Skip to main content

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 

NWCG Latest Announcements

NWCG Equipment Technology Committee Releases Safety Warning: 25-001 Non-specification fire shelters

Date: January 15, 2025
Contact: Equipment Technology Committee

The Equipment Technology Committee (ETC) has released Safety Warning: 25-001 Non-specification fire shelters. Non-specification fire shelters claiming to meet Forest Service (FS) fire shelter specification 5100-606 were first found in February of 2023. As of September 2024, non-specification shelters are again being advertised and sold on the open market.

This Safety Warning outlines details and recommended procedures to purchase FS specification shelters made with materials and components that meet performance criteria and toxicity testing requirements outlined in FS Specification 5100-606. 

For additional information on identifying non-specification shelters, please view ETC Safety Warning 23-01.

References:

ETC Safety Warning 25-001: Non-specification fire shelters

NWCG Equipment Technology Committee

ETC Safety Warning 23-01

Paul Gleason Lead by Example Awards

Date: January 14, 2025
Contact: Leadership Committee

The NWCG Leadership Committee has awarded the 2023 Paul Gleason “Lead By Example” awards to individuals in the categories of Initiative and Innovation, Mentoring and Teamwork, and Motivation and Vision, as well as a Lifetime Achievement Award.

Congratulations to the awardees:

  • Sam Bowen, Superintendent of the Mark Twain Veteran Crew with the U.S. Forest Service.
  • Greg Titus, Zone Fire Management Officer for the St. Marks National Wildlife Refuge with U.S. Fish and Wildlife Service.
  • Renae Crippen, Manager of the Blue Mountain Interagency Dispatch Center with the U.S. Forest Service.
  • Eric Carlson, Instructor with OMNA International.

References:

Paul Gleason Lead by Example Award

Wildland Fire Leadership Development Program

Interview with Paul Gleason

Updated NWCG Standards for Water Scooping Operations, PMS 518

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. 

References:

NWCG Standards for Aerial Supervision, PMS 505