Skip to main content

1.4 Multiplication

MULTIPLICATION: A SHORTCUT TO REPEATED ADDITION

Multiplication is a simpler way of doing repeated addition. Suppose Ron can do 30 push-ups in one minute. If he maintained a steady pace, how many push-ups could he do in five minutes? You could add 30 + 30 + 30 + 30 + 30, or you could multiply 30 × 5 to arrive at the answer of 150 push-ups. Some words and symbols used in multiplication are times, the product of, the "×" sign, or a dot like "•". Sometimes numbers that are being multiplied will be put in parentheses (30)(5)=150. 

Example 1 - Each person on your six-person crew is carrying five quarts of water. How many quarts of water does your crew have in total? 

multiplication graphic


The multiplication problem would be 5 × 6 = 30.
This process is the same as adding 5 six times.

When larger numbers are involved, multiplication is much easier than the repeated addition.

Example 2 - Multiply 17 by 63.

multiplication example 

Step 1. Multiply the top number by the number in the ones spot, which is 3.
17 × 3 = 51

Step 2. Multiply by the number in the tens spot, or 60, by putting a "0" in the ones place and multiplying 17 × 6.
17 × 60 = 1020

Step 3. Add these together.
17 × 63 = 51 + 1020 = 1071

Example 3 - Multiply 374 × 261.

Follow the same steps as shown above.

Step 1. Multiply 374 by 1.

Step 2. Multiply by 60. Put a "0" in the ones place and then multiply 374 by 6.

Step 3. Multiply by 200. Put "0" in the ones and tens places and then multiply 374 by 2.

Step 4. Add the numbers. 
374 + 22,440 + 74,800 = 97,614


The answer to 374 × 261 is 97,614. 
 

MULTIPLYING SIGNED NUMBERS

When multiplying two numbers with the same sign, the answer will be a positive number. A positive number times a positive number always gives a positive answer.
5 × 5 = 25
4 × 8 = 32
2 × 6 = 12

A negative number times a negative number always gives a positive answer.
-5 × (-5) = 25
-5 × (-10) = 50
-9 × (-7) = 63

A positive number times a negative number always gives a negative answer.
5 × (-5) = -25
-70 × 8 = -560
24 × (-2) = -48

 

NWCG Latest Announcements

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

Incident Position Standards and the Next Generation Position Task Books Now Available for ICT5 and FFT1

Date: July 29, 2025
Questions?  Please contact:
Incident Command Subcommittee
Incident Operations Subcommittee

NWCG is excited to announce that Incident Position Standards and the Next Generation Position Task Books are now available for Incident Commander Type 5 (ICT5) and Firefighter Type 1 Squad Boss (FFT1).

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 Incident Commander Type 5 Position Page

NWCG Firefighter Type 1 Squad Boss Position Page