Question

Name the property illustrated by the following equation.

$\left(\frac{1}{4}\right)4=1$

Short answer

The property is inverse property.

Step-by-step solution

Step 1- Define the associative property.

The inverse property of multiplication states that if you multiply a number by its reciprocal, also called the multiplicative inverse, the product will be 1

Mathematically, the property is represented as

$\left(\frac{1}{a}\right)a=1$

Step 2- Step description.

Consider the equation $\left(\frac{1}{4}\right)4=1$.

Simplify the equation as follows:

$\begin{array}{c}\left(\frac{1}{4}\right)4=1\\ 1=1\end{array}$

Step 3- Step description.

Since the number 4 ismultiplied by the reciprocal of 4 that is $\frac{1}{4}$, thus 4 will be canceled out and the property is inverse property.

Therefore, the property is inverse property.