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1.5 Division

DIVISION: DIVIDING INTO SMALLER PARTS

Division is used to split groups up into smaller sections. Suppose there are 24 pairs of gloves in the storage locker and you want to distribute them evenly among 8 crewpeople. How many pairs of gloves would each crewperson receive. Dividing 24 by 8 yields 3; each crewperson would receive 3 pairs of gloves. Some words and symbols often seen in division are divided by, into, the symbol "÷",and the symbol "/". Just as multiplication is thought of as repeated addition, division can be thought of as repeated subtraction.

Some terms used in division include:
Divisor - the number by which a larger number is divided.
Dividend - the sum or amount to be divided and distributed.
Quotient - the number resulting from the division of one number by another .
Remainder - the number left after division that is smaller than the divisor.

In the equation b/a = c, b is the dividend, a is divisor, and c is the quotient.


Example 1- There are 20 nozzles for 5 engines. If the nozzles were to be divided evenly for the engines, how many nozzles would go on each engine?

20 - 5 = 15 - 5 = 10 - 5 = 5 - 5 =0. In this case, 5 was subtracted from 20 a total of 4 times. The answer to 20 divided by 5 is written as 20 ÷ 5 = 4
 

Example 2 - Divide 15 by 4.
15 - 4 = 11 - 4 = 7 - 4 = 3
Because 4 cannot be subtracted from 3, the 3 is called the remainder and is noted by the symbol "R".

The remainder is never larger than the divisor. The divisor in this example is 4. So, 15 / 4 = 3 R 3

If these were fifteen nozzles for four engines on your district, four nozzles would go on three engines and only three nozzles would go on the last engine. 
 

LONG DIVISION FOR LARGER NUMBERS

Long division can be used when working with larger numbers. Here the repeated subtraction is done in a different way. To divide, start from the digit of highest place value and finish with the digit in the lowest place value. At each step, ask if there are multiples of the number in the answer. 

Example 3 - Divide 3654 by 5.

Division Example
Step 1. Start with the thousands digit in the number being divided. 5 is larger than 3, so move to the next step.

Step 2. Look at the hundreds place. Can 5 go into 36? Yes: 7 × 5 = 35. Fill in the ones and tens places with "0"s and subtract.

Step 4. Go to the tens place of the remainder (the number 154) that was subtracted in the previous step. Can 5 go into 15? Yes: 5 × 3 = 15. Fill in the "0" in the ones place and subtract

Step 5. Go to the ones place. Can 5 go into 4? No. 4 is smaller than 5. Put a "0" in the ones spot of the answer. There is a remainder of 4.

The answer to 3,654 ÷ 5 is written 730 R 4
To check the answer to this long division problem, multiply 730 × 5 to give 3,650. Adding the remainder of 4 gives 3654. The original dividend was 3654, so the answer is correct.
 

DIVIDING SIGNED NUMBERS

Dividing signed numbers follows the same general rules as multiplication. When dividing any two numbers having the same sign, the answer is positive, while that of two numbers of opposite sign is negative. When dividing numbers with like signs, the answer is positive. When dividing numbers with unlike signs, the answer is negative.
20 ÷ (-4) = -5
48 ÷ (-8) = -6
-100 ÷ (-10) = 10
-49 ÷ 11 = -4 R 5

 

NWCG Latest Announcements

FAQ Now Available for Archiving Type 1 and Type 2 Incident Positions

Date: Aug 6, 2025
Questions? Please contact:
Incident and Position Standards Committee

To support the transition to Complex Incident Management (CIM), NWCG will archive all Type 1 and Type 2 Command and General Staff (C&G) position qualifications in January 2026, as outlined in NWCG Executive Board Memo 25-002. To assist with this transition, a new Frequently Asked Questions (FAQ) document is now available.

This resource answers common questions about the status of Type 1 and Type 2 qualifications, impacts to incident qualification management, training requirements, and resource ordering considerations. Review the full FAQ to learn more.

For additional information on CIM and the transition of C&G positions, see NWCG Executive Board Memos 23-005, 24-005, and 25-002, as well as the Incident Workforce and Development Group webpage.

References:

NWCG Type 1 & Type 2 Position Archiving FAQ

NWCG Executive Board Correspondence

Incident Workforce Development Group

Incident and Position Standards Committee

Incident Position Standards and the Next Generation Position Task Books Now Available for UASD, UASM, UASL and UASP

Date: July 31, 2025
Questions?  Please contact:
Interagency Fire Unmanned Aircraft Systems Subcommittee
 

NWCG is excited to announce that Incident Position Standards and the Next Generation Position Task Books are now available for all four Unmanned Aircraft Systems positions:

  • Unmanned Aircraft Systems, Data Specialist (UASD)
  • Unmanned Aircraft Systems, Manager (UASM)
  • Unmanned Aircraft Systems, Module Leader (UASL)
  • Unmanned Aircraft Systems Pilot (UASP)

The Performance Support Packages for these positions were developed as part of the Incident Performance and Training Modernization effort. These resources support trainees, qualified personnel, and evaluators in their respective 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, scheduled for January 2026.

References:

NWCG Unmanned Aircraft Systems, Data Specialist Position Page

NWCG Unmanned Aircraft Systems, Manager Position Page

NWCG Unmanned Aircraft Systems, Module Leader Position Page

NWCG Unmanned Aircraft Systems Pilot Position Page

Incident Position Standards and the Next Generation Position Task Books Now Available for RADO and INCM

Date: July 30, 2025
Questions?  Please contact:
Incident Logistics Subcommittee
 

NWCG is excited to announce that Incident Position Standards and the Next Generation Position Task Books are now available for Radio Operator (RADO) and Incident Communications Center Manager (INCM).

The Performance Support Packages for these positions were developed as part of the Incident Performance and Training Modernization effort. These resources support trainees, qualified personnel, and evaluators in their respective 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, scheduled for January 2026.

References:

NWCG Radio Operator Position Page

NWCG Incident Communications Center Manager Position Page

ETC Equipment Bulletin: 25-004 NEW Aquatic Invasive Species – Golden Mussels

Date: July 29, 2025
Questions?  Please contact:
Equipment Technology Committee
 

The Equipment Technology Committee (ETC) issued Equipment Bulletin: 25-004, notifying the wildland fire community about a newly discovered invasive species and actions to take if found. Golden mussels, a highly invasive species recently identified in California, pose a significant risk to native ecosystems, infrastructure, and fire equipment. These mussels rapidly colonize hard and soft surfaces, including aquatic plants and fire equipment, clogging pipes, fouling motors, disrupting water systems, and impacting native species.

To help prevent their spread, fire personnel must follow the decontamination procedures outlined in the NWCG Guide to Preventing Aquatic Invasive Species Transport by Wildland Fire Operations, PMS 444. Additionally, report any sightings immediately to your Lead Resource Advisor and include clear, close-up photos and location details.

Read the complete ETC Equipment Bulletin: 25-004 to learn more. 

References:

NWCG Alerts

ETC Equipment Bulletin: 25-004

NWCG Guide to Preventing Aquatic Invasive Species Transport by Wildland Fire Operations, PMS 444