Pro tip from the firehouse: Reading Comprehension and Situational Judgment catch the most test-takers off guard — even candidates with fire or military backgrounds. Start there. They require a completely different mindset than memorizing facts.
Long Multiplication
Any two numbers. No calculator. Works every time.
Draw a line underneath. Always align by the RIGHTMOST digit.
Write result on first line. 2-digit result? Write ones, carry tens to next column.
The zero placeholder shifts your answer left — the most commonly forgotten step.
×10=add zero | ×5=×10 then halve | ×20=×2 then add zero | ×25=÷4 then ×100
Forgetting the zero placeholder on line 2. Without it, 940 becomes 94 and your entire answer is wrong.
Grid Method — No Carrying
Break apart, multiply 4 pieces, add. Easier for bigger numbers.
Long Division — DMSB
Divide → Multiply → Subtract → Bring down. Repeat until done.
Write that number above the bracket. If it doesn't go in, use more digits.
Remainder must be LESS than the divisor. If not, your quotient was too small.
"Does McDonald's Serve Burgers?" — Divide, Multiply, Subtract, Bring down. Say it before every step.
The Percent Triangle
One triangle, three formulas. Cover the unknown — the rest tells you what to do.
Cover what you want to find — the remaining two show the operation.
Convert % to decimal by dividing by 100 first.
10% = move decimal left 1. 20%=×2 5%=÷2 15%=10%+5% 1%=÷10 of 10%
"12% increase" → ×1.12. "12% of X" → ×0.12. These are completely different!
Ratios — Comparing Two Quantities
Resource allocation, staffing, flow rates — ratios are everywhere on this exam.
Always reduce first. 500:125 — both ÷ 125 = 4:1 instantly. The answer is 4. No long division needed.
Cross Multiplication
Two equal ratios. Solve for the unknown in 3 steps.
Direct: both go up together → A/B = C/D
Inverse: one up, other down → A×B = C×D
Worker/time = ALWAYS inverse.
Fractions ↔ Decimals ↔ Percents
Move between all three forms without a calculator.
3/4 → 3 ÷ 4 = 0.75
0.75 → 75%
35% → 0.35
The 5-Step Word Problem System
Use this on EVERY word problem. No exceptions.
Underline what you're solving for. Don't read the problem until you know the goal.
Extra numbers are intentional bait to confuse you.
1. Using ALL numbers instead of only what's needed.
2. Forgetting to convert units.
3. Solving for the wrong thing — re-read the question after solving.
Number Sequence Patterns
Write differences first. Never spot patterns visually — it's unreliable.
Constant ratio → geometric. Multiply to continue.
If neither works, check every OTHER term as its own sequence (+3, ×2, +3, ×2...).