Materiales de Estudio

Introduction

The Mathematics section tests the numerical skills nurses use every shift, from calculating medication doses to interpreting patient data. It concentrates on two areas: numbers and algebra (arithmetic with fractions, decimals, and percentages; solving equations and proportions) and measurement and data (unit conversion, geometry basics, averages, and reading charts). A basic four-function calculator is permitted, but understanding the operation matters more than button-pushing — you must know which calculation the problem calls for.

Accuracy under time pressure is the whole game. Nursing math is unforgiving: a misplaced decimal or a flipped ratio changes a dose. This chapter teaches each method with a step-by-step worked example and checks the arithmetic, so you can see not just the answer but the reliable procedure that produces it. Learn the procedures cold and the calculator becomes a speed tool rather than a crutch.

Two habits prevent most errors. First, track units through every step so square units, cubic units, milligrams, and milliliters never get mixed up. Second, check your answer by substituting it back or estimating — if 15% of 80 "should be" a little less than a sixth of 80, then an answer of 12 passes the sanity check while an answer of 40 does not.

Key concepts

Whole Numbers, Fractions, and Decimals

Fluency with the four operations across whole numbers, fractions, and decimals is the foundation of everything else. Start with the order of operations (PEMDAS): parentheses, then exponents, then multiplication and division left to right, then addition and subtraction left to right. For 4² + 3 × 2, compute the exponent first (4² = 16), then the multiplication (3 × 2 = 6), then add: 16 + 6 = 22. Reaching for left-to-right addition first would wrongly give 44.

To add or subtract fractions, convert to a common denominator. For 3/4 + 1/8, rewrite 3/4 as 6/8, then add: 6/8 + 1/8 = 7/8. To add or subtract decimals, line up the decimal points and fill in trailing zeros so both numbers have the same number of places. For 5.6 − 2.85, write it as 5.60 − 2.85 = 2.75.

Converting between fractions and decimals is constant in nursing math. Divide the numerator by the denominator to get a decimal: 1/8 = 1 ÷ 8 = 0.125. To reverse, place the decimal over its place value and simplify: 0.75 = 75/100, and dividing top and bottom by 25 gives 3/4. Practice these conversions until they are automatic, because many problems are fastest in one form and clearest in another.

Ratios, Proportions, and Percentages

Ratios compare quantities; simplify them by dividing both terms by their greatest common factor. The ratio 12:18 shares a factor of 6, so it reduces to 2:3. Keeping ratios in lowest terms makes scaling — mixing a solution, adjusting a dose by weight — far easier to reason about.

Proportions are solved by cross-multiplication. To solve 4/6 = x/9, cross-multiply to get 6x = 4 × 9 = 36, then divide both sides by 6: x = 6. This one technique scales recipes and doses reliably; whenever two ratios are set equal, cross-multiply and solve.

Percentages express parts of a whole. To convert a fraction to a percent, divide and multiply by 100: 3/5 = 0.6 = 60%. To take a percent of a number, multiply by its decimal form: 15% of 80 = 0.15 × 80 = 12 (or split it: 10% of 80 is 8, 5% is 4, and 8 + 4 = 12). For percent increase or decrease, find the percent of the original, then add or subtract: a 25% discount on $40 is 0.25 × 40 = $10 off, giving a $30 sale price.

Algebra and Solving Equations

Basic algebra lets you solve for an unknown — a dose, a rate, a missing value. The governing idea is to keep the equation balanced while isolating the variable, undoing operations in reverse order using their inverses. For 3x + 7 = 22, first subtract 7 from both sides (undoing the addition): 3x = 15. Then divide both sides by 3 (undoing the multiplication): x = 5.

Whatever you do to one side, you must do to the other. For y/4 = 9, the variable is divided by 4, so multiply both sides by 4: y = 9 × 4 = 36. To evaluate an expression, substitute the value and simplify, respecting order of operations: for 2(x + 3) when x = 4, do the parentheses first — 2(4 + 3) = 2(7) = 14.

Always check your answer by substituting it back into the original equation. For x = 5 in 3x + 7 = 22: 3(5) + 7 = 15 + 7 = 22 ✓. This ten-second habit catches arithmetic slips before they cost you a question — and, in practice, before they cost a patient a correct dose.

