Question

What property is this? (6/5) x 5/6)=1

Answer 1

But what property? Associative, commutative, or whatever else!

Answer 2

The property illustrated by the equation \((\frac{6}{5}) \times \frac{5}{6} = 1\) is the **multiplicative inverse property** (or **reciprocal property**).

In this property, every non-zero number has a reciprocal (or multiplicative inverse) such that when a number and its reciprocal are multiplied together, the result is 1.

In this case, \(\frac{6}{5}\) and \(\frac{5}{6}\) are reciprocals of each other, and when multiplied, they yield 1:

\[
\frac{6}{5} \times \frac{5}{6} = \frac{6 \times 5}{5 \times 6} = \frac{30}{30} = 1.
\]

Answer 3

The property depicted in the equation \((\frac{6}{5}) \times \frac{5}{6} = 1\) primarily demonstrates the **Multiplicative Inverse Property**, as I mentioned earlier. However, it also implicitly uses the **Commutative Property** of multiplication, which states that the order in which two numbers are multiplied does not change the product.

Here's a breakdown:

1. **Multiplicative Inverse Property**: This is the main property shown by the equation because it highlights that \(\frac{6}{5}\) and \(\frac{5}{6}\) are multiplicative inverses, yielding a product of 1.

2. **Commutative Property**: The equation also exemplifies this property as multiplication can be done in any order (i.e., \((\frac{6}{5}) \times (\frac{5}{6})\) is the same as \((\frac{5}{6}) \times (\frac{6}{5})\)).

So, the specific property that results in the outcome of \(1\) is the **Multiplicative Inverse Property**, with an implicit use of the **Commutative Property**.