Question

Evaluate the following expression and name the property used in each step:

$\left[5÷\left(3\cdot 1\right)\right]\frac{3}{5}$

Short answer

The value of the expression is: $\left[5÷\left(3\cdot 1\right)\right]\frac{3}{5}=1$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\left[5÷\left(3\cdot 1\right)\right]\frac{3}{5}$

Step 2. Write the concept.

The substitution property for multiplication, addition and subtraction is:

$\begin{array}{c}a\cdot b=c\\ a÷b=c\\ a\pm b=c\end{array}$

The property of multiplicative inverse is:

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

And the property of multiplicative identity is:

$a\cdot 1=a=1\cdot a$

Step 3. Evaluate the expression.

The expression $\left[5÷\left(3\cdot 1\right)\right]\frac{3}{5}$can be solved as in below:

role="math" localid="1642016496637" $$\begin{gathered} \left[5÷\left(3\cdot 1\right)\right]\frac{3}{5}=\left[5÷\left(3\right)\right]\frac{3}{5}\left[\text{Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}Multiplicative\hspace{0.17em}\hspace{0.17em}Identity}\right] \\ =\left[\frac{5}{3}\right]\frac{3}{5} \\ =\frac{5}{3}\times \frac{3}{5}\left[\text{Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}Multiplicative\hspace{0.17em}\hspace{0.17em}Inverse}\right] \\ =1\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right] \end{gathered}$$