></ul><ul><li>LXVI = 66 or 50 plus 10 plus 5 plus 1 </li></ul><ul><li>When the second of two letters has a value greater than that of the first, the smaller is to be subtracted from the larger. </li></ul>
4.
Adding or Subtracting Fractions <ul><li>When adding or subtracting fractions with unlike denominators, it is necessary to create a common denominator. </li></ul><ul><ul><li>This is like making both fractions into the same kind of “pie.” </li></ul></ul><ul><li>Common denominator is a number that each of the unlike denominators of two or more fractions can be divided evenly. </li></ul>
5.
Guidelines for Finding a Common Denominator <ul><li>Examine each denominator in the given fractions for its divisors, or factors. </li></ul><ul><li>See what factors any of the denominators have in common. </li></ul><ul><li>Form a common denominator by multiplying all the factors that occur in all of the denominators. If a factor occurs more than once, use it the largest number of times it occurs in any denominator. </li></ul>
6.
<ul><li>Whole 0.5 0.05 0.005 0.0005 </li></ul><ul><li>tenths hundredths thousands ten thousands </li></ul><ul><li>(1 place to (2 places to (3 places to (4 places to </li></ul><ul><li>the right) the right) the right) the right) </li></ul>Decimal Places 1000 mg 500 mg 50 mg 5 mg 0.5 mg
8.
Common Metric Conversions <ul><li>kilograms (kg) to grams (g) </li></ul><ul><ul><li>Multiply by 1000 (move decimal point three places to the right). </li></ul></ul><ul><ul><li>Example: 6.25 kg = 6250 g </li></ul></ul><ul><li>grams (g) to milligrams (mg) </li></ul><ul><ul><li>Multiply by 1000 (move decimal point three places to the right). </li></ul></ul><ul><ul><li>Example: 3.56 g = 3560 mg </li></ul></ul><ul><li>milligrams (mg) to grams (g) </li></ul><ul><ul><li>Multiply by 0.001 (move decimal point three places to the left). </li></ul></ul><ul><ul><li>Example: 120 mg = 0.120 g </li></ul></ul>
9.
Common Metric Conversions <ul><li>Liters (L) to milliliters (mL) </li></ul><ul><ul><li>Multiply by 1000 (move decimal point three places to the right). </li></ul></ul><ul><ul><li>Exmaple: 2.5 L = 2500 mL </li></ul></ul><ul><li>Milliliters (mL) to liters (L) </li></ul><ul><ul><li>Multiply by 0.001 (move decimal point three places to the left). </li></ul></ul><ul><ul><li>Example: 238 mL = 0.238 L </li></ul></ul>
10.
Avoirdupois System <ul><li>1 gr (grain) - 65 mg </li></ul><ul><li>1 oz (ounce) - 437.5 gr or 30 g (28.35 g) </li></ul><ul><li>1 lb (pound) - 16 oz or 7000 gr or 1.3 g </li></ul>
12.
Household Measure: Weight <ul><li>1 oz (ounce) - 30 g </li></ul><ul><li>1 lb (pound) - 16 oz (454 g) </li></ul><ul><li>2.2 lb - 1 kg </li></ul>
13.
Numerical Ratios <ul><li>Ratios represent the relationship between: </li></ul><ul><ul><li>two parts of the whole </li></ul></ul><ul><ul><li>one part to the whole </li></ul></ul><ul><li>Written as follows: 1:2 “1 part to 2 parts” ½ </li></ul><ul><li>3:4 “3 parts to 4 parts” ¾ </li></ul><ul><li>Can use “per,” “in,” or “of,” instead of “to” </li></ul><ul><li>Proportions are frequently used to calculate drug doses in the pharmacy. </li></ul><ul><li>Use the ratio-proportion method any time one ratio is complete and the other is missing a component. </li></ul>
14.
Proportions <ul><li>An expression of equality between two ratios. </li></ul><ul><li>Noted by :: or = </li></ul><ul><li>3:4 = 15:20 or 3:4 :: 15:20 </li></ul>
15.
Rules for Ratio-Proportion Method <ul><li>Three of the four amounts must be known </li></ul><ul><li>The numerators must have the same unit of measure </li></ul><ul><li>The denominators must have the same unit of measure </li></ul>
16.
