Question

Use the properties of real to answer each question

If $mn=m$, what is the value of $n$?

Short answer

Value of n is1.

Step-by-step solution

- Write properties of real numbers 

Properties of real numbers are written in following table:

For any real numbers $a,b,$ and $c:$
Property	Addition	Multiplication
Commutative	$a+b=b+a$	$a·b=b·a$
Associative	$\left(a+b\right)+c=a+\left(b+c\right)$	$\left(a·b\right)·c=a·\left(b·c\right)$
Identity	$a+0=a=0+a$	$a·1=a=1·a$
Inverse	$a+\left(-a\right)=0=\left(-a\right)+a$	If $a\ne 0$, then $a·\frac{1}{a}=1=\frac{1}{a}·a$
Distributive	$a\left(b+c\right)=ab+ac\text{and}\left(b+c\right)a=ba+ca$

- Compare with given equation

Compare identity property of multiplication with given equation to find required value as shown below

$\begin{array}{c}a\cdot 1=a\\ mn=m\end{array}$

Thus, on substituting 1 for n, given equation is satisfied.

- Verification

Substitute 1 for n in given equation

$\begin{array}{c}mn=m\\ m\cdot 1=m\\ m=m\left(\text{True}\right)\end{array}$

Thus, n is multiplicative identity of m