Commutative property


Certainly, in commutative property, we see the word commute which means exchange from the latin word commutare



The word exchange in turn may mean switch. For examples, washing my face and combing my hair is a good example of this property.

Another good example is doing my math homework and then finishing my science reading.

The important thing to notice in the two examples above is that the order we do things can be switched, so it does not matter or will never cause any problems or conflicts.

However, reading a math lesson and then answering the review questions is not commutative.

Here the order does matter because I have to read the lesson before knowing how to answer the review questions

In mathematics, we know that

2 + 5 = 5 + 2

12 + 4 = 4 + 12

-1 + 8 = 8 + -1

All the above illustrates the commutative property of addition. This means that when adding two numbers, the order in which the two numbers are added does not change the sum

All three examples given above will yield the same answer when the left and right side of the equation are added

For example, 2 + 5 = 7 and 5 + 2 is also equal to 7

The property is still valid if we are doing multiplication

Again, we know that

3 × 4 = 4 × 3

12 × 0 = 0 × 12

9 × 6 = 6 × 9

Again, 3 × 4 = 12 and 4 × 3 = 12

More examples: Take a close look at them and study them carefully

(3 + 2) × 4 = 4 × (3 + 2)

x + y = y + x

x × y = y × x

2 × x = x × 2

(x + z) × (m + n) = (m + n) × (x + z)

4 + y = y + 4

Warning! Although addition is commutative, subtraction is not commutative

Notice that 3 − 2 is not equal to 2 − 3

3 − 2 = 1 , but 2 − 3 = -1

Therefore, switching the order yield different results








Recent Articles

  1. How to estimate fractions

    Dec 11, 17 08:45 AM

    Learn how to estimate fractions with this easy to follow lesson.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest





Recent Lessons

  1. How to estimate fractions

    Dec 11, 17 08:45 AM

    Learn how to estimate fractions with this easy to follow lesson.

    Read More

  Our Top Pages

Formula for percentage

Compatible numbers

Basic math test

Basic math formulas

Types of angles

Math problem solver

Algebra word problems

Surface area of a cube

Finding the average 

Scale drawings

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 


Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

 Recommended

Scientific Notation Quiz

Types of Angles Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz