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
The method that works for any two numbers — every time, no exceptions.
Draw a line underneath. Always line up from the rightmost digit — this is where most people slip up before they even start.
If your result is two digits, write the ones place and carry the tens digit to the next column. Write it small above so you don't lose it.
That zero is a placeholder that shifts your second row one column to the left. Skip it and your answer will be wrong every time. Write it first, no exceptions.
Do a quick estimate first to confirm you're in the right range — 47 × 23 is roughly 50 × 20 = 1,000. Your answer should be close to that.
× 10 → add a zero | × 5 → multiply by 10 then cut in half | × 20 → multiply by 2 then add a zero | × 25 → divide by 4 then multiply by 100
The zero placeholder on the second row. When you multiply by the tens digit, write a zero before your result. Without it, 940 becomes 94 and your whole answer is wrong. Write the zero first, every time.
Grid Method — No Carrying Required
If carrying trips you up, this method breaks any problem into four easy multiplications. Same answer, different path.
Long Division
Four steps on repeat: Divide, Multiply, Subtract, Bring down. Once the pattern clicks, it's just a loop.
Write that number directly above the bracket. If it doesn't fit into one digit, look at two digits instead.
Write that product underneath the digits you just divided into.
Your remainder must always be smaller than your divisor. If it isn't, your quotient digit was too small — go back and add one.
"Does McDonald's Serve Burgers?" — Divide, Multiply, Subtract, Bring down. Say it out loud before each step until the loop feels automatic.
Percentages
One triangle covers every percentage question on the exam. Learn the triangle once and all three types of percent problems become the same problem.
Cover whichever piece you're solving for. The two uncovered pieces tell you exactly what to do — the bottom two multiply each other, and the top piece divides.
Turn the percentage into a decimal first by dividing by 100. Then multiply. 35% becomes 0.35.
You know the piece and the percentage — divide to find the total it came from.
Divide the piece by the total, then multiply by 100 to convert back to a percentage.
10% = move the decimal one place left. From there: 20% = double it · 5% = cut it in half · 15% = add 10% and 5% · 1% = one-tenth of your 10%. Build almost any percentage in your head using just these steps.
"A 12% increase" means multiply by 1.12 — you're adding 12% on top of the original. "12% of X" means multiply by 0.12 — you're finding just that piece. The wording is almost identical. The math is completely different. Read carefully.
Ratios
A ratio is just a way of comparing two quantities. Once you write it as a fraction, the rest follows naturally.
This makes it easier to work with and simplify.
If both are even, start by dividing by 2. Keep going until you can't reduce further.
1 supervisor per 6 workers, 42 workers total → 42 ÷ 6 = 7 supervisors.
7 supervisors × 6 workers each = 42. If it matches your total, you're done.
Always reduce the ratio first. 500:125 — both divide by 125, giving you 4:1. The answer is just 4. No long division needed. Simplifying first saves time and cuts down on arithmetic errors.
Proportions
Two equal ratios with one unknown. Set it up, cross-multiply, and you're done in three steps.
Keep the same units on each side — speed over distance on both sides, cost over items on both sides.
Multiply across the equals sign, corner to corner.
Direct: both quantities go up or down together (more items = higher cost) → A/B = C/D
Inverse: one goes up while the other goes down (more workers = less time) → A × B = C × D
Worker-time problems are always inverse. No exceptions.
Fractions, Decimals & Percents
These three forms are all saying the same thing in different ways. Once you can move between them freely, a whole category of exam questions gets a lot easier.
3/4 → 3 ÷ 4 = 0.75. It's just division.
0.75 → 75%. Think of it as multiplying by 100.
35% → 0.35. You're dividing by 100.
18/24 → both divide by 6 → 3/4.
Word Problems
The method that works for every word problem on the exam — no matter how long or complicated it looks. Use it every time.
Underline or circle exactly what you're solving for. If you don't know the goal before you start reading, you'll get lost in the details.
Extra numbers in word problems are intentional distractions. Don't let them pull you off track.
Write "24 workers," "3 hours," "$15/hour" — not just the raw numbers. Labels prevent you from mixing up what goes where.
If 4 workers take 9 hours, 6 workers should take less — not more. If your answer feels off, go back and check.
1. Using every number in the problem instead of only the ones you need.
2. Forgetting to convert units before calculating (minutes vs. hours, feet vs. inches).
3. Solving for the wrong thing — re-read the question after you have an answer to make sure you answered what was actually asked.
Number Patterns & Sequences
Never try to spot patterns visually — you'll miss them half the time. Always write out the differences between terms first. The pattern almost always reveals itself immediately.
This turns a pattern question into simple subtraction, which is much harder to get wrong.
If that ratio is constant, it's geometric — keep multiplying by that number.
Write the differences of the differences to find the rule.
If none of the above work, check every other term as its own separate sequence. Some patterns alternate between two different rules — like +3, ×2, +3, ×2 — and you won't see it unless you look at odd and even positions separately.