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1.8 Order of Operation

ORDER OF OPERATION

Some math problems are a mixture of addition, subtraction, division, and multiplication. An operation to be performed might be true for one item but not another, so parentheses are used () for clarification.

There is a specific order to follow when making calculations.

The order in which operations are performed is:

  1. Parentheses: ( )
  2. Exponents: 23
  3. Multiplication and division
  4. Addition and subtraction
  5. Left to right

Note: It is always useful to add parentheses to clarify the order.

Example 1 - Solve 10 + 10 ÷ 10

Step 1. Division is performed before addition.
10 ÷ 10 = 1

Step 2. Add.
10 + 1 = 11

10 + 10 ÷ 10 = 11

The same example can be rewritten:
10 + 10 ÷ 10
10 + (10 ÷ 10). Using the parentheses helps clarify the order of operation.

Example 2 - Solve 63 ÷ (10 - 8)2 ÷ 2 + 2

Step 1. Parentheses.
63 ÷ (10 - 8)2 ÷ 2 + 2 = 63 ÷ 22 ÷ 2 + 2

Step 2. Exponents.
216 ÷ 4 ÷ 2 + 2

Step 3. Division in order from left to right.
216 ÷ 4 = 54
54 ÷ 2 = 27

Step 4. Addition.
27 + 2 = 29

63 ÷ (10 - 8)2 ÷ 2 + 2 = 29 

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Date: December 19, 2024
Contact: Water Scooper Operations Unit

The NWCG Standards for Water Scooping Operations, PMS 518 establishes the standards for dispatching, utilizing, and coordinating water scooping aircraft on interagency wildland fires. These standards should be used in conjunction with the NWCG Standards for Aerial Supervision (SAS), PMS 505, and any local, state, or geographic/regional water scooping plans.

References:

NWCG Standards for Water Scooping Operations, PMS 518

Updated NWCG Standards for Aerial Supervision, PMS 505

Date: December 19, 2024
Contact: Interagency Aerial Supervision Subcommittee

The Interagency Aerial Supervision Subcommittee has updated the NWCG Standards for Aerial Supervision, PMS 505. PMS 505 establishes standards for aerial supervision operations for national interagency wildland fire operations. 

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NWCG Standards for Aerial Supervision, PMS 505

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Date: December 3, 2024
Contact: NWCG TRAINING

Two new job aids are now available: Packing List for Wildland Fire Fireline Personnel, J-101 and Packing List for Wildland Fire Support Personnel, J-102, should serve as a baseline for items needed on a wildland fire assignment. These lists will help personnel prepare for a 14 to 21-day assignment on the fireline or in a support role.

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Job Aid Catalog

NWCG Packing List for Wildland Fire Fireline Personnel, J-101

NWCG Packing List for Wildland Fire Support Staff, J-102

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Date: November 14, 2024
Contact: Equipment Technology Committee

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This Safety Warning is intended to highlight the details and recommended procedures for the installation of a Stihl chainsaw toolless fuel cap, as well as how to identify and correct a misaligned, damaged, or broken fuel cap to help prevent fuel spillage.

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NWCG Safety Warning: 24-001 Stihl Chainsaw Toolless Fuel Cap Spill Prevention

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