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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

EMC Memo 25-001: Interim Rapid Extraction Module (REMS) Training and Qualification Requirements

Date: June 3, 2025
Questions?  Please contact:
Emergency Medical Committee

The Emergency Medical Committee has issued interim guidance for Rapid Extraction Module Support (REMS) teams. Until further notice, Type I and II REMS teams must designate a team leader qualified at Firefighter Type 1 Squad Boss (FFT1) or higher. This temporary change replaces the Single Resource Boss (SRB) requirement, which is currently not feasible due to administrative barriers.

This memorandum does not include any other changes to the NWCG Standards for Rapid Extraction Module Support, PMS 552. This interim change takes effect immediately and will remain in place until further notice.

References:

EMC Memo 25-001: Interim Rapid Extraction Module (REMS) Training and Qualification Requirements

NWCG Standards for Rapid Extraction Module Support, PMS 552

Equipment Bulletin 25-002: Chaps, Chain Saw, M-2020, Nonconformities Affecting Use, Appearance, and Serviceability

Date: June 2, 2025
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Equipment Technology Committee

The Equipment Technology Committee issued Equipment Bulletin: 25-002 to address a manufacturing nonconformity affecting Forest Service specification, 6170-4K Chain Saw Chaps. The issue applies to chaps manufactured in 2024 and 2025 and distributed through FedMall. These chaps may have incorrectly bound edges that expose inner protective layers.

Independent purchasers should inspect all chain saw chaps received from FedMall beginning in 2024, prior to use. Review the full Equipment Bulletin: 25-002 for inspection criteria and recommended actions.

References:

NWCG Alerts

ETC Equipment Bulletin: 25-002

2024 Wildland Fire Emergency Medical Service Awards

Date: May 22, 2025
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Emergency Medical Committee

The NWCG Emergency Medical Committee (EMC) is proud to announce the recipients of the 2024 Wildland Fire Emergency Medical Service Awards. Each year, EMC recognizes individuals and groups who have demonstrated exceptional actions or accomplishments that go above and beyond their normal mission or job duties.

Congratulations to all the awardees and nominees. Through leadership and initiative, they have made significant contributions to the safety and well-being of the wildland fire community. These honors are well deserved.

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2024 Wildland Fire EMS Awards

NWCG Emergency Medical Committee

NWCG Welcomes the Incident Management Teams Association as an Associate Member

Date: May 21, 2025
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https://www.nwcg.gov/contact-us

The NWCG Executive Board is honored to announce that the Incident Management Teams Association (IMTA) has joined the National Wildfire Coordinating Group as an associate member.

IMTA is a dedicated group of incident management professionals committed to enhancing the profession by promoting standards and fostering collaboration across federal, state, local, Tribal, and private sector partners throughout all phases of incident management.

“Joining NWCG aligns with our mission to elevate incident management professionals nationwide,” said Dr. Randal Collins, President of IMTA. “This is a proud moment for all of us committed to advancing public safety.”

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Incident Management Teams Association

National Wildfire Coordinating Group