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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

Updated NWCG Standards for Fire Unmanned Aircraft Systems Operations, PMS 515

Date: May 10, 2024
Contact: IFUASS Qualification and Curriculum Board (IFUASS) 

The 2024 revision of the NWCG Standards for Fire Unmanned Aircraft Systems Operations, PMS 515 is now available. PMS 515 standardizes the processes and procedures for interagency use of Unmanned Aircraft Systems (UAS), including pilot inspections and approvals. This publication is now available as a PDF for easy use offline.

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Date: May 10, 2024
Contact: Aitor Bidaburu 

The purpose of this memorandum is to provide NWCG direction for removal of the Type 1 Command and General Staff (C&G) incident position qualification pathways to transition to Complex Incident Management (CIM). Responders may continue to utilize available NWCG pathways to attain Type 1 C&G qualifications until December 31, 2024.

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Memorandum 24-003

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2024 Professional Reading Program

Date: April 26, 2024
Contact: Wildland Fire Leadership Development Program (WFLDP) 

The Wildland Fire Leadership Development Program is announcing the 2024 Professional Reading list! The intent of the Professional Reading Program is to promote the reading and discussion of these books throughout the year. Discussion guides are provided and the corresponding Wildland Fire Leadership Levels have been identified.

The five books chosen for this year are: Young Men and Fire by Norman Maclean, The Wisdom of the Bullfrog by William H. McRaven, The Art of Clear Thinking by Hasard Lee, Emotional Agility by Susan David, and Writing to Persuade by Trish Hall.

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The National Wildfire Coordinating Group (NWCG) has migrated the training catalog from the NWCG website to the Wildland Fire Learning Portal (WFLP) as part of our ongoing efforts to streamline processes and improve efficiency. To facilitate this transition, the training catalog remains available on www.nwcg.gov through April 2024.

Starting May 2024, the training catalog will no longer be accessible on www.nwcg.gov. However, you can still access the complete training catalog by logging in as a guest to the WFLP.

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