Question

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

$\mathbf{1}\frac{\mathbf{5}}{\mathbf{6}}\mathbf{\cdot }\mathbf{24}\mathbf{\cdot }\mathbf{3}\frac{\mathbf{1}}{\mathbf{11}}$

Short answer

The value of the expression is: $\mathbf{1}\frac{\mathbf{5}}{\mathbf{6}}\mathbf{\cdot }\mathbf{24}\mathbf{\cdot }\mathbf{3}\frac{\mathbf{1}}{\mathbf{11}}\mathbf{=}\mathbf{136}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$1\frac{5}{6}\cdot 24\cdot 3\frac{1}{11}$

Step 2. Write the concept.

The substitution property for multiplication, addition, and subtraction is:

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

The Commutative property of multiplication is:

$a\cdot b=b\cdot a$

Step 3. Write mixed fraction to fraction.

$\begin{array}{l}1\frac{5}{6}=\frac{11}{6}\\ 3\frac{1}{11}=\frac{34}{11}\end{array}$

Step 4. Evaluate the expression.

The expression $1\frac{5}{6}\cdot 24\cdot 3\frac{1}{11}$can be solved below:

$\begin{array}{l}1\frac{5}{6}\cdot 24\cdot 3\frac{1}{11}=\frac{11}{6}\cdot 24\cdot \frac{34}{11}\left[\text{Commutative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\left(\frac{11}{6}\cdot \frac{34}{11}\right)\cdot 24\left[\text{Commutative\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\left(\frac{34}{6}\right)\cdot 24\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\frac{34\times 24}{6}\end{array}$

Since, $\frac{34\times 24}{6}=\frac{34\times 6\times 4}{6}$. Therefore,

$\begin{array}{l}1\frac{5}{6}\cdot 24\cdot 3\frac{1}{11}=\frac{34\times 6\times 4}{6}\\ =136\end{array}$