Question

The reciprocal ratio of $1\frac{1}{2}:6\frac{3}{4}$ is

• A. $\frac{3}{2}:\frac{27}{4}$
• B. $\frac{2}{3}:\frac{4}{27}$
• C. $\frac{27}{4}:\frac{3}{2}$
• D. $\frac{4}{27}:\frac{2}{3}$

Answer 1

The correct option is C $\frac{27}{4}:\frac{3}{2}$

We first simplify the given ratio $1\frac{1}{2}:6\frac{3}{4}$ by converting the mixed fractions in the antecedent and the consequent into improper fractions.
Thus, $1\frac{1}{2}:6\frac{3}{4}=\frac{3}{2}:\frac{27}{4}$.
Now, note that the reciprocal ratio of a:b is b:a.
$⟹$ Reciprocal ratio of $\frac{3}{2}:\frac{27}{4}$ is $\frac{27}{4}:\frac{3}{2}$.
$⟹$ Reciprocal ratio of $1\frac{1}{2}:6\frac{3}{4}$ is $\frac{27}{4}:\frac{3}{2}$