Pharmacy Tech Math - Alligation tutorial I

Alligation math is a short-cut often used by pharmacy techs and pharmacy students. You'll want to be able to recognize when and how to use it if studying for the national exam. Outside of pharmacy, it's mostly an obscure method, used as an alternative to standard algebra when calculating the volumes for a mixture made from different strengths of a similar chemical.

alligation grid


Most pharmacy tech students initially refer to alligation as Tic-Tac-toe math, because a simple four line grid is used to organize the factors, which looks just like the popular children's strategy game of the same name.




How to use alligation math

Sample Alligation test question :

An order has arrived for 250mL of 2% solution. You stock solutions of: 1 Gal. of 3% solution and 1 Gal. of 1% solution. You must mix together the two solutions to compound the custom ordered volume.How much of the 3% will you use?


  Based on the question:




→ You need 250mL a 2% solution.

→ You have 1% and 3% solutions.


How to do it - Step #1


Grab a pencil and paper to follow along.


First, Draw a
tic-tac-toe grid




alligation math

Step #2

Higher % strength top left

Desired % Strength in middle


Lower % strength bottom left

alligation grid

Step #3

Calculate the difference between the bottom left number and the middle number going up diagonally.

(Not adding or subtracting them, just finding the difference.)

tic-tac-toe math


Do the same thing from the top left, down.

Again figuring the difference between the numbers.

alligation grid

Step #4  - On next page





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