To determine which property of multiplication is illustrated by the equation [tex]\( 17 \times 15.56 = 15.56 \times 17 \)[/tex], let's analyze the given options in detail.
1. Distributive Property:
The distributive property involves both addition and multiplication, and it states that for all real numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
[tex]\[
a \times (b + c) = (a \times b) + (a \times c)
\][/tex]
This property is not related to the given equation as there is no addition involved.
2. Associative Property of Multiplication:
The associative property of multiplication states that when three or more numbers are multiplied, the grouping of the numbers does not change the product. In mathematical terms:
[tex]\[
(a \times b) \times c = a \times (b \times c)
\][/tex]
The given equation does not involve any regrouping of numbers, hence it does not illustrate the associative property.
3. Commutative Property of Multiplication:
The commutative property of multiplication states that the order in which two numbers are multiplied does not affect the product. In other words:
[tex]\[
a \times b = b \times a
\][/tex]
The given equation [tex]\( 17 \times 15.56 = 15.56 \times 17 \)[/tex] clearly shows that the product remains the same even when the order of the numbers is switched. This is a direct application of the commutative property of multiplication.
4. None of the above:
This option can be discarded since we have already identified that one of the given properties applies to the situation.
Given the analysis above, the correct property illustrated by the equation [tex]\( 17 \times 15.56 = 15.56 \times 17 \)[/tex] is the commutative property of multiplication.
Therefore, the answer is:
[tex]\[
\text{commutative property of multiplication}
\][/tex]
