Firefighter Math Test: Practice Questions, Answers and Prep Guide

A firefighter math test measures whether you can solve the basic numerical problems commonly found on firefighter written exams.

Firefighter math questions usually do not require advanced algebra or calculus. They test practical math skills used in public safety work, such as:

• basic arithmetic;
• fractions;
• decimals;
• percentages;
• ratios;
• averages;
• time calculations;
• distance and speed;
• unit conversions;
• word problems;
• charts and tables;
• measurement;
• practical fireground-style reasoning.

Recommended prep:

These are original firefighter math practice questions for study purposes. They are not official questions from any fire department, civil service commission or test provider.

What Is on the Firefighter Math Test?

Firefighter math questions may appear as part of a broader firefighter written exam.

Common topics include:

Math Topic	What It Tests
Addition and subtraction	Basic calculations and counts
Multiplication and division	Totals, rates and quantities
Fractions	Parts of a whole, measurements and comparisons
Decimals	Measurement and practical calculations
Percentages	Increases, decreases and proportions
Ratios	Comparing quantities
Averages	Finding the mean
Time	Schedules, elapsed time and response timing
Distance	Travel, route and spacing calculations
Speed	Distance ÷ time
Measurement	Feet, inches, gallons, pounds and other units
Word problems	Translating a scenario into math
Tables and charts	Reading data accurately

The main challenge is usually not the difficulty of the math. It is reading carefully and choosing the correct operation under time pressure.

Firefighter Math Practice Test

Answer each question before checking the explanation.

Recommended timing:

25 questions
25 minutes

For a harder timed drill:

25 questions
18 minutes

Section 1: Basic Arithmetic

Question 1: Addition

A fire station has 18 helmets in one storage room and 27 helmets in another. How many helmets are there total?

• A. 35
• B. 40
• C. 45
• D. 50

Answer and Explanation

Correct answer: C. 45

18 + 27 = 45

There are 45 helmets total.

Question 2: Subtraction

A supply room has 96 gloves. Firefighters use 38 gloves during training. How many gloves remain?

• A. 48
• B. 52
• C. 58
• D. 62

Answer and Explanation

Correct answer: C. 58

96 - 38 = 58

Question 3: Multiplication

A fire engine carries 6 air cylinders in each compartment. There are 4 compartments. How many air cylinders are carried?

• A. 20
• B. 22
• C. 24
• D. 26

Answer and Explanation

Correct answer: C. 24

6 × 4 = 24

Question 4: Division

A crew distributes 84 water bottles equally among 7 stations. How many bottles does each station receive?

• A. 10
• B. 11
• C. 12
• D. 14

Answer and Explanation

Correct answer: C. 12

84 ÷ 7 = 12

Section 2: Fractions and Decimals

Question 5: Fraction of a Quantity

A tank is filled to 3/4 of its 400-gallon capacity. How many gallons are in the tank?

• A. 250
• B. 275
• C. 300
• D. 350

Answer and Explanation

Correct answer: C. 300

Find 3/4 of 400:

400 ÷ 4 = 100
100 × 3 = 300

Question 6: Fraction Remaining

A crew uses 1/3 of a 90-foot hose section during a drill. How many feet are used?

• A. 20
• B. 25
• C. 30
• D. 35

Answer and Explanation

Correct answer: C. 30

90 ÷ 3 = 30

Question 7: Decimal Addition

A firefighter records hose lengths of 12.5 feet and 8.75 feet. What is the total length?

• A. 20.25 feet
• B. 21.25 feet
• C. 21.75 feet
• D. 22.25 feet

Answer and Explanation

Correct answer: B. 21.25 feet

12.50 + 8.75 = 21.25

Question 8: Decimal Multiplication

A piece of equipment weighs 4.5 pounds. Four identical pieces are loaded. What is the total weight?

• A. 16 pounds
• B. 17 pounds
• C. 18 pounds
• D. 19 pounds

Answer and Explanation

Correct answer: C. 18 pounds

4.5 × 4 = 18

Section 3: Percentages

Question 9: Percentage of a Number

What is 25% of 160?

• A. 30
• B. 35
• C. 40
• D. 45

Answer and Explanation

Correct answer: C. 40

25% is one quarter.

160 ÷ 4 = 40

Question 10: Percentage Increase

A station completed 80 inspections last month and 100 inspections this month. What was the percentage increase?

• A. 20%
• B. 25%
• C. 30%
• D. 40%

Answer and Explanation

Correct answer: B. 25%

Increase:

100 - 80 = 20

Percentage increase uses the original value:

20 ÷ 80 × 100 = 25%

Question 11: Percentage Remaining

A 500-gallon tank is 60% full. How many gallons are in the tank?

• A. 200
• B. 250
• C. 300
• D. 350

Answer and Explanation

Correct answer: C. 300

0.60 × 500 = 300

Question 12: Discount / Reduction

A department reduces a 200-item inventory by 15%. How many items are removed?

