What is the reciprocal of $\frac{2}{3}$?

The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.

$$ \text{The reciprocal of } \frac{2}{3} \text{ is } \frac{3}{2} $$

What Does Reciprocal Mean?

The word reciprocal in mathematics means the number which, when multiplied by the original number, results in 1.

So for this example:

$$ \frac{2}{3} \times x = 1 $$

To solve for $x$, isolate it by dividing both sides by $\frac{2}{3}$:

$$ \begin{align} \frac{2}{3} \times x &= 1 \ \frac{2}{3} \div \frac{2}{3} \times x &= 1 \div \frac{2}{3} \ x &= 1 \times \frac{3}{2} \ x &= \frac{3}{2} \end{align} $$

This shows that the reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.

Find Reciprocal By Flipping The Fraction

The fastest way to find the reciprocal of a number is to flip the fraction.

For example:

  • Original: $\frac{2}{3}$
  • Reciprocal: $\frac{3}{2}$

Check Your Reciprocal Answer

To verify that your reciprocal is correct, multiply it by the original number. If the result is 1, then your answer is correct.

$$ \frac{2}{3} \times \frac{3}{2} = \frac{2 \times 3}{3 \times 2} = \frac{6}{6} = 1 $$

Summary: Reciprocal of $\frac{2}{3}$

  • The reciprocal of a number is what you multiply it by to get 1.
  • The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.
  • You can find it by flipping the numerator and denominator.
  • Always check by multiplying your original by the reciprocal:
    If the result is 1, you’re correct!