Question

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

$3\left(1÷3\right)\cdot 9$

Short answer

The value of the expression is: $3\left(1÷3\right)\cdot 9=9$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$3\left(1÷3\right)\cdot 9$

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:

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

Step 3. Evaluate the expression.

The expression $3\left(1÷3\right)\cdot 9$can be solved as in below:

localid="1642015688492" $$\begin{gathered} 3\left(1÷3\right)\cdot 9=3\left(\frac{1}{3}\right)\cdot 9 \\ =3\times \frac{1}{3}\cdot 9 \\ =1\cdot 9\left[\text{Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}Multiplicative\hspace{0.17em}\hspace{0.17em}Inverse}\right] \\ =9\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right] \end{gathered}$$