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

NEW! NWCG Wildland Urban Interface Mitigation Field Guide, PMS 053

Date: March 12, 2025
Contact: Wildland Urban Interface Mitigation Committee

The NWCG Wildland Urban Interface Mitigation Field Guide, PMS 053 provides mitigation practitioners at all experience levels with recommendations on the most effective and efficient ways to accomplish mitigation work in communities at risk to wildfire damage or destruction. The content in this guide was written in coordination with the NWCG Standards for Mitigation in the Wildland Urban Interface, PMS 052.

References:

NWCG Wildland Urban Interface Mitigation Field Guide, PMS 053 

Updated, NWCG Standards for Wildland Fire Module Operations, PMS 430

Date: March 11, 2025
Contact: Fire Use Subcommittee
Wildland Fire Module Unit

The NWCG Standards for Wildland Fire Module Operations, PMS 430 standardizes procedures and expectations for Wildland Fire Modules (WFMs). These standards are to be used by staff, supervisors, specialists, and technicians for planning, administering, and conducting WFM operations. These standards will also be used as a measure of WFM qualifications, capabilities, and expected performance, for both Type 1 and Type 2 WFMs.

References:

NWCG Standards for Wildland Fire Module Operations, PMS 430

NEW! NWCG Standards for Airtanker Operations, PMS 514

Date: March 7, 2025
Contact: National Interagency Aviation Committee

The NWCG Standards for Airtanker Operations, PMS 514 establishes the standards for dispatching, utilizing, and coordinating airtankers on interagency wildland fires. These standards should be used in conjunction with the NWCG Standards for Aerial Supervision (SAS), PMS 505, NWCG Standards for Airtanker Base Operations (SABO), PMS 508, and any applicable agency plans.

References:

NWCG Standards for Airtanker Operations, PMS 514

Incident Position Standards and Next Gen Position Task Books Now Available for Dispatch Incident Positions

Date: March 5, 2025
Contact: National Coordination System Committee

NWCG is excited to announce that Incident Position Standards and Next Generation Position Task Books are now available for all six Dispatch positions:

  • Aircraft Dispatcher
  • Expanded Dispatch Coordinator
  • Expanded Dispatch Recorder
  • Expanded Dispatch Supervisory Dispatcher
  • Expanded Dispatch Support Dispatcher
  • Initial Attack Dispatcher

The Performance Support Packages for these positions, including the Expanded Dispatch Job Aid, J-601 and the Initial Attack and Aircraft Dispatcher Job Aid, J-602, were developed as part of the Incident Performance and Training Modernization (IPTM) effort. These resources support trainees, qualified personnel, and evaluators in their roles.

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

References:

NWCG Aircraft Dispatcher Position Page 

NWCG Expanded Dispatch Coordinator Position Page 

NWCG Expanded Dispatch Recorder Position Page 

NWCG Expanded Dispatch Supervisory Dispatcher Position Page 

NWCG Expanded Dispatch Support Dispatcher Position Page 

NWCG Initial Attack Dispatcher Position Page 

NWCG Job Aids