Question

The reciprocal ratio of $3\frac{1}{2}:5\frac{1}{4}$ is

• A. 214:72
• B. 32:54
• C. 72:214

Answer 1

The correct option is A 214:72

We first simplify the given ratio $3\frac{1}{2}:5\frac{1}{4}$ by converting the mixed fractions in the antecedent and the consequent.
Thus, $3\frac{1}{2}:5\frac{1}{4}=\frac{7}{2}:\frac{21}{4}$.
Now, note that the reciprocal ratio of $a:b$ is $b:a$.
$⟹$ Reciprocal ratio of $\frac{7}{2}:\frac{21}{4}$ is $\frac{21}{4}:\frac{7}{2}$.
$⟹$ Reciprocal ratio of $3\frac{1}{2}:5\frac{1}{4}$ is $\frac{21}{4}:\frac{7}{2}$