1. 20
Alligations

2. State Standard
22) Calculate correct doses required when given a simulated prescription for a pediatric dose, adult dose, and geriatric dose based on weight (if applicable), length of administration, times per day of administration, and presence of other diseases/disorders.**

3. Objectives Students will be able to…
Identify when to use Alligations calculations
Calculate dosages using Alligations.

4. Alligations
Principle relating to the solution of questions concerning the compounding or mixing of different ingredients
Used when mixing two products with different percent strengths of the same active ingredient
Strength of final product falls between the strengths of each original product.

5. Solving Alligations
Determine how many parts of the same product, with different strengths, you need to create the final strength requested.
Calculate exactly how many milliliters or grams you need of each constituent (beginning) product.

6. Solving Alligations Critical points
Solvents and diluents, such as water, vanishing cream base, and white petrolatum, are considered to be a percent strength of zero.
Liquids, including solutions, syrups, elixirs, and even lotions, are expressed in milliliters.

7. Solving Alligations Critical points
Solids, including powders, creams, and ointments, are expressed in grams.
The alligation formula requires that you express the strength as a percentage when setting up the problem. You must convert any ratio strength in the initial question to a percent strength.

8. Solving Alligations Critical points
When writing percents or using decimals, always use a leading zero (e.g., 0.25%). This helps prevent errors in interpretation. It would be a terrible error—possibly even fatal—to dispense something in 25% strength that was really supposed to be 0.25% strength.

9. Solving Alligations Critical points
1 fl. oz = mL (commonly rounded to 30 mL)
1 avoirdupois oz. = g (used for solids, commonly rounded to 30 g)

10. Solving Alligations The Alligation Grid "Tic-tac-toe board"
Tool to easily solve pharmacy alligation problems
You will need to know:
Higher strength: top left box
Lower strength: bottom left box
Desired strength: center box
Desired quantity

11. Figure 20-1 The alligation grid.

12. Solving Alligations The Alligation Grid
To calculate the number for the top and bottom right boxes, work diagonally and take the difference between the two numbers already in place
Only positive numbers are used in the alligation grid (remove minus sign from any negative numbers)
The procedure is the same for weights or volumes

13. Fill in the Alligation Grid

14. Calculate the Numbers

15. Solving Alligations The Alligation Grid
Subtract the center number from the top left number to find the bottom right number

16. Calculate the Numbers

17. Calculate the Numbers

18. Solving Alligations The Alligation Grid
Subtract the center number from the bottom left number to find the top right number

19. Calculate the Numbers

20. Calculate the Numbers

21. Solving Alligations The Alligation Grid
The numbers on the right-hand side represent the number of parts per ingredient, when read straight across.
Add the numbers in the right column to determine the total number of parts necessary

22. Calculate the Numbers

23. Calculate the Numbers

24. Solving Alligations Set up this proportion. parts needed total parts
For a 2.5% ointment
1 part/1.5 parts or 1/1.5
For a 1% ointment
0.5 parts/1.5 parts or 0.5/1.15

25. Solving Alligations
Multiply the proportion of parts needed of each ointment by the desired quantity to determine the quantity of each needed.
Example
2.5% ointment: 120 g/1.5 × 1 = 80 g
1% ointment: 120 g/1.5 × 0.5 = 40 g

26. Summary
In certain situations, a pharmacy must use the alligation method to combine two varying strengths of a drug, or combine a drug with a base or diluent, to achieve the prescribed strength.
Once you master the alligation grid, the calculations can be performed easily.

27. Activity Complete drug cards for the following…
Dexlansoprazole (Dexilant)
Glyburide (Diabeta)
Olanzapine (Zyprexa)
Individually complete the provided Alligations Activity.