Commutative Law of Multiplication (Math Quiz and Tutorial)

commutative law of multiplication
5 x 2 = 2 x 5 : The commutative law of multiplication allows one to swap numbers and still get the same result.

!! If you are familiar with the elementary concepts of the commutative law of multiplication, 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 Multiplication allows one to change the order of numbers when multiplying them, or to say it in other words:
You can swap numbers and still get the same results when you multiply things!
In elementary arithmetics the commutative laws apply to multiplication and addition.

CAUTION: The commutative laws do not apply to subtraction and division!!


a • b = b • a

Example: 5 • 2 = 2 • 5
Explanation: 5 batches of 2 apples is the same as 2 batches of 5 apples (see picture above).
Benefit: At first you might think applying the commutative law of multiplication 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 that demonstrates this last aspect more clearly:

= 1000 200
= 200000

In everyday-life situations we usually apply the commutative law of multiplication 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 multiplication. 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.