Mathematical Reasoning
Core skills
Mathematical reasoning items test practical arithmetic: whole numbers, fractions, decimals, percentages, ratios and proportions, averages, elapsed time, unit conversion, perimeter, area, volume, and simple fireground formulas such as flow rate (gallons per minute × minutes = gallons), tank volume, and hose capacity. You should be comfortable setting up a proportion and converting units before calculating.
Traps
The biggest trap is mixed units: inches with feet, minutes with hours, ounces with gallons. Convert first, then compute. Another is percent change: a 20% increase is not undone by a 20% decrease. Watch for distractors built from the wrong operation - for example, multiplying when the question asks how much is needed to fill a partially full tank. Do not round in the middle of a multi-step problem; carry the value and round at the end. Check whether the question asks for a total, a difference, or a rate.
Worked example
A 500-gallon booster tank is three-quarters full. How many gallons are needed to fill it? Step 1: amount in tank = 500 × 0.75 = 375 gallons. Step 2: gallons needed = 500 − 375 = 125 gallons. Trap: choosing 375, which is the amount already in the tank, not the amount needed. Estimate first: one-quarter of 500 is 125, so the answer is plausible.
Rule of thumb
Write the units beside every number, state the formula in words, estimate the answer, then calculate. If two answers differ only by a unit conversion, you have found the trap.