Steps for Solving for X <ul><li>Calculate the proportion by placing the ratios in fraction form so that the x is in the upper-left corner. </li></ul><ul><li>Check that the unit of measurement in the numerators is the same and the unit of measurement in the denominators is the same. </li></ul><ul><li>Solve for x by multiplying both sides of the proportion by the denominator of the ratio containing the unknown, and cancel. </li></ul><ul><li>Check your answer by seeing if the product of the means equals the product of the extremes. </li></ul>
17.
Remember When setting up a proportion to solve a conversion, the units in the numerators must match, and the units in the denominators must match.
19.
Percents <ul><li>The number of parts per 100 can be written as a fraction, a decimal, or a ratio. </li></ul><ul><li>Percent means “per 100” or hundredths. </li></ul><ul><li>Represented by symbol %. </li></ul><ul><ul><li>Usually GRAMS PER 100 ml (solutions) </li></ul></ul><ul><li>30% = 30 parts in total of 100 parts </li></ul><ul><li>30:100, 0.30, or </li></ul>
20.
Percents in the Pharmacy <ul><li>Percent strengths are used to describe IV solutions and topically applied drugs. </li></ul><ul><li>The higher the % of dissolved substances, the greater the strength. </li></ul><ul><li>A 1% solution contains </li></ul><ul><ul><li>1 g of drug per 100 mL of fluid </li></ul></ul><ul><ul><li>Expressed as 1:100, 1/100, or 0.01 </li></ul></ul>
22.
Converting a Ratio to a Percent <ul><li>Designate the first number of the ratio as the numerator and the second number as the denominator. </li></ul><ul><li>Multiply the fraction by 100%, and simplify as needed. </li></ul><ul><li>Multiplying a number or a fraction by 100% does not change the value. </li></ul>
23.
Converting a Ratio to a Percent 5:1 = 5/1 × 100% = 5 × 100% = 500% 1:5 = 1/5 × 100% = 100%/5 = 20% 1:2 = 1/2 × 100% = 100%/2 = 50%
24.
Converting a Percent to a Ratio <ul><li>Change the percent to a fraction by dividing it by 100. </li></ul><ul><li>Reduce the fraction to its lowest terms. </li></ul><ul><li>Express this as a ratio by making the numerator the first number of the ratio and the denominator the second number. </li></ul>
25.
Converting a Percent to a Ratio 2% = 2 ÷ 100 = 2/100 = 1/50 = 1:50 10% = 10 ÷ 100 = 10/100 = 1/10 = 1:10 75% = 75 ÷ 100 = 75/100 = 3/4 = 3:4
26.
Converting a Percent to a Decimal <ul><li>Divide by 100% or insert a decimal point two places to the left of the last number, inserting zeros if necessary. </li></ul><ul><li>Drop the % symbol. </li></ul>
27.
Converting a Decimal to a Percent <ul><li>Multiply by 100% or insert a decimal point two places to the right of the last number, inserting zeros if necessary. </li></ul><ul><li>Add the the % symbol . </li></ul>
29.
Example 4 How many milliliters are there in 1 gal, 12 fl oz? According to the values in Table 5.7, 3840 mL are found in 1 gal. Because 1 fl oz contains 30 mL, you can use the ratio-proportion method to calculate the amount of milliliters in 12 fl oz as follows:
30.
Example 4 How many milliliters are there in 1 gal, 12 fl oz?
31.
Example A solution is to be used to fill hypodermic syringes, each containing 60 mL, and 3 L of the solution is available. How many hypodermic syringes can be filled with the 3 L of solution? 1 L is 1000 mL. The available supply of solution is therefore Determine the number of syringes by using the ratio-proportion method:
32.
Example How many hypodermic syringes can be filled with the 3 L of solution?
33.
Example You are to dispense 300 mL of a liquid preparation. If the dose is 2 tsp, how many doses will there be in the final preparation? Begin solving this problem by converting to a common unit of measure using conversion values.
34.
Example 6 If the dose is 2 tsp, how many doses will there be in the final preparation? Using these converted measurements, the solution can be determined one of two ways: Solution 1: Using the ratio proportion method and the metric system.
35.
Example 6 If the dose is 2 tsp, how many doses will there be in the final preparation?
36.
Example 7 How many grains of acetaminophen should be used in a Rx for 400 mg acetaminophen? Solve this problem by using the ratio-proportion method. The unknown number of grains and the requested number of milligrams go on the left side, and the ratio of 1 gr 65 mg goes on the right side, per Table 5.5.
37.
Example 7 How many grains of acetaminophen should be used in the prescription?
38.
