Question

Find the value of $n$. Then name the property used in each step. (Lesson 1-3)

$4\cdot \frac{1}{4}=n$

Short answer

The value of $n$is $1$. The property used is multiplicative inverse property.

Step-by-step solution

Step 1. State the property.

The multiplicative inverse property states that for any number $a$, there exists a single number $\frac{1}{a}$such that the product of $a$and $\frac{1}{a}$is $a$.

So, $a\cdot \frac{1}{a}=1$.

Step 2. Write the given equation.

The given equation is $4\cdot \frac{1}{4}=n$.

Step 3. Solve the given equation.

Put $a=4$in $a\cdot \frac{1}{a}=1$to get,

$4\cdot \frac{1}{4}=1$

Compare $4\cdot \frac{1}{4}=1$with $4\cdot \frac{1}{4}=n$to get,

$n=1$

So, the solution of the given equation is $n=1$and the property used is the multiplicative inverse property.