Q11. - Algebra 1

Question

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

$\frac{\mathbf{3}}{\mathbf{4}}\left[4÷\left(7-4\right)\right]$

Step-by-Step Solution

Answer

The value of the expression is: $\frac{\mathbf{3}}{\mathbf{4}}\left[4÷\left(7-4\right)\right]\mathbf{=}\mathbf{1}$.

Step 1 – Given information.

Given expression is:

$\frac{3}{4}\left[4÷\left(7-4\right)\right]$

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 Division Property is:

$\frac{a}{b}=a÷b$

The property of multiplication is:

$\frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}$

Step 3 – Evaluate the expression.

The expression $\frac{3}{4}\left[4÷\left(7-4\right)\right]$ can be solved in below:

$\begin{array}{c}\frac{3}{4}\left[4÷\left(7-4\right)\right]=\frac{3}{4}\left[4÷\left(3\right)\right]\left[\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\frac{3}{4}\left[\frac{4}{3}\right]\left[\text{Division\hspace{0.17em}\hspace{0.17em}Property}\right]\\ =\frac{3}{4}\times \frac{4}{3}\left[\text{Property of Mulplication}\right]\\ =\frac{3\times 4}{4\times 3}\\ =1\end{array}$