• A. 20
• B. 25
• C. 30
• D. 35

Answer and Explanation

Correct answer: C. 30

15% of 200 = 0.15 × 200 = 30

Section 4: Ratios and Averages

Question 13: Ratio

A crew has 3 firefighters for every 1 officer. If there are 16 people total, how many are firefighters?

• A. 10
• B. 12
• C. 14
• D. 15

Answer and Explanation

Correct answer: B. 12

Ratio:

3 firefighters : 1 officer

Total parts:

3 + 1 = 4

Each part:

16 ÷ 4 = 4

Firefighters:

3 × 4 = 12

Question 14: Average

A firefighter completes four drills in 18, 22, 24 and 28 minutes. What is the average time?

• A. 21 minutes
• B. 22 minutes
• C. 23 minutes
• D. 24 minutes

Answer and Explanation

Correct answer: C. 23 minutes

Add the times:

18 + 22 + 24 + 28 = 92

Divide by 4:

92 ÷ 4 = 23

Question 15: Average With Total

A crew used 45 gallons, 60 gallons and 75 gallons of water during three drills. What was the average amount used per drill?

• A. 55 gallons
• B. 60 gallons
• C. 65 gallons
• D. 70 gallons

Answer and Explanation

Correct answer: B. 60 gallons

45 + 60 + 75 = 180
180 ÷ 3 = 60

Section 5: Time, Distance and Speed

Question 16: Elapsed Time

A drill begins at 9:20 a.m. and ends at 10:05 a.m. How long did it last?

• A. 35 minutes
• B. 40 minutes
• C. 45 minutes
• D. 50 minutes

Answer and Explanation

Correct answer: C. 45 minutes

9:20 to 10:00 = 40 minutes
10:00 to 10:05 = 5 minutes
Total = 45 minutes

Question 17: Schedule Time

A safety inspection starts at 1:35 p.m. and takes 50 minutes. What time does it end?

• A. 2:15 p.m.
• B. 2:20 p.m.
• C. 2:25 p.m.
• D. 2:30 p.m.

Answer and Explanation

Correct answer: C. 2:25 p.m.

1:35 + 25 minutes = 2:00
2:00 + 25 minutes = 2:25

Question 18: Speed

A fire vehicle travels 12 miles in 20 minutes. What is its speed in miles per hour?

• A. 24 mph
• B. 30 mph
• C. 36 mph
• D. 40 mph

Answer and Explanation

Correct answer: C. 36 mph

20 minutes is 1/3 of an hour.

If the vehicle travels 12 miles in 1/3 hour:

12 × 3 = 36 miles per hour

Question 19: Distance

A unit travels at 45 miles per hour for 20 minutes. Approximately how far does it travel?

• A. 10 miles
• B. 15 miles
• C. 20 miles
• D. 25 miles

Answer and Explanation

Correct answer: B. 15 miles

20 minutes is 1/3 of an hour.

45 × 1/3 = 15

The unit travels 15 miles.

Section 6: Measurement and Conversions

Question 20: Feet and Inches

A ladder is 18 feet long. How many inches long is it?

• A. 180 inches
• B. 192 inches
• C. 204 inches
• D. 216 inches

Answer and Explanation

Correct answer: D. 216 inches

There are 12 inches in 1 foot.

18 × 12 = 216

Question 21: Pounds

A supply box weighs 35 pounds. Six boxes are loaded onto a truck. What is the total weight?

• A. 180 pounds
• B. 190 pounds
• C. 200 pounds
• D. 210 pounds

Answer and Explanation

Correct answer: D. 210 pounds

35 × 6 = 210

Question 22: Capacity

A container holds 8 gallons. How many gallons do 7 containers hold?

• A. 48
• B. 54
• C. 56
• D. 64

Answer and Explanation

Correct answer: C. 56

8 × 7 = 56

Section 7: Word Problems

Question 23: Multi-Step Word Problem

A station has 240 feet of hose. During a drill, crews use 3 sections of 50 feet each. How many feet of hose remain unused?

• A. 80
• B. 90
• C. 100
• D. 110

Answer and Explanation

Correct answer: B. 90

Hose used:

3 × 50 = 150 feet

Remaining:

240 - 150 = 90 feet

Question 24: Inventory Word Problem

A fire department has 12 trucks. Each truck carries 4 extinguishers. After inspection, 7 extinguishers are removed for replacement. How many extinguishers remain on the trucks?

• A. 39
• B. 41
• C. 43
• D. 45

Answer and Explanation

Correct answer: B. 41

Initial extinguishers:

12 × 4 = 48

After removing 7:

48 - 7 = 41

Question 25: Practical Rate Problem

A crew can inspect 6 hydrants per hour. How many hydrants can the crew inspect in 4.5 hours?

