Why Math Is Critical on the HESI A2
The Mathematics section of the HESI A2 exam contains approximately 55 questions and is one of the most heavily weighted sections. Strong math skills aren't just important for passing the exam—they're essential for nursing practice. From calculating medication dosages to converting between measurement systems, nurses use math daily to ensure patient safety.
The good news? The HESI A2 math section doesn't require calculus or advanced algebra. It focuses on practical arithmetic skills that you can master with targeted practice. This comprehensive practice test covers every major topic you'll encounter on exam day.
How to Use This Practice Test
Follow these guidelines for maximum benefit:
- No calculator — The actual HESI A2 provides a basic on-screen calculator, but practicing without one strengthens your mental math
- Show your work — Write out each step so you can identify where mistakes occur
- Time yourself — Aim for about 1 minute per question to build test-day pacing
- Review all explanations — The step-by-step solutions teach problem-solving strategies
Section 1: Fractions & Decimals (Questions 1–10)
Question 1
Simplify: 3/4 + 2/3
- A) 5/7
- B) 17/12
- C) 5/12
- D) 1 5/12
Answer: B) 17/12 (or equivalently D) 1 5/12)
Explanation: To add fractions with different denominators, find the least common denominator (LCD). The LCD of 4 and 3 is 12. Convert: 3/4 = 9/12 and 2/3 = 8/12. Add: 9/12 + 8/12 = 17/12 = 1 5/12. Both B and D are equivalent, but on the HESI A2, choose the answer format that matches the options given.
Question 2
What is 5/8 × 2/5?
- A) 7/13
- B) 10/40
- C) 1/4
- D) 2/8
Answer: C) 1/4
Explanation: To multiply fractions, multiply numerators and denominators: (5×2)/(8×5) = 10/40. Then simplify by dividing both by the greatest common factor (10): 10/40 = 1/4. Tip: You can cross-cancel before multiplying—cancel the 5 in the numerator and denominator to get 1/8 × 2/1 = 2/8 = 1/4.
Question 3
Divide: 7/8 ÷ 1/4
- A) 7/32
- B) 7/2
- C) 2/7
- D) 3 1/2
Answer: D) 3 1/2
Explanation: To divide fractions, multiply by the reciprocal of the divisor: 7/8 ÷ 1/4 = 7/8 × 4/1 = 28/8 = 7/2 = 3 1/2. Remember: "Keep, Change, Flip"—keep the first fraction, change division to multiplication, and flip the second fraction.
Question 4
Convert 0.375 to a fraction in lowest terms.
- A) 375/1000
- B) 3/8
- C) 37/100
- D) 15/40
Answer: B) 3/8
Explanation: 0.375 = 375/1000. Find the GCF of 375 and 1000, which is 125. Divide both by 125: 375÷125 = 3, 1000÷125 = 8. So 0.375 = 3/8. Quick check: 3÷8 = 0.375 ✓
Question 5
Which fraction is equivalent to 0.6̄ (0.666...)?
- A) 3/5
- B) 6/10
- C) 2/3
- D) 5/8
Answer: C) 2/3
Explanation: The repeating decimal 0.666... equals 2/3. You can verify: 2 ÷ 3 = 0.666... Common repeating decimal conversions to memorize: 1/3 = 0.333..., 2/3 = 0.666..., 1/6 = 0.1666..., 5/6 = 0.8333..., 1/9 = 0.111...
Question 6
Subtract: 4.205 − 1.78
- A) 2.425
- B) 2.325
- C) 3.425
- D) 2.025
Answer: A) 2.425
Explanation: Line up decimal points and subtract: 4.205 − 1.780 = 2.425. Adding a trailing zero to 1.78 (making it 1.780) helps align the columns correctly. Always line up decimal points when adding or subtracting decimals.
Question 7
Arrange from least to greatest: 3/5, 0.55, 7/12
- A) 0.55, 3/5, 7/12
- B) 0.55, 7/12, 3/5
- C) 7/12, 3/5, 0.55
- D) 3/5, 7/12, 0.55
Answer: B) 0.55, 7/12, 3/5
Explanation: Convert all to decimals: 3/5 = 0.600, 0.55 = 0.550, 7/12 = 0.583. From least to greatest: 0.550, 0.583, 0.600 → 0.55, 7/12, 3/5. Converting to a common format (all decimals or all fractions) is the fastest way to compare.
Question 8
What is 2 3/4 expressed as an improper fraction?
