## Related questions with answers

Question

Find the reciprocal.

$3 \frac{1}{2}$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2Two numbers are reciprocals if their product is 1. That is, $\dfrac{a}{b}$ and $\dfrac{b}{a}$ are reciprocals since $\dfrac{a}{b}\cdot\dfrac{b}{a}=\dfrac{ab}{ab}=1$.

To find the reciprocal of a mixed number, you can then convert it to an improper fraction and then flip the fraction so the numerator and denominator switch places.

Converting $3\dfrac{1}{2}$ to an improper fraction gives $\dfrac{3\cdot2+1}{2}=\dfrac{7}{2}$.

The reciprocal of $3\dfrac{1}{2}$ is then $\boxed{\dfrac{2}{7}}$.

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