• A. 24
• B. 25
• C. 27
• D. 30

Answer and Explanation

Correct answer: C. 27

6 × 4.5 = 27

Firefighter Math Test Answer Key

Question	Skill Tested	Correct Answer
1	Addition	C
2	Subtraction	C
3	Multiplication	C
4	Division	C
5	Fractions	C
6	Fractions	C
7	Decimals	B
8	Decimals	C
9	Percentages	C
10	Percentage increase	B
11	Percentages	C
12	Percentages	C
13	Ratios	B
14	Averages	C
15	Averages	B
16	Elapsed time	C
17	Schedule time	C
18	Speed	C
19	Distance	B
20	Unit conversion	D
21	Multiplication	D
22	Capacity	C
23	Word problem	B
24	Word problem	B
25	Rate problem	C

How to Solve Firefighter Math Questions

Use this process.

Step 1: Identify What the Question Asks

Before calculating, ask:

What do I need to find?

Examples:

• total;
• remaining amount;
• average;
• percentage;
• elapsed time;
• distance;
• speed;
• number of items;
• gallons;
• feet or inches.

Many mistakes happen because candidates solve the wrong problem.

Step 2: Circle or Note the Key Numbers

For example:

A station has 240 feet of hose.
Crews use 3 sections of 50 feet each.
How many feet remain?

Key numbers:

240
3
50

Step 3: Choose the Correct Operation

Question Wording	Likely Operation
total, combined, altogether	Add
remain, left, difference	Subtract
each, per, groups of	Multiply
shared equally, per unit	Divide
percent of	Multiply by percentage
average	Add, then divide
per hour	Rate
elapsed time	Time difference

Step 4: Solve in Steps

Do not try to solve multi-step word problems all at once.

Example:

12 trucks × 4 extinguishers = 48
48 - 7 removed = 41

Step 5: Check Units

Always check the unit in the answer:

• feet;
• inches;
• gallons;
• pounds;
• minutes;
• hours;
• miles;
• mph;
• items;
• people.

A correct number with the wrong unit can be wrong.

Firefighter Math Formulas to Know

Topic	Formula
Average	total ÷ number of values
Percentage of a number	decimal percentage × total
Percentage increase	increase ÷ original × 100
Speed	distance ÷ time
Distance	speed × time
Time	distance ÷ speed
Rate	total work ÷ time
Total work	rate × time
Remaining amount	starting amount - used amount
Ratio total parts	add ratio parts

Useful Percentage Shortcuts

Percentage	Shortcut
10%	Divide by 10
20%	Divide by 5
25%	Divide by 4
50%	Divide by 2
75%	Find 3/4
100%	Whole amount

Examples:

25% of 160 = 160 ÷ 4 = 40
50% of 90 = 90 ÷ 2 = 45
10% of 250 = 25

Common Firefighter Math Mistakes

Mistake 1: Misreading the Question

Example:

How many remain?

is different from:

How many were used?

Read the final sentence carefully.

Mistake 2: Using the Wrong Percentage Base

For percentage increase, use the original value.

Example:

80 to 100
Increase = 20
20 ÷ 80 = 25%

Do not divide by 100.

Mistake 3: Forgetting Unit Conversion

Example:

18 feet = 18 × 12 = 216 inches

Do not treat feet and inches as the same unit.

Mistake 4: Confusing Time Units

20 minutes is not 0.20 hours.

20 minutes is:

20 ÷ 60 = 1/3 hour

Mistake 5: Rushing Simple Arithmetic

Most firefighter math errors are not from difficult concepts.

They come from rushing:

96 - 38
35 × 6
240 - 150

Mistake 6: Skipping Intermediate Steps

Write or mentally separate steps in word problems.

This reduces mistakes.

Firefighter Math Topics by Exam Type

Different firefighter exams may emphasize different math skills.

Exam Style	Math Topics Often Tested
Civil service firefighter exam	Arithmetic, reading, practical word problems
FACT-style firefighter exam	Math, reading, mechanical aptitude, judgment
FireTEAM-style assessments	Math may appear in practical reasoning or written sections
Department-specific written exam	Basic math, charts, tables and job-related scenarios
Mechanical aptitude section	Ratios, force, distance, measurement and diagrams

Always check the official candidate guide for your exam.

Firefighter Math vs Mechanical Aptitude

Math and mechanical aptitude overlap, but they are not the same.

Firefighter Math	Mechanical Aptitude
Numbers, calculations and word problems	Tools, force, motion and mechanical principles
Example: 25% of 160	Example: which pulley requires less force
Uses arithmetic formulas	Uses diagram reasoning
Often practical and written	Often visual

Related guide:

• Firefighter Mechanical Aptitude

Firefighter Math vs Reading Comprehension

Math questions often require reading comprehension.

