Question

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

• A. $\frac{13}{2}:\frac{7}{2}$
• B. $\frac{2}{13}:\frac{2}{7}$
• C. $\frac{7}{2}:\frac{13}{2}$
• D. $\frac{7}{2}:\frac{13}{2}$

Answer 1

The correct option is A $\frac{13}{2}:\frac{7}{2}$

We first simplify the given ratio $3\frac{1}{2}:6\frac{1}{2}$ by converting the mixed fractions in the antecedent and the consequent.
Thus, $3\frac{1}{2}:6\frac{1}{2}=\frac{7}{2}:\frac{13}{2}$.
Now, note that the reciprocal ratio of a:b is b:a.
$⟹$ Reciprocal ratio of $\frac{7}{2}:\frac{13}{2}$ is $\frac{13}{2}:\frac{7}{2}$.
$⟹$ Reciprocal ratio of $3\frac{1}{2}:6\frac{1}{2}$ is $\frac{13}{2}:\frac{7}{2}$