MEGA Elementary Education Multi-Content Practice Test

Which equation illustrates the associative property of multiplication?

1. 5(x + 2) = 5x + 10

2. 4(6x) = (6x) • 4

3. 7(3x) = (7 • 3)x

4. (8x)((1/(8x)) = 1

The correct answer is: 7(3x) = (7 • 3)x

The associative property of multiplication states that the way in which numbers are grouped in a multiplication problem does not change the product. This means that when multiplying three or more numbers, the product remains the same regardless of how the numbers are paired or grouped in the multiplication. In the chosen example, 7(3x) = (7 • 3)x, the multiplication of 7 and 3 is grouped separately from the variable x. This demonstrates that whether you multiply 7 by 3 before multiplying by x or simply multiply them in the other arrangement, the final result is unchanged. The key aspect here is the demonstration of associativity through regrouping, reflecting that (a * b) * c = a * (b * c) regardless of how the operations are ordered. In contrast, the other options illustrate different mathematical properties or equations. The first option depicts the distributive property, where a single number is distributed across an addition operation within parentheses. The second shows a commutative property, where the order of multiplication is changed but not the grouping. The fourth option represents the identity property of multiplication, indicating that any number multiplied by its reciprocal will yield one. Thus, option C clearly exemplifies the associative property of multiplication.