Key Takeaways
- The Mathematics section has 45 questions (40 scored) in 60 minutes — about 1.3 minutes per question
- A basic 4-function calculator is allowed on the NEX (unlike the old PAX which banned calculators)
- Numbers & Operations covers approximately 12 items: fractions, decimals, percentages, and ratios
- To add or subtract fractions, find a common denominator; to multiply, multiply straight across; to divide, multiply by the reciprocal
- Percent problems use three formulas: Part = Whole x Rate, Rate = Part / Whole, Whole = Part / Rate
- Ratios compare two quantities (e.g., 3:1) and can be solved using cross-multiplication in proportions
- Order of operations (PEMDAS): Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
- Always check your answer for reasonableness — if a dosage calculates to 50 tablets, something is wrong
Numbers & Operations
The Mathematics section of the NLN NEX contains 45 questions to be completed in 60 minutes (40 scored, 5 pretest). A basic 4-function calculator is allowed — a key difference from the old PAX exam.
Numbers & Operations makes up approximately 12 items (~30%) of the math section and covers the foundational arithmetic skills that underlie all nursing mathematics.
Fractions
Key Fraction Operations
| Operation | Method | Example |
|---|---|---|
| Adding/Subtracting | Find common denominator, then add/subtract numerators | 2/3 + 1/4 = 8/12 + 3/12 = 11/12 |
| Multiplying | Multiply numerators, multiply denominators | 3/4 x 2/5 = 6/20 = 3/10 |
| Dividing | Multiply by the reciprocal (Keep-Change-Flip) | 3/4 / 2/5 = 3/4 x 5/2 = 15/8 |
| Simplifying | Divide numerator and denominator by GCF | 12/18 = (12/6)/(18/6) = 2/3 |
Mixed Numbers and Improper Fractions
- Mixed to Improper: Multiply whole number by denominator, add numerator, keep denominator
- Example: 3 1/4 = (3 x 4 + 1)/4 = 13/4
- Improper to Mixed: Divide numerator by denominator; quotient = whole number, remainder = numerator
- Example: 17/5 = 3 remainder 2 = 3 2/5
Decimals
| Operation | Key Rule |
|---|---|
| Adding/Subtracting | Line up decimal points, then add/subtract normally |
| Multiplying | Multiply as whole numbers, count total decimal places in both factors, place decimal |
| Dividing | Move divisor decimal to make it a whole number, move dividend decimal the same places |
| Rounding | Look at the digit to the right: 5+ round up, 4 or less round down |
Decimal-Fraction-Percent Conversion:
| Fraction | Decimal | Percent |
|---|---|---|
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333... | 33.3% |
| 1/2 | 0.50 | 50% |
| 2/3 | 0.667... | 66.7% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.20 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.10 | 10% |
Percentages
Three core percentage formulas:
| Find | Formula | Example |
|---|---|---|
| Part | Part = Whole x Rate | What is 25% of 80? → 80 x 0.25 = 20 |
| Rate | Rate = Part / Whole | 15 is what percent of 60? → 15/60 = 0.25 = 25% |
| Whole | Whole = Part / Rate | 30 is 75% of what number? → 30/0.75 = 40 |
Percent increase/decrease:
- Percent Change = (New - Original) / Original x 100
- Example: Weight went from 180 lbs to 171 lbs → (171-180)/180 x 100 = -5% (5% decrease)
Ratios and Proportions
A ratio compares two quantities: 3:1, 3/1, or "3 to 1"
A proportion states two ratios are equal: a/b = c/d
Cross-multiplication solves proportions: if a/b = c/d, then a x d = b x c
Nursing example: If a medication concentration is 250 mg per 5 mL, how many mL are needed for 400 mg?
250/5 = 400/x → 250x = 2000 → x = 8 mL
What is 3/8 + 1/4?
A patient must receive medication at a ratio of 2 mg per 1 kg of body weight. If the patient weighs 70 kg, what dose should be administered?
What is 35% of 240?
Convert 5/8 to a decimal: 5/8 = _____
Type your answer below
If 3 tablets contain 900 mg of medication, how many mg are in 5 tablets?
A nursing class starts with 48 students. By graduation, only 36 remain. What percentage of students completed the program?
Arrange these fractions from SMALLEST to LARGEST.
Arrange the items in the correct order