Question

Which of the following is the quotient of $(2\frac{1}{4}+50\frac{1}{8})$ when it is divided by its multiplicative inverse?

• A. ${\left(\frac{419}{8}\right)}^2$
• B. $1$
• C. $2\times \frac{419}{8}$
• D. $\frac{419}{8}$

Answer 1

The correct option is A ${\left(\frac{419}{8}\right)}^2$

$2\frac{1}{4}+50\frac{1}{8}=\frac{8+1}{4}+\frac{400+1}{8}=\frac{9}{4}+\frac{401}{8}=\frac{18}{8}+\frac{401}{8}=\frac{419}{8}$

The multiplicative inverse of $\frac{419}{8}=\frac{8}{419}$

The quotient of $\frac{419}{8}$ and $\frac{8}{419}=\frac{419}{8}÷\frac{8}{419}=\frac{419}{8}\times \frac{419}{8}={\left(\frac{419}{8}\right)}^2$