Let’s examine each of the given statements to determine which one exemplifies the Associative Property of Multiplication. The Associative Property of Multiplication states that the way in which factors are grouped in a multiplication problem does not affect the product. In other words, [tex]\((a \times b) \times c = a \times (b \times c)\)[/tex].
1. [tex]\(3 \times 0 = 0\)[/tex]
- This statement is correct, but it doesn't illustrate the associative property. This is simply the multiplication of a number by zero, yielding zero.
2. [tex]\(3(7+4) = (3 \times 7) \times (3 \times 4)\)[/tex]
- This is not a correct application of the associative property. The left-hand side shows multiplication applied after addition inside the parentheses, while the right-hand side incorrectly multiplies [tex]\(3\)[/tex] with the sum and the product separately, which is not how the associative property is defined.
3. [tex]\((8 \times 4) \times 5 = 8 \times (4 \times 5)\)[/tex]
- This statement correctly demonstrates the associative property. Here, the multiplication grouping is changed but the product remains the same. On the left, [tex]\((8 \times 4) \times 5\)[/tex] groups [tex]\(8\)[/tex] and [tex]\(4\)[/tex] together first, then multiplies by [tex]\(5\)[/tex]. On the right, [tex]\(8 \times (4 \times 5)\)[/tex] groups [tex]\(4\)[/tex] and [tex]\(5\)[/tex] together first, then multiplies by [tex]\(8\)[/tex]. Both expressions give the same result.
4. [tex]\(5 \times 9 = 9 \times 5\)[/tex]
- This statement is true and demonstrates the commutative property of multiplication, not the associative property. It shows that the order of factors can be swapped, but it doesn't involve changing the grouping of the factors.
5. None of these answers are correct.
- This option can be ruled out since statement 3 is correct.
Thus, the correct answer is:
[tex]\((8 \times 4) \times 5 = 8 \times (4 \times 5)\)[/tex]
This statement perfectly illustrates the Associative Property of Multiplication.