Example 8 A physician wants a patient to be given 0.8 mg of nitroglycerin. On hand are tablets containing nitroglycerin 1/150 gr. How many tablets should the patient be given? Begin solving this problem by determining the number of grains in a dose by setting up a proportion and solving for the unknown.
39.
Example 8 How many tablets should the patient be given?
40.
Common Calculations in the Pharmacy <ul><ul><li>Calculations of Doses </li></ul></ul>Active ingredient (to be administered)/solution (needed) = Active ingredient (available)/solution (available)
41.
Example 9 You have a stock solution that contains 10 mg of active ingredient per 5 mL of solution. The physician orders a dose of 4 mg. How many milliliters of the stock solution will have to be administered?
42.
Example 9 How many milliliters of the stock solution will have to be administered?
43.
Example 10 An order calls for Demerol 75 mg IM q4h prn pain. The supply available is in Demerol 100 mg/mL syringes. How many milliliters will the nurse give for one injection?
44.
Example 10 How many milliliters will the nurse give for one injection?
45.
Example 11 <ul><li>An average adult has a BSA of 1.72 m 2 and requires an adult dose of 12 mg of a given medication. A child </li></ul><ul><li>has a BSA of 0.60 m 2 . </li></ul><ul><li>If the proper dose for pediatric and adult patients is a linear function of the BSA, what is the proper pediatric dose? Round off the final answer. </li></ul>
48.
Example 12 <ul><li>A dry powder antibiotic must be reconstituted for use. The label states that the dry powder occupies 0.5 mL. Using the formula for solving for powder volume, determine the diluent volume (the amount of solvent added). You are given the final volume for three different examples with the same powder volume. </li></ul>
49.
Example 12 Using the formula for solving for powder volume, determine the diluent volume.
50.
Example 12 Using the formula for solving for powder volume, determine the diluent volume.
51.
Example 13 <ul><li>You are to reconstitute 1 g of dry powder. The label states that you are to add 9.3 mL of diluent to make a final solution of 100 mg/mL. What is the powder volume? </li></ul>
52.
Example 13 What is the powder volume? Step 1. Calculate the final volume. The strength of the final solution will be 100 mg/mL .
54.
Example 14 <ul><li>Dexamethasone is available as a 4 mg/mL preparation. An infant is to receive 0.35 mg. Prepare a dilution so that the final concentration is 1 mg/mL. How much diluent will you need if the original product is in a 1 mL vial and you dilute the entire vial? </li></ul>
55.
Example 14 How much diluent will you need if the original product is in a 1 mL vial and you dilute the entire vial?
56.
Example 14 How much diluent will you need if the original product is in a 1 mL vial and you dilute the entire vial?
57.
Example 15 <ul><li>Prepare 250 mL of dextrose 7.5% weight in volume (w/v) using dextrose 5% (D5W) w/v and dextrose 50% (D50W) w/v. How many milliliters of each will be needed? </li></ul>
58.
Example 15 How many milliliters of each will be needed? Step 1. Set up a box arrangement and at the upper-left corner, write the percent of the highest concentration (50%) as a whole number.
59.
Example 15 How many milliliters of each will be needed? Step 2. Subtract the center number from the upper-left number (i.e., the smaller from the larger) and put it at the lower-right corner. Now subtract the lower-left number from the center number (i.e., the smaller from the larger), and put it at the upper-right corner.
60.
Example 15 How many milliliters of each will be needed? 7.5 2.5 mL parts D50W 42.5 mL parts D5W 45 mL total parts D7.5W 50 5
61.
Example 15 How many milliliters of each will be needed?
62.
Example 15 How many milliliters of each will be needed?
63.
Example 15 How many milliliters of each will be needed ?
64.
Example 15 How many milliliters of each will be needed?
65.
Example 15 How many milliliters of each will be needed?
66.
Terms to Remember <ul><li>1. Body surface area </li></ul><ul><li>2. Concentration </li></ul><ul><li>3. Conversions </li></ul><ul><li>4. Denominator </li></ul><ul><li>5. Flow rate </li></ul><ul><li>6. Least common denominator </li></ul><ul><li>7. Milliequivalent (meq) </li></ul><ul><li>8. Nomogram </li></ul><ul><li>9. Numerator </li></ul><ul><li>10. Positional notation </li></ul><ul><li>11. Qs ad </li></ul><ul><li>12. Total parenteral nutrition </li></ul><ul><li>13. Usual and customary (U&C) </li></ul><ul><li>14. Valence </li></ul><ul><li>15. Variable </li></ul>
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