- A) 8/4
- B) 11/4
- C) 9/4
- D) 23/4
Answer: B) 11/4
Explanation: To convert a mixed number to an improper fraction: multiply the whole number by the denominator and add the numerator. (2 × 4) + 3 = 8 + 3 = 11. Keep the same denominator: 11/4. This conversion is essential for performing calculations with mixed numbers.
Question 9
Round 14.6738 to the nearest hundredth.
- A) 14.67
- B) 14.68
- C) 14.674
- D) 14.70
Answer: A) 14.67
Explanation: The hundredths place is the second digit after the decimal (7 in 14.6738). Look at the next digit (3): since 3 < 5, round down. So 14.6738 rounds to 14.67. Rounding rules: digits 0–4 round down, digits 5–9 round up.
Question 10
What is 3/4 of 48?
- A) 32
- B) 36
- C) 40
- D) 64
Answer: B) 36
Explanation: "Of" in math means multiply: 3/4 × 48 = (3 × 48)/4 = 144/4 = 36. Shortcut: divide 48 by 4 first (= 12), then multiply by 3 (= 36). This type of calculation is common in dosage problems.
Section 2: Percentages & Ratios (Questions 11–20)
Question 11
Convert 7/20 to a percentage.
- A) 70%
- B) 35%
- C) 14%
- D) 28%
Answer: B) 35%
Explanation: To convert a fraction to a percentage, divide and multiply by 100: 7 ÷ 20 = 0.35 × 100 = 35%. Alternative method: since 20 × 5 = 100, multiply both parts by 5: 7/20 = 35/100 = 35%.
Question 12
A patient's weight dropped from 180 lbs to 171 lbs. What is the percentage decrease?
- A) 9%
- B) 5%
- C) 5.3%
- D) 10%
Answer: B) 5%
Explanation: Percentage change = (change ÷ original) × 100. Change: 180 − 171 = 9 lbs. Percentage: (9 ÷ 180) × 100 = 5%. Always divide by the original value, not the new value, when calculating percentage change.
Question 13
Express the ratio 15:25 in simplest form.
- A) 3:5
- B) 1:2
- C) 5:3
- D) 15:25
Answer: A) 3:5
Explanation: To simplify a ratio, divide both numbers by their greatest common factor (GCF). The GCF of 15 and 25 is 5. 15÷5 = 3, 25÷5 = 5. So 15:25 = 3:5. Simplifying ratios uses the same process as simplifying fractions.
Question 14
If 40% of a number is 60, what is the number?
- A) 24
- B) 100
- C) 150
- D) 240
Answer: C) 150
Explanation: Set up the equation: 0.40 × x = 60. Solve: x = 60 ÷ 0.40 = 150. Check: 40% of 150 = 0.40 × 150 = 60 ✓. This type of "working backwards" from a percentage is common on the HESI A2.
Question 15
A nurse works 36 hours per week. If she spends 25% of her time on documentation, how many hours is that?
- A) 7 hours
- B) 9 hours
- C) 12 hours
- D) 6 hours
Answer: B) 9 hours
Explanation: 25% of 36 = 0.25 × 36 = 9 hours. Quick shortcut: 25% = 1/4, and 36 ÷ 4 = 9. Knowing common percentage-fraction equivalents saves time: 25% = 1/4, 50% = 1/2, 75% = 3/4, 10% = 1/10, 20% = 1/5.
Question 16
In a group of 200 patients, the ratio of male to female is 3:5. How many female patients are there?
- A) 75
- B) 100
- C) 120
- D) 125
Answer: D) 125
Explanation: Total ratio parts = 3 + 5 = 8. Each part represents 200 ÷ 8 = 25 patients. Female patients = 5 × 25 = 125. Check: male = 3 × 25 = 75, total = 75 + 125 = 200 ✓. Ratio problems require you to find the value of one "part" first.
Question 17
Convert 0.045 to a percentage.
- A) 45%
- B) 0.45%
- C) 4.5%
- D) 0.045%
Answer: C) 4.5%
Explanation: To convert a decimal to a percentage, multiply by 100 (move the decimal point two places to the right): 0.045 × 100 = 4.5%. A common mistake is moving the decimal the wrong number of places.
Question 18
A medication is available in a 250 mg/5 mL concentration. What is the ratio strength expressed as mg per 1 mL?
- A) 25 mg/mL
- B) 50 mg/mL
- C) 125 mg/mL
- D) 1250 mg/mL
Answer: B) 50 mg/mL
Explanation: Divide both parts by 5: 250 mg ÷ 5 = 50 mg, 5 mL ÷ 5 = 1 mL. The concentration is 50 mg per 1 mL. Understanding concentration calculations is a foundational skill for safe medication administration.
