Skill: Apply the commutative property

Explanation and Free Practice Resources

The commutative property establishes that changing the order of addends or factors does not change the sum or product: $a+b=b+a$ and $a\times b=b\times a$ for whole numbers. It supports efficient mental calculation and recognizing equivalent expressions, while distinguishing operations for which the property does not hold, such as subtraction and division; this scope does not extend to more abstract algebraic structures.

On this page:

Learn “Apply the commutative property” with a detailed explanation of the concept
Master “Apply the commutative property” with unlimited, free practice problems
Download (or modify) a free worksheet on Apply the commutative property you can use at home or in class with practice problems that scaffold and explore “Apply the commutative property” from different perspectives.
Start working on adaptive units like “Multiplication - 2 Digit” that introduce, teach, or practice “Apply the commutative property” to maximize your learning.

Detailed Explanation: Apply the commutative property

The commutative property means you can change the order of numbers in addition or multiplication without changing the answer.

Addition: $a+b=b+a$
Multiplication: $a\times b=b\times a$

Example: Find $4\times 25$ .

Switch the order of the factors:

4\times 25=25\times 4

Multiply:

25\times 4=100

So,

4\times 25=100

Changing the order can make a problem easier to solve mentally. Remember, this property works for addition and multiplication, but not generally for subtraction or division.

Learn by doing: Apply the commutative property

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Your results

Practice with unlimited practice problems

Multiplication - Commutative Property

Earned ?

Download/Modify Free Grade 6 'Apply the commutative property' Worksheet

Print this free 'Apply the commutative property' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.

Units Teaching This Skill

These adaptive units introduce, teach, or reinforce this skill (Apply the commutative property) through scaffolded problems that grow in difficulty as concepts are understood.