Question

Evaluate the following expression. Name the property used in each step:

$\frac{1}{4}\cdot 24\cdot \frac{2}{3}$

Short answer

The value of the expression is: $\frac{\mathbf{1}}{\mathbf{4}}\mathbf{\cdot }\mathbf{24}\mathbf{\cdot }\frac{\mathbf{2}}{\mathbf{3}}\mathbf{=}\mathbf{4}$.

Step-by-step solution

Step 1. Given information.

Given expression is:

$\frac{1}{4}\cdot 24\cdot \frac{2}{3}$

Step 2. Write the concept.

The substitution property for multiplication, addition and subtraction is:

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

The associative property is:

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

Step 3. Evaluate the expression.

The expression $\frac{1}{4}\cdot 24\cdot \frac{2}{3}$ can be solved in below:

$\begin{array}{l}\frac{1}{4}\cdot 24\cdot \frac{2}{3}=\left(\frac{1}{4}\cdot 24\right)\cdot \frac{2}{3}\left[\text{Associative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\left(6\right)\cdot \frac{2}{3}\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\frac{6\cdot 2}{3}\left[\because \frac{6}{3}=\frac{3\cdot 2}{2}\right]\\ =2\cdot 2\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =4\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\end{array}$