Skip to main content

1.3 Subtraction

SUBTRACTION: COMPUTING A DIFFERENCE

Subtraction is used in two types of situations. The first is "How much is left?" and the second is "How much more is needed?" Some words used in subtraction are "minus", "take away", "less", and "difference".

Example 1 - How many are left? 
 

Subtraction


In the figure above, the fire station has 7 shovels. Mark "takes away" 3 shovels. How many shovels are left? 

Set up the problem as 7 shovels minus 3 shovels. The answer to 7 - 3 is 4 shovels.

SUBTRACTING LARGE NUMBERS

Example 2 - Subtracting numbers. Subtract 5342 from 9854.
subtraction example
As shown in the example above, first subtract the ones. Next, subtract the tens. Keeping moving from right to left, so next subtract the hundreds, and finally, subtract the thousands.
The answer to 9854 - 5342 is 4512.

"BORROWING" NUMBERS

As you subtract numbers in the ones, tens, hundreds, etc. position, you might find that the number being subtracted is larger than the one from which you are subtracting. In this case, "borrowing" from the next column to the left is necessary.

Example 3 - Subtract 932 minus 784.

First, subtract the number in the ones column. Because 4 cannot be taken away from 2, 1 ten must be borrowed to get 12 ones. Now take away 4 from 12 to get 8.
Move to the tens column. Because 8 cannot be taken away from 2, borrow 1 hundred to get 12 tens, and take away 8 from 12 to get 4.
Finally, we move to the hundreds column. There are 8 hundreds left and we will take away 7 to get 1. 
The answer to 932 - 784 is 148.

SUBTRACTING SIGNED NUMBERS

Signs are important in subtracting numbers. Subtracting a negative number changes the sign of the number subtracted. When subtracting a negative number, the subtraction sign and negative sign together produce a positive number. Subtracting a negative number therefore has the result of adding a positive number. See the examples below.

7 - (-3) = ? becomes 7 + 3 = 10.
50 - (-20) = ? becomes 50 + 20 = 70
84 - (+26) = ? becomes 84 - 26 = 58
192 - (-301) = ? becomes 192 + 301 = 493
-50 - (-20) = ? becomes -50 + 20 = -30 
In the last case, because a larger negative number (-50) was added to a smaller positive number (20), the end result was negative. See Chapter 1, Section 1.2 for more information on adding numbers of different signs.

 

NWCG Latest Announcements

2025-2026 Wildland Fire Leadership Campaign: "Leadership Levels" Now Available

Date: October 15, 2025
Questions? Please contact:
Leadership Committee

NWCG is excited to announce the release of the Leadership Committee’s 2025–2026 Leadership Campaign, themed “Leadership Levels.” 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.

The campaign is structured into four quarters and may be completed at any time between October 1, 2025 -December 31, 2026. Leadership levels will be released quarterly.

Quarter One materials are now available on the Wildland Fire Leadership Development Program website and focus on Leadership Level 1, Follower (Self-Leadership).

References:

2025/2026 NWCG Leadership Campaign - Leadership Levels

Wildland Fire Leadership Development Program

Leadership Committee

Updated! L-280, Followership to Leadership (Instructor-led) Course

Date: October 3, 2024
Questions? Please contact:
Leadership Committee

NWCG is pleased to announce the updated L-280, Followership to Leadership (Instructor-led) course is now available. L-280 is intended for operational personnel at the Firefighter Type 1 level, and for individuals pursuing Leadership Level 2, New Leader. 

This instructor-led course is a primer on leadership and the second formal course in the Wildland Fire Leadership Development Program. It helps emerging leaders build the confidence, skills, and mindset needed to lead effectively in high-risk environments. 

For more information about leadership development and available courses, visit the Leadership Committee Web Portal.

References:

L-280, Followership to Leadership (Instructor-led)

Wildland Fire Leadership Development Program

Wildland Fire Learning Portal

Equipment Advisory 25-01: Pre-2006 Fire Shelter Degradation and Discontinuation of Use

Date: Sept 26, 2025
Questions? Please contact:
Equipment Technology Committee 

The Equipment Technology Committee (ETC) has released Equipment Advisory 25-01: Pre-2006 Fire Shelter Degradation and Discontinuation of Use. This advisory recommends all pre-2006 fire shelters should be removed from service by January 1, 2026.

This advisory recommends firefighters and fire managers to:

  • Inspect fire shelters immediately
  • Replace and destroy any pre-2006 shelters (identified by white or pink insert label)
  • Order replacements as needed

For further details, please refer to the complete advisory. 

References:

Equipment Advisory 25-01: Pre-2006 Fire Shelter Degradation and Discontinuation of Use

NWCG Fire Inspection Flowchart, PMS 411-1

NWCG Alerts

NEW! S-219, Firing Operations (Blended) Now Available

Date: Sept 11, 2025
Questions? Please contact:
Fuels Management Committee 

The S-219, Firing Operations (Blended) course is now available on the Wildland Fire Learning Portal. Developed through the Incident Performance and Training Modernization (IPTM) effort, this training supports individuals working towards Firing Boss, Single Resource (FIRB) incident qualifications.

This blended course combines online and instructor-led training to provide students with the knowledge and skills required to perform the duties of the FIRB, as described in the NWCG Incident Position Standards for Firing Boss, Single Resource, PMS 350-105.

Any changes to qualification pathways will take effect with the next update of the NWCG Standards for Wildland Fire Position Qualifications, PMS 310-1, scheduled for January 2026.

References:

S-219, Firing Operations (Blended)

NWCG Firing Boss, Single Resource Position Page

Wildland Fire Learning Portal