Question 19
What is 15% of 240?
- A) 36
- B) 30
- C) 24
- D) 42
Answer: A) 36
Explanation: 15% of 240 = 0.15 × 240 = 36. Quick method: 10% of 240 = 24, plus 5% of 240 = 12. Total: 24 + 12 = 36. Breaking percentages into easier parts (10% + 5%) is a useful mental math strategy.
Question 20
A solution is 2% saline. How many grams of salt are in 500 mL of this solution?
- A) 2 g
- B) 5 g
- C) 10 g
- D) 100 g
Answer: C) 10 g
Explanation: A 2% solution means 2 grams per 100 mL. For 500 mL: (2/100) × 500 = 10 grams. In healthcare, percentage solutions indicate grams of solute per 100 mL of solution. Normal saline (0.9% NaCl) contains 0.9 g of salt per 100 mL.
Section 3: Unit Conversions & Dosage Calculations (Questions 21–35)
Question 21
Convert 2.5 liters to milliliters.
- A) 250 mL
- B) 2,500 mL
- C) 25 mL
- D) 25,000 mL
Answer: B) 2,500 mL
Explanation: 1 liter = 1,000 milliliters. Multiply: 2.5 × 1,000 = 2,500 mL. When converting from a larger unit to a smaller unit, you multiply. The metric system uses powers of 10, making conversions straightforward.
Question 22
How many kilograms is a 154-pound patient?
- A) 70 kg
- B) 77 kg
- C) 339 kg
- D) 56 kg
Answer: A) 70 kg
Explanation: To convert pounds to kilograms, divide by 2.2: 154 ÷ 2.2 = 70 kg. This is one of the most important nursing conversions because medication dosages are often calculated per kilogram of body weight. Memorize: 1 kg = 2.2 lbs.
Question 23
Convert 98.6°F to Celsius.
- A) 35°C
- B) 37°C
- C) 39°C
- D) 42°C
Answer: B) 37°C
Explanation: °C = (°F − 32) × 5/9 = (98.6 − 32) × 5/9 = 66.6 × 5/9 = 37°C. Normal body temperature is 98.6°F = 37°C. This conversion is essential for healthcare professionals who may encounter either temperature scale.
Question 24
A doctor orders 500 mg of medication. The available tablets are 250 mg each. How many tablets should be administered?
- A) 1 tablet
- B) 1.5 tablets
- C) 2 tablets
- D) 4 tablets
Answer: C) 2 tablets
Explanation: Desired dose ÷ Available dose = Number of tablets. 500 mg ÷ 250 mg = 2 tablets. This is the most basic dosage calculation formula: D/H × Q (Desired dose / Have on hand × Quantity). Always double-check that your answer makes clinical sense.
Question 25
Convert 3 cups to milliliters. (1 cup = 240 mL)
- A) 480 mL
- B) 600 mL
- C) 720 mL
- D) 960 mL
Answer: C) 720 mL
Explanation: 3 cups × 240 mL/cup = 720 mL. Household-to-metric conversions are commonly tested on the HESI A2. Key conversions: 1 cup = 240 mL, 1 tablespoon = 15 mL, 1 teaspoon = 5 mL, 1 ounce = 30 mL.
Question 26
A patient needs 0.5 g of amoxicillin. The liquid form is 250 mg/5 mL. How many mL should be given?
- A) 5 mL
- B) 10 mL
- C) 2.5 mL
- D) 15 mL
Answer: B) 10 mL
Explanation: First convert grams to milligrams: 0.5 g = 500 mg. Then use D/H × Q: (500 mg / 250 mg) × 5 mL = 2 × 5 = 10 mL. Always ensure units match before calculating. Converting between grams and milligrams (1 g = 1,000 mg) is a critical step in medication calculations.
Question 27
How many inches are in 5 feet?
- A) 50 inches
- B) 55 inches
- C) 60 inches
- D) 72 inches
Answer: C) 60 inches
Explanation: 1 foot = 12 inches. 5 × 12 = 60 inches. This basic conversion is needed for height measurements and BMI calculations. Other important length conversions: 1 inch = 2.54 cm, 1 meter = 100 cm.
Question 28
A medication requires a dosage of 5 mg/kg/day. For a 70 kg patient, what is the daily dose?
- A) 35 mg
- B) 70 mg
- C) 350 mg
- D) 500 mg
Answer: C) 350 mg
Explanation: Multiply: 5 mg/kg/day × 70 kg = 350 mg/day. Weight-based dosing is extremely common in nursing, especially in pediatrics and critical care. Always verify the patient's current weight before calculating weight-based doses.
