# Commutative Property of Multiplication

The commutative property of multiplication states that changing the order of the numbers or the factor being multiplied does not change the product. The first factor is called the multiplicand, while the other is the multiplier.

For any two numbers a and b, the generic formula is given by:

a × b = b × a

For example, multiplying 4 × 2 gives the same result as 2 × 4, i.e., 8. The concept can be more easily understood if we rearrange 4 rows of 2 blue balls into 2 rows of 4 orange balls. Both give the same result, as shown below:

Let us solve some more examples involving the commutative property of multiplication.

Find the value of x using the commutative property of multiplication.
a) 6 × 4 = x × 6
b) 0.4 × 0.7 = 0.7 × x
c) 8 × 10 × x = 6 × 10 × 8

Solution:

As we know, according to the commutative property of multiplication:
a × b  = b × a
a) Since 6 × 4 = 24 and multiplication is satisfied by the commutative property, thus
x × 6 = 24
=> x = 4
b) Since 0.4 × 0.7 = 0.28 and multiplication is satisfied by the commutative property, thus
0.7 × x = 0.28
=> x = 0.4
c) Since 6 × 10 × 8 = 480 and multiplication is satisfied by the commutative property, thus
8 × 10 × x = 480
=> 80x = 480
=> x = 6

Prince made a vertical row of 2 balls and a horizontal row of 3 balls separately. How can she rearrange the rows and columns of the balls to get the same number of balls?

Solution:

Prince arranged,
A vertical row of 2 balls and a horizontal row of 3 balls separately
Total number of balls Prince has = 2 × 3 = 6
To make a new row and column with the same number of balls, according to the commutative property of multiplication, he needs to arrange the balls as 3 × 2 = 6 to get the same result. Thus Prince needs to arrange a vertical row of 3 balls and a horizontal row of 2 balls.