Numerical / Mathematical Reasoning
Numerical reasoning covers arithmetic with fractions, decimals, and percentages; ratios and proportions; unit conversions; averages; and word problems framed in fire-service terms (flow rates, hose lengths, ladder angles, elapsed time). Know how to convert units (feet to inches, gallons per minute to gallons per minute per line), compute a rate (distance ÷ time, volume ÷ time), and solve proportions by cross-multiplying. For averages, remember total = average × count, which lets you work backward.
Traps include mixing units (minutes vs. hours), answering the wrong quantity (the question asks for the remainder, not the total), and distractors built from one wrong operation. Estimate first to catch impossible answers; on multiple choice, an answer far outside your estimate is wrong. Show your setup in words before calculating.
Worked example: A crew pumps 150 gallons per minute through one line. How many gallons in 8 minutes? 150 × 8 = 1,200 gallons. If asked how many minutes to move 1,200 gallons, divide instead: 1,200 ÷ 150 = 8. Rule of thumb: write the units next to each number and let the units tell you whether to multiply or divide.