Question

Which of the following is an example of the associative property of multiplication?

a) (3+5) = 21+35
b) (3 * 5) = (7 * 3) * 5
c) (3 * 5) = 7 * (5 * 3)
d) 5⁻1

Answer 1

The correct answer to the question, which illustrates the associative property of multiplication, is option c: (3 × 5) = 7 × (5 × 3). This answer demonstrates that the grouping of factors can be changed without altering the product.

Step-by-step explanation:

An example of the associative property of multiplication can be seen in how numbers being multiplied can be grouped differently without changing the product. The associative property is expressed as (a × b) × c = a × (b × c). Using this property, we manipulate the parentheses to group numbers differently while still getting the same result. Now, let's look at your options:

• Option a: (3+5) = 21+35 does not represent multiplication.
• Option b: (3 × 5) = (7 × 3) × 5 is an equality, but it does not demonstrate the associative property.
• Option c: (3 × 5) = 7 × (5 × 3) is the correct choice. It shows that no matter how we group the numbers, the multiplication yields the same product.
• Option d: 5⁻¹ is an example of an exponent and is unrelated to the associative property.

Therefore, the correct answer is option c, which demonstrates the associative property clearly.