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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

The Incident Position Standards and Next Generation Position Task Book are now available for Status/Check-In Recorder (SCKN)

Date: August 27, 2024
Contact: Incident Planning Subcommittee 

NWCG is excited to announce that the NWCG Incident Position Standards for Status/Check-In Recorder, PMS 350-32, NWCG Position Task Book for Status/Check-In Recorder (SCKN), PMS 311-32, and Checking In Resources Customer Service Job Aid, J-111 are now available.

The Performance Support Package, which for SCKN includes the Incident Position Standards, Next Generation Position Task Book, and job aid were developed through the Incident Performance and Training Modernization (IPTM) effort. The Performance Support Package will support trainees, those qualified in the position, and evaluators.

References:

NWCG Status/Check-In Recorder Position Page

NWCG Incident Position Standards for Status/Check-In Recorder, PMS 350-32

NWCG Position Task Book for Status/Check-In Recorder (SCKN), PMS 311-32

Checking In Resources Customer Service Job Aid, J-111

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Date: July 26, 2024
Contact: Risk Management Committee 

NWCG is excited to announce that the NWCG Incident Position Standards for Safety Officer, Field, PMS 350-81 and NWCG Position Task Book for Safety Officer, Field (SOFF), PMS 311-81 are now available.

The Safety Officer, Field (SOFF) is responsible for monitoring operations on an incident from a risk management perspective to provide for the welfare of incident resources and the public. The new Incident Position Standards and Next Generation Position Task Book are developed through the Incident Performance and Training Modernization (IPTM) effort.

References:

NWCG Safety Officer, Field (SOFF) Position

NWCG Incident Position Standards for Safety Officer, Field, PMS 350-81

NWCG Position Task Book for Safety Officer, Field (SOFF), PMS 311-81

Updated NWCG Standards for Electronic Documentation (eDoc), PMS 277

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Contact: Incident Planning Subcommittee 

The Incident Planning Subcommittee has updated the NWCG Standards for Electronic Documentation (eDoc), PMS 277.

The NWCG Standards for Electronic Documentation (eDoc) establishes the standards for collection and retention of records on wildland fires. This July 2024 update will provide incident management teams the most current standards required to maintain incident records and submit them to host units at the close of an incident.

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NWCG Standards for Electronic Documentation (eDoc), PMS 277

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Date: July 24, 2024
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The Mobile Fire Equipment Subcommittee has released Equipment Bulletin 24-002 NWCG Off-Highway Vehicle (OHV) Typing Standard - Request for Comment. This bulletin outlines the proposed NWCG OHV typing standard, as well as the business need for establishing the standard. Comments on the proposed standard will be accepted through August 15th using the comment form linked below.

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ETC-EB-2024-02: NWCG Off-Highway Vehicle (OHV) Typing Standard - Request for Comment

NWCG Off-Highway Vehicle (OHV) Typing Standard Comment Form