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Med math · 40 free problems

Med math practice: dosage calculation problems with worked answers

Try all 40 problems with worked answers, no account needed.

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How to round

These exercises use fictional medication labels. Follow the rounding instruction in each question. Keep the full value during your calculation and round only the final answer. Use a zero before a decimal below one, and leave off unnecessary zeros at the end.

Your course may use different rounding instructions. This set does not set a rounding rule for clinical practice.

Practice by category

Quick set: match the units and calculate the amount

Question 1 of 12

Grams to milligrams

A practice label lists 0.48 g of a fictional medication. How many milligrams is that? Use 1 g = 1,000 mg. Give the exact answer in mg; no rounding is needed.

Worked solution and answer

Answer: 480 mg.

0.48 g × (1,000 mg / 1 g) = 480 mg. The grams cancel, leaving milligrams. The number increases because a milligram is a smaller unit than a gram.

Check: 480 mg ÷ 1,000 mg/g = 0.48 g.

If you got 0.00048: You divided by 1,000. Arrange the conversion so grams cancel and mg remains.

Question 2 of 12

Micrograms to milligrams

A practice label lists 650 mcg of a fictional medication. Express that amount in mg. Use 1 mg = 1,000 mcg. Give the exact answer; no rounding is needed.

Worked solution and answer

Answer: 0.65 mg.

650 mcg × (1 mg / 1,000 mcg) = 0.65 mg. Micrograms cancel, leaving mg.

Check: 0.65 mg × 1,000 mcg/mg = 650 mcg.

If you got 650,000: You multiplied by 1,000. Moving from the smaller mcg unit to the larger mg unit makes the number smaller.

Question 3 of 12

Whole tablets

In a fictional medication-math exercise, the amount requested for one dose is 180 mg. Each tablet contains 60 mg. How many whole tablets contain that amount? Give the exact number of tablets; no rounding is needed.

Worked solution and answer

Answer: 3 tablets.

180 mg × (1 tablet / 60 mg) = 3 tablets. The mg units cancel.

Check: 3 tablets × 60 mg/tablet = 180 mg.

If you got one-third of a tablet: The requested amount is greater than the amount in one tablet. Dividing the supplied amount by the requested amount reverses the relationship.

Question 4 of 12

Liquid labeled per 5 mL

A fictional oral-liquid exercise requests 210 mg for one dose. The practice label states 140 mg in 5 mL. What volume contains 210 mg? Give the exact answer in mL; no rounding is needed.

Worked solution and answer

Answer: 7.5 mL.

210 mg × (5 mL / 140 mg) = 7.5 mL. The label gives 140 mg per 5 mL, so keep those two numbers together.

Check: 140 mg ÷ 5 mL = 28 mg/mL; 7.5 mL × 28 mg/mL = 210 mg.

If you got 1.5 mL: 210 ÷ 140 = 1.5 counts portions of the labeled 5 mL volume. Multiply by 5 mL to find the volume.

Question 5 of 12

Round the final liquid volume

A fictional oral-liquid exercise requests 285 mg for one dose. The practice label states 175 mg in 5 mL. Calculate the volume in mL. For this exercise, round the final answer to the nearest tenth of a mL. Do not round intermediate calculations.

Worked solution and answer

Answer: 8.1 mL.

285 mg × (5 mL / 175 mg) = 57/7 mL = 8.142857… mL. Round the final result to 8.1 mL.

Check: The concentration is 35 mg/mL. Before rounding, (57/7 mL) × 35 mg/mL = 285 mg. The rounded result represents 283.5 mg; the small difference comes from the requested rounding. This is an arithmetic exercise, not an assessment of whether that difference is clinically acceptable.

If you got 8 mL: Rounding 285 ÷ 175 to 1.6 before multiplying by 5 changes the final result. Keep full precision until the last step.

Try 7 more: small volumes, weight and time

Question 6 of 12

A volume below 1 mL

A fictional oral-liquid exercise requests 3.7 mg for one dose. Its practice label states 25 mg in 1 mL. Calculate the volume in mL. For this exercise, round the final answer to the nearest hundredth of a mL. Do not round intermediate calculations.

Worked solution and answer

Answer: 0.15 mL.

3.7 mg × (1 mL / 25 mg) = 0.148 mL. The thousandths digit is 8, so the final answer rounds to 0.15 mL.

Check: 0.148 mL × 25 mg/mL = 3.7 mg before rounding. The requested amount is less than the amount in 1 mL, so the calculated volume should be below 1 mL.

