Question

Evaluate the value of$\mathit{x}$and name the property used in each step:

$\frac{\mathbf{1}}{\mathbf{3}}\mathbf{\cdot }\mathit{x}\mathbf{=}\mathbf{1}$

Short answer

The solution of the expression is $\mathit{x}\mathbf{=}\mathbf{3}$.

Step-by-step solution

– Given information.

The given expression is:

$\frac{1}{3}\cdot x=1$

– Write the concept.

Use the Multiplication Property of Equality.

It says, ‘If two expressions are equal to each other and multiply or divide by same number both side by same number, the resulting expression will also equivalent.’

The property of Multiplicative inverse is:

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

The associative property of multiplication is:

$\left(a\cdot b\right)\cdot c=a\cdot \left(b\cdot c\right)$

– Evaluate the expression.

The expression $\frac{1}{3}\cdot x=1$can be solved in below:

$\frac{1}{3}\cdot x=1$

Multiply both sides by 3,

$\begin{array}{c}\frac{1}{3}\cdot x=1\\ \frac{1}{3}\cdot x\cdot 3=1\cdot 3\\ \left(\frac{1}{3}\cdot 3\right)\cdot x=3\left[\text{Associative\hspace{0.17em}\hspace{0.17em}property}\right]\\ x=3\left[\text{Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}multiplicative\hspace{0.17em}\hspace{0.17em}inverse}\right]\end{array}$