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 Standards for Wildland Fire Chainsaw Operations, PMS 212, and Next Generation Position Task Book for Basic Faller Are Now Available

Date: April 14, 2025
Questions?  Please contact:
Hazard Tree and Tree Felling Subcommittee

The updated NWCG Standards for Wildland Fire Chainsaw Operations, PMS 212, and NWCG Position Task Book for Basic Faller (FAL3), PMS 311-19 are now available.

The NWCG Standards for Wildland Fire Chainsaw Operations, PMS 212 includes position standards designed to be used in conjunction with the Next Generation Position Task Book (Next Gen PTB). The Next Gen PTB for Basic Faller (FAL3) includes an evaluation guide with suggested rating elements to consider when assessing trainees.

References:

NWCG Standards For Wildland Fire Chainsaw Operations, PMS 212

NWCG Position Task Book for Basic Faller (FAL3), PMS 311-119

NWCG Basic Faller (FAL3)

RMC Memo 25-01: Summary of Updates to Safety Officer Positions

Date: April 9, 2025
Questions?  Please contact:
RMC Member Eric Fransted

The Risk Management Committee (RMC) serves as the position steward for all Safety Officer incident positions and continues to improve position standards, training, and naming conventions. The implementation of Complex Incident Management (CIM) required changes to position titles. RMC collaborated with the NWCG Incident Position Standards Committee (IPSC) to propose and implement these updates. 

References:

RMC Memo 25-01: Summary of Updates to Safety Officer Positions 

NWCG Position Catalog

Updated, NWCG Guide to Wildland Fire Origin and Cause Determination, PMS 412

Date: April 8, 2025
Questions?  Please contact:
Wildland Fire Investigation Subcommittee

PMS 412 provides guidance for wildland fire investigations. This guide outlines recommended procedures, practices, techniques, and methods to promote a systematic approach. The last update to this publication was in 2016.

References:

NWCG Guide to Wildland Fire Origin and Cause Determination PMS 412

Updated NWCG Standards for Airtanker Base Operations, PMS 508

Date: March 31, 2025
Questions?  Please contact:
Airtanker Base Operations Unit

The updated NWCG Standards for Airtanker Base Operations (SABO), PMS 508 standardizes operations and procedures at interagency airtanker bases to ensure safe, efficient, and effective operations in support of interagency goals and objectives.

References:

NWCG Standards for Airtanker Base Operations, PMS 508