If you got 0.1 mL: That is rounding to tenths. This question asks for hundredths. Write the leading zero in 0.15 mL.

Question 7 of 12

Weight conversion using the supplied factor

A practice problem gives a weight of 143 lb. Convert it to kg using the exercise's approximation of 1 kg = 2.2 lb. Give the exact result using that supplied factor; no rounding is needed.

Worked solution and answer

Answer: 65 kg.

143 lb × (1 kg / 2.2 lb) = 65 kg.

Check: 65 kg × 2.2 lb/kg = 143 lb.

If you got 314.6 kg: You multiplied by 2.2. To cancel lb and leave kg, place lb in the denominator of the conversion factor.

Question 8 of 12

An amount specified per dose

A fictional weight-based exercise specifies 12 mg/kg per dose and a weight of 22.5 kg. How many mg does the exercise specify for one dose? Give the exact answer in mg per dose; no rounding is needed. Use only the stated exercise values; this is not a recommended medication regimen.

Worked solution and answer

Answer: 270 mg per dose.

22.5 kg × (12 mg / kg / dose) = 270 mg/dose. The kg units cancel. The question already states an amount per dose.

Check: 270 mg/dose ÷ 22.5 kg = 12 mg/kg/dose.

If you divided by a number of daily doses: No daily total is given here. “Per dose” already describes each dose.

Question 9 of 12

A daily total divided into three doses

A fictional weight-based exercise specifies a total of 18 mg/kg per day, divided into three equal doses per day. The given weight is 31.5 kg. How many mg are in each dose? Give the exact answer in mg per dose; no rounding is needed. This is an arithmetic exercise using a supplied regimen.

Worked solution and answer

Answer: 189 mg per dose.

First find the daily total: 31.5 kg × 18 mg/kg/day = 567 mg/day. Then divide: (567 mg/day) ÷ (3 doses/day) = 189 mg/dose.

Check: 189 mg/dose × 3 doses/day = 567 mg/day; 567 mg/day ÷ 31.5 kg = 18 mg/kg/day.

If you got 567 mg per dose: That is the daily total. The question asks for one of three equal doses.

Question 10 of 12

Volume per hour

In an infusion-math exercise, 750 mL is to run over 6 hours. What is the calculated rate in mL/hour? Give the exact answer; no rounding is needed. Calculate the rate from the supplied values without judging an actual patient's fluid needs.

Worked solution and answer

Answer: 125 mL/hour.

750 mL ÷ 6 hours = 125 mL/hour.

Check: 125 mL/hour × 6 hours = 750 mL.

If you got 4,500: Multiplying volume by time produces mL·hours, not mL/hour. Divide by time to find the amount delivered each hour.

Question 11 of 12

Convert minutes before finding mL/hour

In an infusion-math exercise, 90 mL is to run over 45 minutes. What is the calculated rate in mL/hour? Use 60 minutes = 1 hour. Give the exact answer; no rounding is needed.

Worked solution and answer

Answer: 120 mL/hour.

(90 mL / 45 minutes) × (60 minutes / 1 hour) = 120 mL/hour. Minutes cancel.

Check: 45 minutes = 0.75 hour; 120 mL/hour × 0.75 hour = 90 mL.

If you got 2 mL/hour: 90 ÷ 45 = 2 is the rate in mL/minute. Multiply by 60 to express that rate per hour.

Question 12 of 12

Drops per minute with a stated drop factor

In a gravity-infusion math exercise, 385 mL is to run over 3 hours. The supplied practice tubing label states 20 drops per mL. Calculate drops per minute (gtt/min). Use 60 minutes = 1 hour. Round only the final answer to the nearest whole drop per minute.

Worked solution and answer

Answer: 43 gtt/min.

(385 mL / 3 hours) × (20 drops / 1 mL) × (1 hour / 60 minutes) = 385/9 drops/minute = 42.777… drops/minute. Round to 43 drops/minute.

Check: Using the unrounded rate, (385/9 drops/minute) × 180 minutes ÷ 20 drops/mL = 385 mL. Rounding changes the calculated volume slightly. The drop factor is supplied by this problem; do not assume every tubing set has the same factor.

If you got about 2,567: That is the unrounded rate in drops per hour. Convert hours to minutes before giving gtt/min.

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About these exercises

These are original fictional nursing-math exercises, not actual exam questions or instructions for treating a patient. Finishing this set is not a readiness assessment.

The method follows Open RN’s Nursing Skills chapter on math calculations: identify the requested unit, cancel units, and check the result. Course instructions can differ; the New River Community College dosage study guide is one example of a course-specific rounding policy.

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