Mathematics: Arithmetic, Percents, and Word Problems
What the questions test
NPOST math questions are practical: arithmetic with whole numbers, fractions, and decimals; ratio and proportion; percentage change; averages; and single-step algebra hidden inside word problems. You are not expected to know advanced formulas, but you are expected to compute cleanly and quickly without a calculator.
Concepts to master
- Order of operations: parentheses, exponents, multiply/divide left to right, then add/subtract left to right.
- Fraction and decimal conversion: know that 1/8 = 0.125, 1/4 = 0.25, 1/3 ≈ 0.333, 1/2 = 0.5, 3/4 = 0.75.
- Percent change: change ÷ original × 100. A 20% increase then a 20% decrease does not return to the original value.
- Averages: sum ÷ count; if you know the average and the count, the sum is average × count.
- Rates and proportions: set up a ratio and cross-multiply.
Traps to watch
- Mixing up "percent of" with "percent increase."
- Rounding too early in a multi-step problem.
- Answering the wrong quantity (the discount instead of the final price).
- Unit mismatches (minutes vs. hours).
Worked example
A jacket costs $80 and is marked down 25%. What is the sale price?
Discount = 0.25 × 80 = $20. Sale price = 80 − 20 = $60.
Rule of thumb: write down what the question is asking for before you compute, then check that your final number answers that exact question.