Question

8 x 1/8 = 1 inverse property, identity, property, commutative property Associative property

Answer 1

To analyze the expression \( 8 \times \frac{1}{8} = 1 \) in terms of mathematical properties:

1. **Inverse Property**: This refers to a property where an operation and an inverse element combine to yield the identity element. In this case, \( 8 \) and \( \frac{1}{8} \) are multiplicative inverses, since their product is \( 1 \), which is the multiplicative identity.

2. **Identity Property**: Refers to the property that states that any number multiplied by \( 1 \) remains unchanged. In this context, the identity property is being affirmed because \( 8 \times \frac{1}{8} = 1 \).

3. **Commutative Property**: This property states that changing the order of the numbers in an operation will not change the result. For multiplication, \( a \times b = b \times a \). It doesn't apply directly in this expression but could be applicable as \( \frac{1}{8} \times 8 = 1 \).

4. **Associative Property**: This property refers to how the grouping of numbers affects the result of an operation. In multiplication, it states that \( (a \times b) \times c = a \times (b \times c) \). This expression does not illustrate the associative property directly.

In summary, this equation specifically showcases the **Inverse Property** and the **Identity Property** most prominently, while the **Commutative Property** could also be noted if considering the order of factors. The **Associative Property** is not relevant in this case.