Many students can solve a math equation when it's placed in front of them — but freeze when the same concept is buried inside a paragraph of words. The HESI A2 Math section is almost entirely word problems, meaning your ability to translate English into math is just as important as your ability to calculate. This guide gives you a systematic framework for breaking down any word problem, plus 12+ fully worked examples from the most common HESI A2 categories.
📊 What the Data Shows: In our analysis of student performance across 1,000+ practice attempts, math word problems — not raw computation — account for the majority of missed points. The students who improved the most were those who practiced a consistent problem-solving method, not just formulas.
The RUCSQ Method: A Universal Word Problem Framework
Before diving into specific problem types, you need a repeatable system for approaching any word problem. We recommend the RUCSQ method:
| Step | What to Do |
|---|---|
| Read | Read the entire problem slowly. Don't start calculating yet. |
| Underline | Underline or note the key numbers, units, and what's being asked. |
| Choose | Choose the operation or formula needed (multiply, divide, ratio, conversion). |
| Solve | Set up the equation and solve step by step. |
| Question | Re-read the question — does your answer make sense? Are the units correct? |
Let's apply this method across the major word problem categories on the HESI A2.
Category 1: Ratio & Proportion Problems
Ratio problems are the most common word problem type on the HESI A2. They always follow the same pattern: you're given a known ratio and asked to find a missing value.
The Cross-Multiplication Method
Set up two equivalent fractions, then cross-multiply and solve for the unknown.
Example 1: "A patient needs to receive medication at a ratio of 5 mg per 2 mL. How many mL are needed for a 15 mg dose?"
Step 1 (Read & Underline): 5 mg per 2 mL; need 15 mg; find mL
Step 2 (Choose): Ratio/proportion → cross-multiply
Step 3 (Solve):
5 mg / 2 mL = 15 mg / x mL
5x = 2 × 15 = 30
x = 30 ÷ 5 = 6 mL
Step 4 (Question): 6 mL is 3× the original 2 mL, and 15 mg is 3× the original 5 mg. ✅ Consistent.
Example 2: "If 3 out of every 8 students in a nursing program are male, how many males are in a program of 120 students?"
3/8 = x/120
8x = 360
x = 45 male students
Category 2: Percentage Problems
Percentage problems come in three flavors — learn to recognize each one:
| Type | What's Missing? | Formula |
|---|---|---|
| Find the part | What is 25% of 80? | Part = Whole × (% ÷ 100) |
| Find the percent | 20 is what % of 80? | % = (Part ÷ Whole) × 100 |
| Find the whole | 20 is 25% of what? | Whole = Part ÷ (% ÷ 100) |
Example 3: "A hospital reports that 15% of its 840 patients were readmitted within 30 days. How many patients were readmitted?"
Type: Find the part
Part = 840 × (15 ÷ 100) = 840 × 0.15 = 126 patients
Example 4: "A nurse answers 68 out of 80 questions correctly. What percentage did she score?"
Type: Find the percent
% = (68 ÷ 80) × 100 = 0.85 × 100 = 85%
Example 5: "A discount of $12 represents 20% off the original price. What was the original price?"
Type: Find the whole
Whole = 12 ÷ 0.20 = $60
Category 3: Unit Conversion Problems
The HESI A2 tests metric-to-metric, household-to-metric, and time conversions. The key technique is dimensional analysis (also called the factor-label method).
How Dimensional Analysis Works
Multiply by conversion factors arranged so unwanted units cancel out.
Example 6: "Convert 2.5 liters to milliliters."
2.5 L × (1,000 mL / 1 L) = 2,500 mL
The "L" cancels, leaving "mL." ✅
Example 7: "A patient weighs 176 pounds. What is the weight in kilograms? (1 kg = 2.2 lbs)"
176 lbs × (1 kg / 2.2 lbs) = 176 ÷ 2.2 = 80 kg
Example 8: "How many teaspoons are in 3 tablespoons? (1 tbsp = 3 tsp)"
3 tbsp × (3 tsp / 1 tbsp) = 9 teaspoons
⚠️ Common Trap: Students often multiply when they should divide (or vice versa). If you're converting to a smaller unit, the number gets bigger. If converting to a larger unit, the number gets smaller. Use this as a sanity check.
Category 4: Fraction & Decimal Problems
Example 9: "A patient's IV bag contains 3/4 of a liter. If 1/3 of the bag has been administered, how much fluid remains?"
Step 1: Find amount administered: 1/3 × 3/4 = 3/12 = 1/4 liter
Step 2: Subtract from total: 3/4 − 1/4 = 2/4 = 1/2 liter
Example 10: "Arrange the following from least to greatest: 0.45, 3/8, 0.5, 7/20"
Convert all to decimals:
- 0.45 = 0.45
- 3/8 = 0.375
- 0.5 = 0.5
- 7/20 = 0.35
Order: 7/20 (0.35), 3/8 (0.375), 0.45, 0.5 → 7/20, 3/8, 0.45, 0.5
Category 5: Dosage Calculation Word Problems
These use the Desired-over-Have method (also called "D/H × Q"):
Dose = (Desired ÷ Have) × Quantity on Hand
Example 11: "The physician orders 500 mg of amoxicillin. The pharmacy supplies 250 mg tablets. How many tablets should the nurse administer?"
Dose = (500 mg ÷ 250 mg) × 1 tablet = 2 tablets
Example 12: "A physician orders 0.5 g of medication. The available concentration is 250 mg/5 mL. How many mL should be given?"
Step 1: Convert 0.5 g to mg: 0.5 × 1,000 = 500 mg
Step 2: Apply D/H × Q: (500 mg ÷ 250 mg) × 5 mL = 2 × 5 = 10 mL
Category 6: Multi-Step & Real-World Problems
Example 13: "A nurse works three 12-hour shifts per week and earns $32.50 per hour. If she picks up an extra 8-hour shift at time-and-a-half, what is her total weekly pay?"
Step 1: Regular pay: 3 × 12 × $32.50 = $1,170
Step 2: Overtime rate: $32.50 × 1.5 = $48.75
Step 3: Overtime pay: 8 × $48.75 = $390
Step 4: Total: $1,170 + $390 = $1,560
The 5 Most Common Word Problem Mistakes (And How to Avoid Them)
- Not reading the full question — Many students start calculating after the first sentence and miss critical information in the last sentence.
- Unit mismatch — If the question gives grams but the answer choices are in milligrams, you must convert before solving.
- Rounding too early — Carry all decimal places through your calculations and only round at the final answer.
- Choosing the wrong operation — "Of" usually means multiply. "Per" usually means divide. "How many more" means subtract.
- Not checking reasonableness — If a question asks for a dosage and your answer is 500 tablets, something went wrong.
💡 Keyword Decoder for Word Problems:
- "Total," "sum," "combined," "altogether" → Addition
- "Difference," "how many more," "remaining," "left" → Subtraction
- "Of," "product," "times," "each" → Multiplication
- "Per," "ratio," "out of," "for every," "divided equally" → Division
Your Study Action Plan
- Print this page and keep it in your study binder
- Practice 5–10 word problems daily using the RUCSQ method on paper
- Categorize each problem before solving — is it a ratio, percentage, conversion, or multi-step?
- Track your weak categories — spend extra time on the types you get wrong
- Time yourself — aim for under 90 seconds per problem to simulate exam conditions
🎯 Practice Makes Perfect: Our practice exams include 100+ math word problems across all the categories above — with instant scoring and detailed explanations for every answer. Start a math-focused practice test →