A candidate may know the arithmetic but still miss the question because they misread:

• total vs remaining;
• per hour vs total hours;
• increase vs decrease;
• gallons used vs gallons left;
• feet vs inches;
• minutes vs hours.

Related guide:

• Firefighter Reading Comprehension

How to Prepare for the Firefighter Math Test

Use this process:

1. Review basic arithmetic.
2. Practice fractions and percentages.
3. Practice averages and ratios.
4. Review time calculations.
5. Review distance, speed and rate.
6. Practice unit conversions.
7. Complete firefighter-style word problems.
8. Review mistakes by category.
9. Practice under time limits.
10. Take full firefighter written practice tests.

Recommended prep:

Best Firefighter Math Test Prep

JobTestPrep is useful for firefighter math preparation because it provides firefighter-style practice across written exam topics, including math, reading comprehension, mechanical aptitude and situational judgment.

Use JobTestPrep for:

• firefighter math practice;
• word problems;
• mechanical aptitude;
• reading comprehension;
• firefighter written exam practice;
• timed practice tests;
• answer explanations.

Recommended prep:

Free vs Paid Firefighter Math Practice

Prep Type	Best Use
Free math questions	Learn common formats
Official firefighter study guides	Confirm test topics
Arithmetic drills	Build fundamentals
Timed word problems	Build exam speed
Paid JobTestPrep	More firefighter-specific practice
Full firefighter practice tests	Build test readiness

Free resources are useful for basics. Paid prep is more useful when you need realistic firefighter exam practice and explanations.

7-Day Firefighter Math Study Plan

Day	Study Focus
Day 1	Diagnostic math test and arithmetic review
Day 2	Fractions, decimals and percentages
Day 3	Ratios, averages and word problems
Day 4	Time, distance and speed
Day 5	Measurement and unit conversions
Day 6	Timed firefighter math practice
Day 7	Review mistakes and take mixed firefighter practice

24-Hour Firefighter Math Study Plan

If your exam is tomorrow:

1. Review percentage shortcuts.
2. Practice 10 arithmetic questions.
3. Practice 10 word problems.
4. Review time and distance formulas.
5. Review feet-to-inches conversion.
6. Practice 5 average or ratio questions.
7. Take one timed mixed math drill.
8. Review wrong answers.
9. Rest.

Firefighter Math Test-Day Checklist

Before the exam, confirm:

[ ] I know whether calculators are allowed.
[ ] I know the math topics listed in the official guide.
[ ] I can calculate percentages.
[ ] I can solve average questions.
[ ] I can solve time and distance questions.
[ ] I can convert feet to inches.
[ ] I can solve basic word problems.
[ ] I have practiced under a timer.
[ ] I will read the final question carefully.
[ ] I will check units before answering.

Firefighter exam practice can support extra practice with explanations when you want more timed drills.

For additional preparation, pre-employment assessment practice may be useful when your invitation includes similar question types.

Before test day, mechanical aptitude test practice can help you rehearse timed sections and build answer consistency.

Firefighter exam practice can help candidates become familiar with common question formats before the live assessment.

When your hiring step includes mixed sections, pre-employment assessment practice can support broader review before test day.

Yes. Mechanical aptitude test practice can offer practice materials for similar assessment formats.

Firefighter exam practice can support extra practice with explanations when you want more timed drills.

For additional preparation, pre-employment assessment practice may be useful when your invitation includes similar question types.

Before test day, mechanical aptitude test practice can help you rehearse timed sections and build answer consistency.

Firefighter exam practice can help candidates become familiar with common question formats before the live assessment.

Related Firefighter Test Guides

Use these related pages to continue preparing:

Guide	Best For
Firefighter Practice Test	Full firefighter practice
Firefighter Written Exam	Exam overview
Firefighter Written Test Questions	More question examples
Firefighter Mechanical Aptitude	Tools, force and diagrams
Firefighter Reading Comprehension	Reading passages
Firefighter Situational Judgment	Judgment scenarios
Common Public Safety Test Mistakes	Mistakes to avoid
Public Safety Test Study Plan	Study schedule

Sources / Information to Verify Before Publication

Before publication, verify firefighter math test details with current official and provider sources.

Use sources such as:

• official firefighter exam announcement;
• official firefighter candidate guide;
• Louisiana firefighter study guide;
• Huntington FD FACT candidate guide;
• Peterson’s firefighter test prep;
• JobTestPrep firefighter exam sample questions;
• civil service firefighter exam guides;
• department hiring pages.

Verify:

• exact exam name;
• test provider;
• whether math is included;
• whether calculators are allowed;
• time limits;
• passing score;
• whether mechanical aptitude is included;
• whether reading comprehension is included;
• whether situational judgment is included;
• current JobTestPrep product contents;
• current affiliate URL;
• access duration and refund terms.

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