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

Intermediate Faller (FAL2) Position Task Book Update

Date:  July 24, 2026
Questions? 
Please contact: Tree Felling Subcommittee

NWCG Operations Management Committee (OMC) has issued an update to the NWCG Position Task Book for Intermediate Faller (FAL2), PMS 311-91. To ensure clarity for both trainees and evaluators, the updated FAL2 Position Task Book (PTB) explicitly states who is authorized to sign off on your tasks:

“Evaluators must be qualified as a FAL2, or an Advanced Faller (FAL1).”

If you are currently working out of a previously published version of the FAL2 PTB, you do not need to restart. However, OMC highly encourages you to take the following step to prevent any confusion in the field:

  • Print and replace the updated evaluator information page (page 2) in your current physical PTB.

References:

Intermediate Faller (FAL2) Position Page

RMC Memo 26-01: Transition Plan for Implementing Updates to Intermediate Faller (FAL2) Position Qualifications

NWCG Position Task Book for Intermediate Faller (FAL2), PMS 311-91

Equipment Advisory 26-001: Potential Front Driveline Joint Failure on 2018 and Earlier Ram Pickups

Date:  July 10, 2026
Questions? 
Please contact: Equipment and Technology Subcommittee

The Logistics/Equipment Management Committee (LMC) has released Equipment Advisory 26-001: Potential Front Driveline Joint Failure on 2018 and Earlier Ram Pickups. This advisory highlights multiple U.S. Forest Service regions reporting front driveline joint failure incidents.

This advisory recommends firefighters and fire managers to: 

  • Follow all Ram-issued inspection, maintenance, and service guidance for front driveline joints. 
  • Consider installing a driveline loop. 
  • Coordinate with fleet managers and service providers to determine the most appropriate driveline loop kit for each pickup.

For further details, please refer to the complete advisory.

References:

Equipment Advisory 26-001: Potential Front Driveline Joint Failure on 2018 and Earlier Ram Pickups

Technical Service Bulletin: 03-002-21

NEW! NWCG Standard Operating Procedures, PMS 900

Date:  July 9, 2026
Questions? 
Please contact: NWCG Staff

NWCG is excited to announce the publication of the NWCG Standard Operating Procedures, PMS 900.

The new publication establishes general, consistent, and uniform standards for conducting business with the National Wildfire Coordinating Group.

References:

NWCG Standard Operating Procedures, PMS 900

Quarter Four Materials for the 2025-2026 Wildland Fire Leadership Campaign Now Available

Date:  July 8, 2026
Questions? 
Please contact: Leadership Development Subcommittee

NWCG is excited to announce that Fourth Quarter materials for the 2025/2026 Wildland Fire Leadership Campaign are now available. This annual initiative offers all students of leadership and wildland fire management an opportunity to engage with essential leadership skills and knowledge needed to lead effectively in dynamic environments.

Quarter Four materials focus on Leadership Level 4: Leader of Leaders (Provide Direction). Leadership Level 4 is where you are setting the conditions for others to do things well, even when you are not present. This quarter focuses on equipping experienced leaders with skills to provide direction, build trust across teams, and foster strong decision making. 

References:

2025/2026 NWCG Leadership Campaign - Leadership Levels

Wildland Fire Leadership Development Program

Leadership Development Subcommittee