2.1 Numbers & Operations

Numbers & Operations on the NLN NEX

The NLN Nursing Entrance Exam (NEX) Mathematics section delivers 45 questions in 60 minutes — 40 scored items plus 5 unscored pretest items you cannot identify. That is roughly 80 seconds per question, so accuracy on setup matters more than long hand computation. A basic on-screen 4-function calculator is provided (a change from the older NLN PAX, which forbade calculators), so the exam tests whether you know which operation to perform, not whether you can divide by hand.

Numbers & Operations is about 12 items (~30%) of the math section. Every dosage, IV-rate, and lab-value question downstream depends on the skills below.

Fractions

Mixed and improper conversions (tested in pill-fraction problems):

• Mixed to improper: 3 1/4 = (3 x 4 + 1)/4 = 13/4
• Improper to mixed: 17/5 = 3 remainder 2 = 3 2/5

Common trap: students add denominators (2/3 + 1/4 = 3/7). Denominators are never added — only numerators are combined after a common denominator is found.

Comparing fractions (a frequent ranking item): convert each to a decimal, or cross-multiply pairs. To compare 3/8 and 2/5, cross-multiply 3 x 5 = 15 versus 8 x 2 = 16; since 15 < 16, 3/8 < 2/5. The larger cross-product sits over the larger fraction.

Decimals and conversions

Memorize the high-frequency fraction–decimal–percent equivalents — they appear in conversion and ranking items:

A leading zero is a clinical-safety convention: write 0.5 mg, never .5 mg (a missed decimal point causes a tenfold overdose).

Percentages

Every percent item is one of three relationships. Convert the percent to a decimal first.

Percent change = (New - Original) / Original x 100. A patient's weight falling from 180 to 171 lb is (171 - 180)/180 x 100 = -5% (a 5% loss). Trap: divide by the original, never the new value.

Ratios and proportions

A ratio compares quantities (3:1). A proportion sets two ratios equal (a/b = c/d) and is solved by cross-multiplication. This is the engine of dosage math:

A drug is 250 mg per 5 mL. How many mL deliver 400 mg? 250/5 = 400/x -> 250x = 2,000 -> x = 8 mL

Proportions can be direct (more weight, more dose) or inverse (faster IV rate, less time). Most NEX items are direct, but read carefully: 'if 2 nurses staff a unit in 6 hours, how long for 3 nurses' is inverse (2 x 6 = 3 x t -> t = 4 hours), because more workers means less time.

Order of operations (PEMDAS)

Resolve Parentheses, Exponents, Multiplication/Division (left to right), then Addition/Subtraction. Example: 6 + 2 x (3 + 1)^2 = 6 + 2 x 16 = 6 + 32 = 38. The frequent error is adding 6 + 2 before multiplying.

Rounding and estimation strategy

Because the NEX gives only a 4-function calculator, estimate first to catch typos. For 'What is 19% of 412?', round to 20% of 400 = 80; any answer near 78 is plausible, while 800 or 8 is clearly a misplaced decimal. Rounding rules: identify the place value, look one digit to the right, and round up at 5 or more. Rounding 0.625 to the tenths place gives 0.6 (the 2 in hundredths is less than 5); rounding 0.675 gives 0.7.

Integers and signed numbers

A few items use negative values (a temperature change, a fluid-balance deficit). Rules to recall: adding numbers with the same sign keeps the sign and adds magnitudes (-3 + -4 = -7); with different signs, subtract and keep the larger sign (-9 + 4 = -5). Multiplying or dividing two negatives gives a positive (-6 / -2 = 3); one negative gives a negative. A patient with intake 1,200 mL and output 1,650 mL has a net fluid balance of 1,200 - 1,650 = -450 mL (a deficit).