Basic Mathematics and Reasoning
Basic Mathematics and Reasoning tests practical arithmetic in corrections contexts: counts, percentages, ratios, time, averages, and simple word problems. You do not need advanced math, but you must set up the problem correctly and check units.
Core rules
- Identify what is asked and the units. Convert hours to minutes, or days to shifts, before calculating.
- Use order of operations: parentheses, exponents, multiplication/division left to right, addition/subtraction left to right.
- For percentages, convert to decimals or use part = percent × whole.
- For averages, add then divide by the number of items; do not average averages.
- For ratios, keep the same units on both sides.
- Round only at the end unless the question specifies otherwise.
Worked example
A unit has 240 inmates. A memo states 15 percent are on restricted movement. How many are on restriction? Reasoning: 15 percent = 0.15. 0.15 × 240 = 36. Check: 10 percent is 24; 5 percent is 12; 24 + 12 = 36. The answer is 36 inmates. A second check: 36/240 = 0.15, so the percentage is correct.
Traps
- Mixing calendar and working days.
- Calculating a percentage increase by adding the percent to the original number incorrectly.
- Averaging totals instead of individual values.
- Losing a zero when multiplying decimals.
- Answering with the wrong unit, such as hours instead of shifts.