Essential Fraction, Decimal, and Percent Conversion Rules
On the HESI A2, the ability to pivot between different numerical representations is a foundational skill. Many questions require you to convert a Fraction into a decimal or a percentage before performing a final calculation. To convert a fraction to a decimal, divide the numerator by the denominator. For example, in a scenario where a patient receives 3/8 of a solution, the decimal equivalent is found by calculating 3 ÷ 8, resulting in 0.375. To then convert this decimal to a percentage, you must multiply by 100 and append the percent sign, moving the decimal point two places to the right (37.5%).
Understanding the Reciprocal is also vital when dividing fractions. The rule of "invert and multiply" is the standard mechanism here: to divide 1/2 by 3/4, you multiply 1/2 by 4/3. This mechanical shift is frequently tested in the context of scaling recipes or adjusting fluid volumes. Scoring highly on these items requires recognizing that percentages are always parts of 100. If a question asks for 15% of 80, the most efficient path is converting 15% to the decimal 0.15 and multiplying (0.15 × 80 = 12). This Decimal-to-Percent fluidity prevents simple calculation errors that can lower your overall math subscore.
Metric System Prefixes and Conversion Factors
The metric system is the universal language of medicine, and the HESI A2 heavily emphasizes your ability to jump between scales using powers of ten. You must memorize the hierarchy of prefixes: kilo (1,000), hecto (100), deka (10), deci (0.1), centi (0.01), and milli (0.001). The most frequent metric conversions HESI A2 candidates encounter involve kilograms to grams, grams to milligrams, and liters to milliliters.
A critical rule for the exam is the Decimal Shift Method. When converting from a larger unit to a smaller unit (e.g., grams to milligrams), you move the decimal three places to the right because there are 1,000 milligrams in a single gram. Conversely, when moving from a smaller unit to a larger one (e.g., milliliters to liters), move the decimal three places to the left. For instance, 250 milliliters becomes 0.25 liters. The exam often presents these problems within a clinical context, such as converting a patient’s weight in kilograms to grams to determine a weight-based dosage. Precision is paramount; a misplaced decimal point in a healthcare setting is a sentinel event, and the HESI scoring logic reflects this by offering distractors that are off by exactly one decimal place.
Mastering Ratio, Proportion, and Dosage Calculations
Setting Up and Solving Proportion Equations
Proportions are the backbone of the HESI A2 math section. A proportion is simply a statement that two ratios are equal, expressed as a/b = c/d. This is the primary tool for solving for an unknown variable (x). The most reliable mechanism for solving these is the Cross-Multiplication rule, often referred to as finding the product of the extremes and the means. If you are given the ratio 2:5 = x:20, you set up the equation 2/5 = x/20. Multiplying 2 by 20 gives you 40, and 5 by x gives you 5x. Dividing 40 by 5 reveals that x = 8.
In a HESI A2 math study guide context, these problems often appear as "If 3 tablets contain 450 mg, how many tablets are needed for a 750 mg dose?" By setting up the proportion 3/450 = x/750, you can solve for the unknown quantity of tablets. This method ensures that the units remain consistent; you must always keep the same units in the numerators and the same units in the denominators across the equals sign. Failure to align units—such as placing milligrams over tablets on one side and tablets over milligrams on the other—is a common trap that leads to incorrect answers.
While the HESI A2 is an entrance exam, it introduces the Desired over Have formula, which is the standard for dosage calculation practice. The formula is expressed as (D ÷ H) × Q = X, where D is the Desired dose (the amount ordered by the physician), H is the amount you Have on hand (the dosage strength available), and Q is the Quantity or volume in which the drug is delivered (e.g., 1 tablet, 5 mL).
Consider a scenario where the order is for 500 mg of a medication, and the supply is 250 mg per capsule. Using the formula, (500 mg / 250 mg) × 1 capsule = 2 capsules. This Dimensional Analysis approach ensures that the "mg" units cancel out, leaving you with the "capsule" unit. The exam may complicate these questions by requiring a unit conversion before applying the formula. If the order is in grams and the supply is in milligrams, you must convert the grams to milligrams first to ensure the H and D values are in the same unit. This multi-step process tests your ability to maintain accuracy across complex, sequential operations.
Working with Measurements and Basic Geometry
Geometry on the HESI A2 is focused on fundamental shapes: rectangles, squares, triangles, and circles. You must memorize the Perimeter and Area formulas for each. For a rectangle, the perimeter is P = 2L + 2W, while the area is A = L × W. For a circle, you must be familiar with Pi (π), which is typically rounded to 3.14 for exam purposes. The circumference (the perimeter of a circle) is C = 2πr or C = πd, and the area is A = πr².