Measurement and Unit Conversion

The metric system is built on powers of ten, so conversions are multiply-or-divide by 10, 100, or 1000. Since 1 meter = 100 centimeters, 2.5 meters = 2.5 × 100 = 250 centimeters. Moving to a smaller unit multiplies; moving to a larger unit divides.

Know the basic geometry formulas. The area of a rectangle is length × width — an 8 cm by 5 cm rectangle has area 8 × 5 = 40 cm². The perimeter of a square is four times a side — a 7-inch square has perimeter 4 × 7 = 28 inches. Report area in square units and volume in cubic units; mismatched units are a common and avoidable error, which is why you should write the unit beside every number and let them cancel.

Finally, round by identifying the target place value and looking at the digit immediately to its right: 5 or more rounds up, less than 5 rounds down. To round 3,847 to the nearest hundred, the hundreds digit is 8 and the digit to its right (tens) is 4 — less than 5 — so round down to 3,800.

Data, Statistics, and Graphs

Interpreting data means computing averages, reading charts, and drawing conclusions from tables — exactly what nurses do with vital signs and intake/output records. The mean (average) is the sum of the values divided by how many there are. Reversed, the sum equals the mean times the count: if five test scores average 82, their sum is 82 × 5 = 410, which you can use to back out a missing score.

Know the three center measures. The mean is the average; the median is the middle value when the data are put in order; the mode is the most frequent value. Choose the one the question asks for — they are not interchangeable.

To find a part of a whole as a percentage, divide the part by the total: 12 boys in a class of 30 is 12/30 = 0.4 = 40%. When reading a chart or table, check the title, axis labels, and units before interpreting anything, and note whether values are rising, falling, or peaking to answer trend questions. The data are only as trustworthy as your reading of the labels.

Key facts & formulas

Mathematics cram box - PEMDAS: Parentheses → Exponents → Multiply/Divide (left→right) → Add/Subtract (left→right). - Add fractions: common denominator first (3/4 + 1/8 → 6/8 + 1/8 = 7/8). - Fraction ↔ decimal: 1/8 = 0.125; 0.75 = 3/4; 3/5 = 0.6 = 60%. - Percent of a number: multiply by the decimal (15% of 80 = 0.15 × 80 = 12). - Percent change: find the percent of the original, then add/subtract (25% off $40 → $30). - Proportion: cross-multiply (4/6 = x/9 → 6x = 36 → x = 6). - Solve linear: inverse operations, same to both sides; check by substituting back. - Metric: ×/÷ by 10, 100, 1000 (1 m = 100 cm → 2.5 m = 250 cm). - Area = L × W (square units); perimeter of a square = 4 × side. - Mean = sum ÷ count; sum = mean × count. Median = middle; mode = most frequent. - Rounding: digit to the right is 5+ → round up (3,847 → nearest hundred = 3,800).

Worked example

Problem: Solve the proportion 4/6 = x/9. Then convert the resulting fraction 4/6 to a percentage.

Step 1 — Solve the proportion. Cross-multiply: 4 × 9 = 6 × x, so 36 = 6x. Divide both sides by 6: x = 36 ÷ 6 = 6. Check: 4/6 and 6/9 both reduce to 2/3 ✓.

Step 2 — Convert 4/6 to a percent. First reduce: 4/6 = 2/3. Divide: 2 ÷ 3 = 0.6667. Multiply by 100: ≈ 66.7%. (For a cleaner example, 3/5 = 0.6 = 60% exactly.)

The two moves to internalize: cross-multiply for any proportion, and divide-then-×100 for any fraction-to-percent. Both are verified by reducing the fractions to the same lowest terms.

Common exam traps

• Breaking PEMDAS. Adding before multiplying, or working left-to-right through everything. Exponents and grouping come first.
• Adding unlike fractions. You cannot add 3/4 + 1/8 as "4/12." Find the common denominator first.
• Percent vs. percentage points, and margin vs. markup. "25% off $40" means $10 off → $30, not $40 − 25.
• Unit mismatches. Area in square units, volume in cubic units, and metric conversions by powers of ten. Carry units through every step.
• Skipping the check. Not substituting the solution back into the equation, so an arithmetic slip survives.

Self-check

1. What is 4² + 3 × 2? (22 — exponent, then multiply, then add.)
2. Solve 3x + 7 = 22. (x = 5.)
3. Convert 3/5 to a percent. (60%.)
4. How many centimeters are in 2.5 meters? (250 cm.)
5. Five scores average 82. What is their sum? (410.)