Use of deductive methods in pharmaceutical calculations
Let’s practice using reasoning, proportion, and dosage formulas in medication calculations with a few more examples.
Example 8.
The patient has been prescribed a dose of 470 000 IU of penicillin. The concentration of the drug solution you are using is 300 000 IU/ml. How many milliliters of solution will you give the patient?
Calculate the dose to be administered to the patient using both the proportion and the dosage formula and then check the result by reasoning.
Proportion:
Let's solve the comparison by cross-referencing:
1. Multiply the numerator (superscript) of the first ratio by the denominator (subscript) of the second ratio, and also the denominator of the first ratio by the numerator of the second ratio. Both inputs give the same value, resulting in a new equation that is the same as the original equation.
2.Divide the equation by the coefficient of the unknown variable.
The result is 1.5 ml of medicine, because medicine invoices usually round down.
Dosage formula:
The result is therefore, as above, a rounded dose of 1.5 millilitres of medicine. The patient is therefore given 1.5 ml.
Check the result of the calculations by reasoning:
By deduction, the amount of solution to be administered is between 1.5 and 1.6 millilitres. We can therefore be confident of the result.
| | active substance (IU) | solution (ml) |
| in a bottle | 300 000 | 1 |
| given to the patient | 470 000 | x |
| solution (ml) | active substance (IU) |
| 1 | 300 000 |
| 0,5 | 150 000 |
| 1,5 | 450 000 |
| 0,1 | 30 000 |
| 1,6 | 480 000 |
Example 9.
The patient has been prescribed paracetamol 250 mg four times a day. A 24 mg/ml paracetamol solution is available. How many millilitres of solution do you give the patient at a time?
Calculate the single dose for the patient using a dose formula and a ratio:
Dosage formula:
Proportion:
Let's solve the equation:
1. Cross-referencing.
2. Solving the unknown.
This gives a rounded result of a single dose of 10.4 millilitres of medicine.
Check the result of the calculations by reasoning:
The amount of paracetamol solution given to the patient should be between 10 and 11 millilitres, so 10.4 millilitres is a reasonable result.
| | active substance (mg) | solution (ml) |
| in the bottle | 24 | 1 |
| given to the patient | 250 | x |
| solution (ml) | active substance (mg) |
| 1 | 24 |
| 10 | 240 |
| 11 |