Chapter 1.3, Problem 61PFA

To determine

To find the equation from the options which best illustrates the multiplicative inverse property that R wishes to solve.

Answer to Problem 61PFA

Option (D) $\frac{c}{d}\times \frac{d}{c}=1(c\ne 0,d\ne 0)$

Explanation of Solution

Given information : 

R wants to solve the equation $\frac{3}{4}b=6$

 

She wants to use Multiplicative Inverse Property to solve it. So, here we have to select the option which best illustrates this property.

Multiplicative Inverse of a variable or number is the reciprocal of that particular variable or number. The multiplicative inverse of $\frac{c}{d}$ is $\frac{d}{c}$ .

  $\frac{c}{d}\times \frac{d}{c}=1(c\ne 0,d\ne 0)$

Or, $\frac{c}{d}=\frac{1}{\frac{d}{c}}(c\ne 0,d\ne 0)$

The Solution of R would be as follows:

  $\begin{array}{l}\frac{3}{4}b=6\\ \Rightarrow b=\frac{6}{\frac{3}{4}}\\ \Rightarrow b=\frac{6\times 4}{3}\\ \Rightarrow b=8\end{array}$