Triangle calculations frequently appear as well. The area of a triangle is found using A = 1/2(bh), where b represents the base and h represents the height. A common exam scenario might involve calculating the area of a rectangular hospital room to determine floor space or finding the circumference of a circular dial. It is important to remember that area is always expressed in Square Units (e.g., cm²), whereas perimeter and circumference are linear measures. If a question provides the diameter of a circle but the area formula requires the radius, you must remember the relationship: r = d/2. Forgetting this simple step is a frequent cause of error on geometry-based items.
Converting Between Measurement Systems (Metric & Household)
In the United States, healthcare providers must bridge the gap between the metric system and the Household System of measurement. The HESI A2 tests specific conversion factors that are non-negotiable for nursing students. The most critical "nursing math formulas" involve volume and weight. You must know that 1 teaspoon (tsp) = 5 milliliters (mL), 1 tablespoon (tbsp) = 15 mL, and 1 ounce (oz) = 30 mL. For weight, the standard conversion is 1 kilogram (kg) = 2.2 pounds (lb).
When converting from pounds to kilograms, you divide the weight in pounds by 2.2. For example, a 154 lb patient weighs 70 kg (154 ÷ 2.2). When converting from kilograms to pounds, you multiply by 2.2. Another frequent conversion is temperature, moving between Celsius and Fahrenheit. The formulas are: F = (C × 1.8) + 32 and C = (F - 32) / 1.8. These conversions are not just academic; they are essential for calculating fluid intake (I&O) and ensuring patient safety during weight-based medication administration. The HESI often uses "cups" or "glasses" in word problems, requiring you to know that 1 cup = 8 oz = 240 mL.
Solving for Unknowns: Basic Algebraic Concepts
Isolating Variables in Simple Equations
The algebra on the HESI A2 is primarily centered on Linear Equations where you must isolate a single variable. This involves the use of inverse operations: if a number is being added to the variable, you subtract it from both sides; if it is being multiplied, you divide. For instance, in the equation 3x + 7 = 22, you first subtract 7 from both sides to get 3x = 15, then divide by 3 to find x = 5.
This skill is crucial because it underlies almost every complex problem on the test. Whether you are solving for a missing part of a ratio or determining a missing value in a geometry problem, the logic of Equation Balancing remains the same. The exam may present these in abstract form or as part of a word problem. A key detail to remember is the Order of Operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Applying operations in the wrong order will lead to an incorrect value for the variable, a mistake the exam often anticipates with its multiple-choice options.
Beyond simple isolation, you will encounter formulas that describe the relationship between multiple physical properties. The most common is the Distance Formula: d = rt (distance = rate × time). These problems test your ability to manipulate the formula based on which variable is missing. If the question asks for the rate, you must rearrange the formula to r = d/t.
For example, if a nurse travels 150 miles to a remote clinic and it takes 3 hours, the rate of travel is 50 miles per hour. These problems often include a "distractor" involving units, such as giving the time in minutes while the rate is in hours. You must perform a Unit Consistency check before plugging numbers into the formula. If the time is given as 90 minutes, you must convert that to 1.5 hours before calculating the rate. This level of attention to detail is what separates high-scoring candidates from those who struggle with the math subtest’s time constraints.
Tackling Word Problems and Real-World Applications
Strategies for Translating Word Problems into Math Equations
Word problems are often the most intimidating part of the fractions and decimals on HESI section because they require translating English prose into mathematical syntax. The key is identifying "signal words." The word "is" typically represents the equals sign (=), "of" indicates multiplication (×), and "per" or "out of" signifies division or a fraction bar. When a problem says "25 percent of a 200 mg dose," you should immediately see "0.25 × 200."
To succeed, use a systematic approach: first, identify what the question is asking for (the "target unit"). Second, list the given values and their units. Third, determine which formula connects the given values to the target unit. This process of Quantitative Reasoning helps filter out irrelevant information. Sometimes, the HESI includes "extra" numbers—like a patient's age or room number—that are not needed for the calculation. By focusing strictly on the units and the required formula, you avoid the cognitive overload that leads to mistakes on word problems.
Common Nursing Scenario Calculations (IV Rates, Solution Strength)
While advanced IV drip rates are often reserved for later nursing school exams, the HESI A2 may touch upon basic Infusion Calculations. This involves determining the total time for an infusion or the volume delivered over a set period. The fundamental formula is Total Volume / Total Time = Flow Rate (usually in mL/hr). If a patient is to receive 1,000 mL of normal saline over 8 hours, the flow rate is 125 mL/hr.
Another scenario involves Solution Strength or concentration. This is often expressed as a percentage or a ratio, such as a 1:1,000 solution. This means there is 1 gram of solute in 1,000 mL of solvent. If the exam asks how many milligrams are in 5 mL of a 1% solution, you must know that 1% means 1 gram per 100 mL. Therefore, 1,000 mg / 100 mL = 10 mg/mL. Multiplying by the 5 mL volume gives you 50 mg. These problems combine metric conversion, percentage-to-decimal shifts, and basic multiplication, serving as a comprehensive test of your mathematical readiness for the nursing profession.