1. Introduction to Pharmaceutical Calculation

3. Ratio and Proportion "Ratio and Proportion“
- is a key concept in dealing with most pharmaceutical problems. 
Ratio
- is the relationship or comparison of two quantities. A ratio may be expressed as a true ratio or fraction.
The value of a ratio is an abstract number expressing how many times greater or smaller the numerator (top or first term) is than the denominator (bottom or second term).
Ratio
Fraction
Read As
1: 5
1/5
1 is to 5
8: 3
8/3
8 is to 3

4. Ratio and Proportion Proportion
- is the equality of two ratios. It may be written in any of three standard forms.
The two quantities MUST BE of the same unit or type in order to be properly compared as a valid ratio
All colons
Colon with equal sign
Fraction Method
Read As
1:8::2: 5
1:8= 2:5
1/8 = 2/5
1 is to 8 as 2 is to 5
6:10:: 3 : 14
6:10 = 3: 14
6/10 = 3/14
6 is to 10 as 2 is to 5

5. Cross multiplication Cross multiply
- multiply the numerator of the first ratio times the denominator of the second ratio. Then,
-multiply the numerator of the second ratio times the denominator of the first ratio. If the ratios are equal, the results of the cross multiplication will be the same.
Example:
1:2 = 3:6
1 x 6 = 6 and 3 x 2 = 6
The ratios are equal.

6. Unknown factor
If one factor of either ratio is unknown, it may be solved by substituting "X" for the unknown factor in the proportion.
Three of the four variables must be known.
Example : 12: 32::80: X
X = 32 x 80 12
X =

7. 12: 32::80: X
Step 1: Cross Multiply 12 x X = 32 x 80 Step 2: Divide to isolate the X X = 32 x Step 3: Calculate for X X =

8. Sample calculation 7/ X = 5/23 or 7: X :: 5: 23 Cross multiply:
7x 23 :: 5 x X
Isolate X:
X = 7 x 23 5
Calculate
X = 32.2

9. Prescription Problem
Patient Fatima (6 years old, female) was prescribed with Amoxicillin 350 mg suspension to be taken 3 times daily for 7 days. Calculate the amount of medication (in mls) per dose and the total medication needed for 7 days. Available in the pharmacy: Amoxicillin 250mg / 5 mls suspension available in 100mls container.

10. Perform Ratio and Proportion
Step 1 : Calculate the mls (volume) of Amoxicillin suspension needed for 350mg dose. 250mg : 5 mls :: 350 mg : X Step 2: Divide to isolate the X X = 350 mg x 5 mls 250mg Step 3: Calculate X = 7 mls of Amoxicillin 250mg/ 5mls to be given per dose

11. Calculate the Quantity to be dispensed
Quantity per dose x frequency x duration of treatment = 7 mls per dose x 3 times daily x 7 days = 7 x 3 x 7 = 147 mls of Amoxicillin 250mg per 5 mls needed for the duration of treatment = round up to 200 mls or 2 bottles of 100mls

12. Sample Problem
The doctor ordered 200mg of Ranitidine HCl to be injected IM to Rajesh (25 yr old male). You have Ranitidine (50mg/ml) 5 ml ampule in the pharmacy stock. Calculate the amount needed by the patient in mls. Available in Stock: Ranitidine 50 mg per ml x 5 mls = 250mg of Ranitidine per 5 ml ampule. Perform ratio and proportion: 250mg: 5 mls :: 200mg : X X = 250 mg x 5 mls 200 mg X = 4 mls of Ranitidine 50mg/ml to be injected

13. Percentage
Percent means "per one hundred" or "part per one hundred parts."
Percent is expressed in the following manner:
# OF PARTS /100 PARTS
The percentage values on a prescription must be changed to amounts which can be weighed most commonly in grams or measured most commonly in milliliters

14. Volume/Volume Condition
Volume/Volume % or V/V%
- number of milliliters of active ingredient (solute) in every 100 ml of the final solution (solvent).
- V/V% is the percent of volume of active ingredient in the total (final) volume of preparation (v/v) = X ml/100 ml.
- The active ingredient and total preparation are measured in milliliters.

15. Example
A 70% (v/v) alcoholic solution would contain 70 ml of alcohol in every 100 ml of the final solution.
There is 70 ml alcohol and 30 ml of base solution which yields 100 ml final volume of a 70% (v/v) alcoholic solution.

16. Formula
To determine the percentage strength, use ratio and proportion with amounts measured in milliliters. Given % / 100% = Active ingredient in milliliters / Total volume in milliliters

17. Example problem
A solution of 4730 ml (v/v) contains 1.5 pt of methyl salicylate. What is the percentage strength?
Calculation: Convert units if needed and determine factors.
= 1.5 pint x 473 ml = 709.5ml
1 pint
Set up the proportion:
X% :100% ::709.5 ml : 4730 ml

18. Cross multiply: X% x 4730 ml = 709.5 ml x 100%
Divide to isolate the X.
X = 709.5ml x 100%
4730ml
X = 15% is the percentage strength of the solution

19. Weight/Volume Condition
W/V% or Weight/Volume %
- defined as the number of grams of active ingredient in 100 ml of the final solution.
- to determine the percentage strength, use ratio and proportion with amounts measured in grams over milliliters.
Formula
- Given % / 100% = Active ingredient in grams / Total volume in milliliters

20. Sample Calculations X%:100% ::0.625 g:250 ml 2. Cross multiply:
If 250 ml of a solution contains grams of Methyl Salicylate, what is the percentage strength (w/v) of the solution?
1. Set up the proportion:
X%:100% ::0.625 g:250 ml
2. Cross multiply:
X% x 250 ml = g x 100%
3. Divide to isolate the X:
X% = 100% x g
250ml
X = 0.25% is the percentage strength