Skip to main content

Firefighter Math: 1.4 Multiplication

MULTIPLICATION: A SHORTCUT TO REPEATED ADDITION

Multiplication is a simpler way of doing repeated addition. Suppose Ron can do 30 push-ups in one minute. If he maintained a steady pace, how many push-ups could he do in five minutes? You could add 30 + 30 + 30 + 30 + 30, or you could multiply 30 × 5 to arrive at the answer of 150 push-ups. Some words and symbols used in multiplication are times, the product of, the "×" sign, or a dot like "•". Sometimes numbers that are being multiplied will be put in parentheses (30)(5)=150. 

Example 1 - Each person on your six-person crew is carrying five quarts of water. How many quarts of water does your crew have in total? 

multiplication graphic


The multiplication problem would be 5 × 6 = 30.
This process is the same as adding 5 six times.

When larger numbers are involved, multiplication is much easier than the repeated addition.

Example 2 - Multiply 17 by 63.

multiplication example 

Step 1. Multiply the top number by the number in the ones spot, which is 3.
17 × 3 = 51

Step 2. Multiply by the number in the tens spot, or 60, by putting a "0" in the ones place and multiplying 17 × 6.
17 × 60 = 1020

Step 3. Add these together.
17 × 63 = 51 + 1020 = 1071

Example 3 - Multiply 374 × 261.

Follow the same steps as shown above.

Step 1. Multiply 374 by 1.

Step 2. Multiply by 60. Put a "0" in the ones place and then multiply 374 by 6.

Step 3. Multiply by 200. Put "0" in the ones and tens places and then multiply 374 by 2.

Step 4. Add the numbers. 
374 + 22,440 + 74,800 = 97,614


The answer to 374 × 261 is 97,614. 
 

MULTIPLYING SIGNED NUMBERS

When multiplying two numbers with the same sign, the answer will be a positive number. A positive number times a positive number always gives a positive answer.
5 × 5 = 25
4 × 8 = 32
2 × 6 = 12

A negative number times a negative number always gives a positive answer.
-5 × (-5) = 25
-5 × (-10) = 50
-9 × (-7) = 63

A positive number times a negative number always gives a negative answer.
5 × (-5) = -25
-70 × 8 = -560
24 × (-2) = -48

 

NWCG Latest Announcements

WFSTAR 2026 Core Components Module Package and 2025 Fire Year in Review Now Available

Date:  March 23, 2026
Questions? 
Please contact: Joe Schindel

The 2026 Core Components Module Package for RT-130, Wildland Fire Safety Training Annual Refresher (WFSTAR) and the 2025 Fire Year in Review are now available on the NWCG website. The 2026 Core Components Module Package provides all content needed to deliver RT-130.

References:

2026 Core Components Module Package

2025 Fire Year in Review Module

NEW! S-490, Advanced Fire Behavior Calculations (Blended) Available Now

Date:  March 17, 2026
Questions? 
Please contact: Fire Behavior Subcommittee

NWCG is pleased to announce that the new S-490, Advanced Fire Behavior Calculations (Blended), 2026 course is now available.

This training includes performance-based activities that allow students to apply the knowledge and concepts required for the Fire Behavior Analyst (FBAN), Long Term Fire Analyst (LTAN), and Prescribed Fire Burn Boss Type 1 (RXB1) positions. It supports individuals working towards these incident qualifications.

This blended course begins with a self-paced online training (OLT) in the Wildland Fire Learning Portal (WFLP), followed by an in-person instructor-led training (ILT).

References:

S-490, Advanced Fire Calculations (Blended)

NWCG Fire Behavior Analyst (FBAN) Position Page

NWCG Long Term Fire Analyst (LTAN) Position Page

NWCG Prescribed Fire Burn Boss Type 1 (RXB1) Position Page

2024 Paul Gleason Award Winners Announced

Date:  March 13, 2026
Questions? 
Please contact: Leadership Committee

The NWCG Leadership Committee is proud to announce the recipients of the 2024 Paul Gleason "Lead By Example" awards. Award categories include Initiative and Innovation, Mentoring and Teamwork, Motivation and Vision, as well as a Lifetime Achievement Award.

Congratulations to the awardees:

  • Justin Baxter, National Unmanned Aerial System (UAS) Operations Specialist, with the U.S. Forest Service — Initiative and Innovation
  • Kelly Woods, Director of the Wildland Firefighting Lessons Learned Center — Mentoring and Teamwork
  • Doug Booster, Instructor, ProHealth Net, Inc. — Motivation and Vision
  • Pam McDonald, Writer-Editor for the National Interagency Fire Center — Lifetime Achievement Award

References:

Paul Gleason Lead By Example Award

Wildland Fire Leadership Development Program (WFLDP)

Leadership Committee

NEW! S-231, Engine Boss Course Available Now

Date:  March 6, 2026
Questions? 
Please contact: Incident Operations Subcommittee

NWCG is pleased to announce the new S-231, Engine Boss (Single Resource) course is now available on the Wildland Fire Learning Portal (WFLP). Developed through the Incident Performance and Training Modernization (IPTM) effort, this training supports individuals working towards Engine Boss, Single Resource (ENGB) incident qualifications. 

This is a performance-based instructor-led training (ILT) that focuses on the application of ENGB responsibilities during wildland fire operations, emphasizing readiness, information gathering, risk management, engine tactics, and Wildland Urban Interface (WUI) operations. Trainees apply these skills through scenario-based group work and an optional field day that reinforces hands-on engine operation tasks. 

References:

S-231, Engine Boss (Single Resource) (Instructor-led)

NWCG Engine Boss, Single Resource (ENGB) Position Page

Wildland Fire Learning Portal