Questions: Decide whether the statement is an example of a commutative, associative, identity or inverse property, or of the distributive property. (left(8/3right)) * (left(3/8right))=1 Choose the correct answer below. A. Distributive property B. Associative property C. Commutative property D. Identity property E. Inverse property

Decide whether the statement is an example of a commutative, associative, identity or inverse property, or of the distributive property.

(left(8/3right)) * (left(3/8right))=1

Choose the correct answer below.
A. Distributive property
B. Associative property
C. Commutative property
D. Identity property
E. Inverse property

Transcript text: Decide whether the statement is an example of a commutative, associative, identity or inverse property, or of the distributive property. \[ \left(\frac{8}{3}\right) \cdot\left(\frac{3}{8}\right)=1 \] Choose the correct answer below. A. Distributive property B. Associative property C. Commutative property D. Identity property E. Inverse property

Solution

Solution Steps

Step 1: Identify the operation in the statement

The given statement involves multiplication: \(\left(\frac{8}{3}\right) \cdot \left(\frac{3}{8}\right) = 1\).

Step 2: Analyze the relationship between the numbers

The numbers \(\frac{8}{3}\) and \(\frac{3}{8}\) are multiplicative inverses of each other because their product equals 1.

Step 3: Determine the property being demonstrated

The property being demonstrated is the inverse property of multiplication, which states that any non-zero number multiplied by its reciprocal equals 1.

Step 4: Match the property to the correct option

The correct option is E. Inverse property.