HESI A2 Exam — Complete Study Guide (2026)

Sample chapter from HESI A2 Exam — Complete Study Guide (2026 Edition) · Published by PrepPass · PrepPass.org. AI-assisted study aid — not affiliated with or endorsed by Elsevier or HESI. There is no single national HESI A2 passing score; each nursing program sets its own. Verify against the official Elsevier/HESI materials and your program.

Introduction

The math section tests the practical arithmetic a nurse uses every shift: reading a dose, scaling a solution, converting a weight from pounds to kilograms, checking a temperature. You will work with fractions, decimals, ratios and proportions, percentages, and unit conversions. There is no advanced algebra or geometry here — just careful, accurate arithmetic, usually without a calculator.

Because the skills are practical, the exam rewards a reliable method over cleverness. For every problem type in this chapter you will learn one repeatable procedure, see it worked step by step, and get a way to check your answer. Speed comes from trusting the method, not from rushing.

Two habits protect your score more than anything else. First, write the numbers down and line them up — most math errors on this test are copying and place-value slips, not real misunderstandings. Second, check units before you compute: milligrams with milligrams, milliliters with milliliters. A right calculation on the wrong units is still wrong.

Key concepts

Working with Fractions

A fraction shows a part of a whole: the numerator on top counts the parts, the denominator on the bottom says how many equal parts make the whole. The four operations follow two different logics, and mixing them up causes most fraction mistakes. Addition and subtraction need a common denominator; multiplication and division do not.

To add or subtract, rewrite each fraction over the least common denominator (LCD), then combine only the numerators and keep the denominator. For example, to add 3/4 + 1/6, the LCD of 4 and 6 is 12: 3/4 becomes 9/12 and 1/6 becomes 2/12, so the sum is 9/12 + 2/12 = 11/12. To subtract 5/6 − 1/4, the LCD is 12: 5/6 = 10/12 and 1/4 = 3/12, so 10/12 − 3/12 = 7/12.

To multiply, go straight across: multiply the numerators, multiply the denominators, then reduce. For 2/3 × 3/5, that is (2×3)/(3×5) = 6/15, which reduces to 2/5 by dividing top and bottom by 3. To divide, multiply by the reciprocal — flip the second fraction. For 3/8 ÷ 1/2, rewrite it as 3/8 × 2/1 = 6/8, which reduces to 3/4.

Finally, reduce every answer to lowest terms by dividing the numerator and denominator by their greatest common factor, and know how to turn a mixed number into an improper fraction: multiply the whole number by the denominator and add the numerator. For 2 1/4, that is 2 × 4 + 1 = 9 over the same denominator, or 9/4.

Decimals and Place Value

Decimals are just fractions written with place values — tenths, hundredths, thousandths — to the right of the decimal point. The single most important habit is to line up the decimal points when adding or subtracting, filling empty places with zeros. To add 4.25 + 3.7, write it as 4.25 + 3.70 so the columns align, and the sum is 7.95.

Multiplying decimals ignores the point until the end: multiply as whole numbers, then give the product as many decimal places as the two factors have combined. For 0.4 × 0.05, multiply 4 × 5 = 20; the factors have one and two decimal places, three in total, so the answer is 0.020, or 0.02. Dividing by a decimal means first making the divisor whole: shift its decimal point to the right and shift the dividend's point the same number of places. To divide 12.6 by 3, the divisor is already whole, so 12.6 ÷ 3 = 4.2 (check: 4.2 × 3 = 12.6).

Rounding uses the digit just to the right of your target place: 5 or more rounds up, less than 5 leaves it. To round 7.348 to the nearest hundredth, the hundredths digit is 4 and the digit to its right is 8, so the 4 rounds up to give 7.35. You should also move fluidly between decimals and fractions: 0.6 is 6 in the tenths place, so 0.6 = 6/10 = 3/5 reduced.

Ratios and Proportions

A ratio compares two quantities (nurses to patients, milligrams to milliliters); a proportion states that two ratios are equal. Proportions are the workhorse of clinical math — you use them to scale recipes, mix solutions, and calculate doses. The fastest solving tool is cross multiplication: in a/b = c/d, multiply a × d and b × c, set the two products equal, and solve for the unknown.

The one discipline that keeps proportions correct is consistent order. Whatever you put on top on the left must be the same kind of quantity on top on the right. To solve 3/4 = x/20, cross multiply to get 4x = 3 × 20 = 60, so x = 15. To find how much water a 2-cups-flour-to-3-cups-water recipe needs for 8 cups of flour, set 2/3 = 8/x, cross multiply to 2x = 24, and x = 12 cups.

A unit rate is a ratio reduced to "per one" — divide to find how much of one quantity goes with a single unit of the other. A car going 150 miles on 5 gallons runs at 150 ÷ 5 = 30 miles per gallon. And staffing at 1 nurse per 8 patients for 56 patients is 1/8 = x/56, so 8x = 56 and x = 7 nurses. Always confirm the labels line up — compare milligrams with milligrams, not milligrams with milliliters.