Question 29
Convert 1,500 milligrams to grams.
- A) 0.15 g
- B) 1.5 g
- C) 15 g
- D) 150 g
Answer: B) 1.5 g
Explanation: 1 gram = 1,000 milligrams. To convert mg to g, divide by 1,000: 1,500 ÷ 1,000 = 1.5 g. When converting from smaller units to larger units, divide. Metric prefix pattern: kilo (1,000), base unit, milli (1/1,000), micro (1/1,000,000).
Question 30
An IV is running at 125 mL/hour. How many mL will be infused over 8 hours?
- A) 500 mL
- B) 750 mL
- C) 1,000 mL
- D) 1,500 mL
Answer: C) 1,000 mL
Explanation: Total volume = Rate × Time = 125 mL/hour × 8 hours = 1,000 mL (or 1 liter). IV calculations are among the most practical math skills you'll use as a nurse. Understanding rate × time = volume is the foundation for IV management.
Question 31
A child weighs 44 pounds. What is their weight in kilograms?
- A) 18 kg
- B) 20 kg
- C) 22 kg
- D) 97 kg
Answer: B) 20 kg
Explanation: Divide pounds by 2.2: 44 ÷ 2.2 = 20 kg. Pediatric dosing almost always requires weight in kilograms. A common error is multiplying by 2.2 instead of dividing—this would give 96.8 kg, which is clearly too high for a child.
Question 32
How many tablespoons are in 1/2 cup? (1 cup = 16 tablespoons)
- A) 4 tablespoons
- B) 6 tablespoons
- C) 8 tablespoons
- D) 12 tablespoons
Answer: C) 8 tablespoons
Explanation: 1 cup = 16 tablespoons. Half cup = 16 ÷ 2 = 8 tablespoons. Understanding household measurements helps nurses communicate intake and output instructions to patients in familiar terms.
Question 33
A patient is prescribed 1,200 mg of medication daily, divided into 3 equal doses. How much per dose?
- A) 200 mg
- B) 300 mg
- C) 400 mg
- D) 600 mg
Answer: C) 400 mg
Explanation: Divide the daily total by the number of doses: 1,200 mg ÷ 3 = 400 mg per dose. This is called divided dosing and ensures therapeutic drug levels are maintained throughout the day. Always confirm whether a prescribed dose is per administration or total daily.
Question 34
Convert 104°F to Celsius.
- A) 38°C
- B) 40°C
- C) 42°C
- D) 44°C
Answer: B) 40°C
Explanation: °C = (°F − 32) × 5/9 = (104 − 32) × 5/9 = 72 × 5/9 = 40°C. A temperature of 104°F (40°C) indicates a high fever and potential medical emergency. Key temperature benchmarks: normal = 98.6°F/37°C, fever = 100.4°F/38°C, high fever = 104°F/40°C.
Question 35
A nurse needs to give 0.25 mg of a drug. The available tablets are 0.125 mg each. How many tablets are needed?
- A) 0.5 tablet
- B) 1 tablet
- C) 2 tablets
- D) 3 tablets
Answer: C) 2 tablets
Explanation: D/H = 0.25 mg ÷ 0.125 mg = 2 tablets. When working with small decimals, you can simplify by multiplying both numbers by 1,000: 250 ÷ 125 = 2. Always verify your answer is reasonable—giving half a tablet or more than 3 tablets should prompt you to double-check.
Score Interpretation
- 32–35 correct (90–100%) — Excellent! Your math skills are exam-ready
- 28–31 correct (80–89%) — Strong performance; review missed problems carefully
- 24–27 correct (70–79%) — Solid foundation; dedicate more practice time to conversions and dosage calculations
- Below 24 correct (<70%) — Needs focused study; revisit fundamental fraction, decimal, and percentage skills
Essential Formulas to Memorize
Keep these formulas at your fingertips for test day:
- Dosage formula: D/H × Q = Amount to give (Desired ÷ Have × Quantity)
- Percentage: Part ÷ Whole × 100
- Temperature: °C = (°F − 32) × 5/9 and °F = (°C × 9/5) + 32
- Weight: lbs ÷ 2.2 = kg
- IV rate: Volume ÷ Time = Rate
Continue Your Math Preparation
Mastering the math section requires consistent practice. For access to hundreds more practice questions with adaptive difficulty, progress tracking, and detailed performance analytics, explore our complete HESI A2 preparation program designed to help you achieve your target score.