Basic Arithmetic: Rates, Percentages, and Unit Sense
What this domain tests
Basic arithmetic is tested without a calculator and with fire-service framing: flow rates, tank duration, elapsed time, percentages, averages, ratios, and unit conversion. Accuracy depends on setting up the operation and keeping units attached, not on speed alone.
Core operations
- Rate multiplied by time equals total: rate x time = total. Rearrange to time = total / rate or rate = total / time.
- Percent: part = percent x whole. A percent increase uses a multiplier greater than 1; a decrease uses one less than 1.
- Average = sum / count. Do not average averages unless the groups are the same size.
- Convert to one unit before calculating, and carry labels through each step.
- Cancel fractions before multiplying; convert decimals to percent by multiplying by 100.
Worked example
A 500-gallon tank feeds a line at 125 gallons per minute. After 3 minutes, how many gallons remain, and how much longer can the line flow at the same rate?
Reasoning: water used = 125 x 3 = 375 gallons. Remaining = 500 - 375 = 125 gallons. Remaining time = 125 / 125 = 1 minute. Answer: 125 gallons remain, enough for 1 more minute.
The trap is reporting 375 gallons as remaining, which is the amount used. Another trap is dividing 500 by 125 to get 4 minutes and stopping; that is total duration, not remaining duration after 3 minutes.
Traps that cost marks
- Mixing gallons with gallons per minute.
- Taking a percent of a percent without a reason.
- Rounding early and carrying the error forward.
- Answering the quantity that is asked for in the setup rather than the question.
- Skipping the unit check that would expose a wrong operation.