Percentages

A percent is a number out of one hundred, and it shows up in discounts, statistics, and dosage strengths. The first move in almost every percent problem is to convert the percent to a decimal by dividing by 100 (moving the decimal two places left): 25% becomes 0.25. Going the other way, multiply a decimal by 100: 0.35 becomes 35%.

To find a percent of a number, convert and multiply. 25% of 80 is 0.25 × 80 = 20 (or, since 25% is one quarter, 80 ÷ 4 = 20). To find what percent one number is of another, divide the part by the whole and multiply by 100: 15 out of 60 is 15 ÷ 60 = 0.25 = 25%.

Percent change compares the amount of change to the original value, not the new one — a frequent trap. Divide the change by the original and multiply by 100. A population growing from 200 to 250 has a change of 50, and 50 ÷ 200 = 0.25 = 25% increase. For a discount, find the discount amount first: a $40 shirt at 15% off loses 0.15 × 40 = $6, so it costs 40 − 6 = $34.

Measurement Conversions

Nurses convert constantly — between metric units, between household and metric measures, and between temperature scales. The metric system is built on steps of 1000: 1000 milligrams (mg) in a gram (g), 1000 grams in a kilogram (kg), and 1000 milliliters (mL) in a liter (L). So 2.5 L × 1000 = 2500 mL, 5000 g ÷ 1000 = 5 kg, and 0.75 g × 1000 = 750 mg.

The most-tested household-to-metric fact is weight: 1 kilogram ≈ 2.2 pounds, so you divide pounds by 2.2 to get kilograms. A 154-pound patient weighs 154 ÷ 2.2 = 70 kg. For temperature, the exam gives you the formula: F = (9/5)C + 32. At 37 °C, (9/5)(37) = 66.6, plus 32 is 98.6 °F — normal body temperature, a value worth memorizing as a sanity check.

The safest way to run any conversion is dimensional analysis: write each conversion factor as a fraction arranged so the unit you don't want cancels, leaving the unit you do want. For a dose of 20 mg per 5 mL when you need 60 mg, notice 60 mg is 3 × 20 mg, so you need 3 × 5 mL = 15 mL. Set the units up to cancel and the arithmetic follows.

Key facts & formulas

Fractions. Add/subtract → common denominator first. Multiply → straight across, then reduce. Divide → invert the second fraction and multiply. Mixed → improper: (whole × denominator) + numerator, over the denominator. Decimals. Add/subtract → line up the points. Multiply → total the decimal places of both factors. Divide by a decimal → make the divisor whole and shift both points equally. Round → look one place right; ≥5 rounds up. Proportions. a/b = c/d → a × d = b × c. Keep the comparison order the same on both sides. Unit rate = divide to get "per one." Percent. Percent → decimal: ÷100 (point two left). Percent of a number: convert × the number. What percent: part ÷ whole × 100. Percent change = change ÷ original × 100 (original, not new). Metric. 1 g = 1000 mg · 1 kg = 1000 g · 1 L = 1000 mL. 1 kg ≈ 2.2 lb → kg = lb ÷ 2.2. Temperature. F = (9/5)C + 32. 37 °C = 98.6 °F.

Worked example

1. A doctor orders 500 mg of a medication. The tablets on hand are 250 mg each. How many tablets do you give?

• Confirm units match: order in mg, tablet strength in mg. Good.
• Divide the ordered dose by the dose per tablet: 500 ÷ 250 = 2.
• Check: 2 tablets × 250 mg = 500 mg. ✔ Give 2 tablets.

2. A patient weighs 154 lb. Convert to kilograms, then compute the mean of four temperature readings: 98.6, 99.0, 100.4, and 98.0 °F.

• Weight: 154 ÷ 2.2 = 70 kg (check: 70 × 2.2 = 154 ✔).
• Mean: add the four readings → 98.6 + 99.0 + 100.4 + 98.0 = 396.0. Divide by 4 → 396.0 ÷ 4 = 99.0 °F.
• Check the mean is between the smallest (98.0) and largest (100.4) reading. ✔

Common exam traps

• Adding fractions without a common denominator. 3/4 + 1/6 is not 4/10. Convert to twelfths first (11/12).
• The percent-change base. Percent change divides by the original amount, not the new total. 200 → 250 is 25%, not 20%.
• Decimal-place slips in multiplication. 0.4 × 0.05 has three decimal places → 0.02, not 0.2. Count the places every time.
• Converting weight the wrong direction. Pounds → kilograms is divide by 2.2 (kg is the smaller number). Multiplying gives an impossibly heavy patient.
• Answer left unreduced. 6/15 is correct arithmetic but the listed choice is 2/5. Always reduce before matching.