Skip to main content

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

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

Date:  April 1, 2026
Questions? 
Please contact: Leadership Committee

NWCG is excited to announce that Quarter Three 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 Three materials focus on Leadership Level 3: Leader of People (Develop Intent). Leadership Level 3 is where your values, your team, and your influence come together. Leaders of People put their teams first, build trust, and lead with authenticity. They mentor future leaders and shape decisions up and down the chain.

References:

2025/2026 NWCG Leadership Campaign - Leadership Levels

Wildland Fire Leadership Development Program

Leadership Committee

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