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Firefighter Math: 1.9 Fractions

FRACTIONS: BITS AND PIECES

Fractions are used often, for instance when adding leftover pails of foam or mixing gas and oil for chain saw fuel. Fractions allow the use of parts of a number or combinations of parts and whole numbers, such as  half, two and a half, or two eights. The remainder found in long division can be changed to a fraction. Like whole numbers, fractions can be added, subtracted, divided, and multiplied. Fractions can also be represented as decimals (see Section 1.6).

A fraction consists of a numerator (top number) and a denominator (bottom number).

The numerator represents the number of parts available.

The denominator represents the number of parts in a whole.

Example 1 - What fraction of the box in the figure below is shaded? What fraction is not shaded?

fraction example

The box is divided into five parts. Two of those five parts are shaded. The shaded fraction represents two fifths. In this case, two fifths of the figure is shaded.
Three of the five parts are not shaded. The unshaded fraction represents three fifths. In this case, three fifths of the figure is not shaded.

WHOLE NUMBERS AS FRACTIONS

Fractions can also describe whole numbers or a whole number with a remainder expressed as a fraction. For example, a whole number can be written as: 

four over two, eight over four, or thirty-two over sixteen

 

The whole number 1 can be written as:

one over one, three over three, seven over seven, etc.

Fractions larger than 1 have a larger number in the numerator or top part of the fraction.

four thirds, eight fifths, and three seconds are all larger than 1.

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