Commutative Law of Addition (Math Quiz and Tutorial)

commutative laws of addition and multiplication
The commutative laws of addition and multiplication allow one to swap the order of the terms and still get the same results.

!! If you are familiar with the elementary concepts of the commutative law of addition, e.g. because you have taken the quiz before, YOU MAY SKIP THE THEORY PART and head down to take the math quiz and test your knowledge !!


The Commutative Law of Addition allows one to change the order of numbers when adding them, or to say it in other words:
You can swap numbers and still get the same results when you add things!
In elementary arithmetics the associative law applies to addition and subtraction.

CAUTION: The commutative law does not apply to subtraction and division!!


a + b = b + a

Example: 2 + 8 = 8 + 2
Benefit: At first you might think applying the commutative law of addition is of no use, but often when you have more than 2 terms and in combination with other arithmetic laws (e.g. the associative law), this can be a real time-saver.

Another example of the commutative law in combination with the associative law that demonstrates this last aspect more clearly:

115 + 746 + 17 + 254 + 25 + 43          (now swap terms : commutative law)
= (115 + 25) + (746 + 254) + (17 + 43)          (now regroup terms : associative law)
= 140 + 1000 + 60          (now swap terms again : commutative law)
= (140 + 60) + 1000
= 200 + 1000
= 1200

In everyday-life situations we usually apply the commutative law of addition intuitively and in combination with two other laws: the associative and distributive laws of elementary arithmetics.
All three laws combined can speed up your mental arithmetics significantly. It is therefore recommended that you also read those related articles and take the quizzes to freshen up your knowledge and make it a routine behavior to look out for terms that can be regrouped, swapped or factored out (distributive law) to facilitate calculations.


In the following a quiz with a variety of questions that test your knowledge and skill level in applying the commutative law of addition. Do not use a digital calculator, but try to solve the questions in your head.


Once you push the button below the clock starts ticking!!

Click the button to take the test!

This quiz must be completed in 3 minutes.