Dosage calculation practice
Endless pharmacy math problems, each with the work shown. Free, no account.
Alligation
How many grams of 20% ointment do you mix with plain ointment base (0%) to make 120 g of 15%?
Round to the nearest tenth.
Show the worked answer
- Alligation: subtract across the grid. Parts of 20%: 15 − 0 = 15. Parts of 0%: 20 − 15 = 5. Together, 20 parts.
- So 15 of every 20 parts is the 20%.
120 g×15
partsper 20parts=90 g - The other 30 g is the 0%.
Answer: 90 g
One of each, worked
The setups the PTCE asks about, with the conversions it uses.
Days supply
Quantity ÷ what’s used in a day, rounded down.
Sig: 1 tab PO q6h. You dispense 30 tablets. What is the days supply?
Round down to whole days.
Show the worked answer
- q6h is every 6 hours, or 4 doses a day. That’s 4 tablets a day.
- Divide the quantity by what the patient takes in a day.
30
tab×1 day per 4tab=7.5 days - Round down to 7: part of a day isn’t a day’s supply.
Answer: 7 days
mg/kg
Weight in kg × mg/kg = mg; mg ÷ strength = mL.
A child weighs 22 lb. The order is 15 mg/kg per dose, and the suspension is 200 mg/5 mL. How many mL is one dose? (1 kg = 2.2 lb)
Round to the nearest tenth.
Show the worked answer
- Pounds to kilograms, kilograms to mg, mg to mL: each unit cancels the one before it.
22
lb×1kgper 2.2lb×15mgper 1kg×5 mL per 200mg=3.75 mL - 3.75 rounds to 3.8.
Answer: 3.8 mL
IV rates
Volume ÷ time; an order ÷ the bag’s strength.
A bag holds 25,000 units in 250 mL. The order is 1,200 units/hr. What rate do you set, in mL/hr?
Round to the nearest tenth.
Show the worked answer
- Start from the order, then turn units into mL with the bag’s strength.
1,200
unitsper 1 hr×250 mL per 25,000units=12 mL/hr
Answer: 12 mL/hr
Dilutions
C1 × V1 = C2 × V2.
How many mL of a 50% stock solution do you need to make 1,000 mL of a 5% solution?
Round to the nearest tenth.
Show the worked answer
- C1V1 = C2V2, so the stock you measure is V1 = V2 × C2 ÷ C1.
1,000 mL×5
%per 50%=100 mL - Then add diluent up to 1,000 mL: 900 mL.
Answer: 100 mL
Alligation
Parts of each = the distance from the other to the target.
How many grams of 2.5% cream do you mix with plain cream base (0%) to make 90 g of 1.5%?
Round to the nearest tenth.
Show the worked answer
- Alligation: subtract across the grid. Parts of 2.5%: 1.5 − 0 = 1.5. Parts of 0%: 2.5 − 1.5 = 1. Together, 2.5 parts.
- So 1.5 of every 2.5 parts is the 2.5%.
90 g×1.5
partsper 2.5parts=54 g - The other 36 g is the 0%.
Answer: 54 g
Conversions
1 kg = 2.2 lb · 1 tsp = 5 mL · 1 tbsp = 15 mL · 1 fl oz = 30 mL · 1 g = 1,000 mg · 1 mg = 1,000 mcg.
A patient weighs 255 lb. What is that in kg? (1 kg = 2.2 lb)
Round to the nearest tenth.
Show the worked answer
- Put the unit you want on top and the one you have underneath.
255
lb×1 kg per 2.2lb=115.9091 kg - 115.9091 rounds to 115.9.
Answer: 115.9 kg
Learn it in five-minute lessons.
Pharmacy Tech Exam Prep covers sigs, days supply, dilutions and mg/kg dosing for the PTCE. Lesson 1 plays free.
Practice math, not dosing advice. A real dose follows the prescription and your pharmacist.