Q19. - Algebra 2

Question

Compare the quantity in Column A and the quantity in Column B. Then determine whether:

 

A. the quantity in Column A is greater;

 

B. the quantity in Column B is greater;

 

C. the two quantities are equal;

 

D. the relationship cannot be determined from the information given.

 

Column A     Column B

 

$\frac{\frac{3}{4}}{{\left(\frac{3}{4}\right)}^2}$                 $\frac{4}{3}$

Step-by-Step Solution

Answer

The quantity in Colum A is equal to the quantity in Column B. So, the correct option is C.

Step 1 - Consider the two quantities.

The quantity in column A is:

$\frac{\frac{3}{4}}{{\left(\frac{3}{4}\right)}^2}$

The quantity in column B is:

$\frac{4}{3}$

Step 2 - Evaluate the two quantities.

Calculate the quantity in column A as:

$\begin{array}{c}\frac{\frac{3}{4}}{{\left(\frac{3}{4}\right)}^2}=\frac{\frac{3}{4}}{\frac{9}{16}}\\ =\frac{3}{4}\times \frac{16}{9}\\ =\frac{4}{3}\end{array}$

The the quantity in colum B is $\frac{4}{3}$.

Thus, the quantity in Column A is equal to Column B.

Step 3 - State the conclusion.

Both the quantities are equal. Therefore, option C is correct.