Solve Fraction Division: 1/2 ÷ 5/3 Step-by-Step

To solve the problem of dividing the fractions $\frac{1}{2}$ by $\frac{5}{3}$, we proceed as follows:

We can simplify a division of fractions by multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.

First, we find the reciprocal of $\frac{5}{3}$, which is $\frac{3}{5}$.

Next, we multiply the fractions $\frac{1}{2}$ and $\frac{3}{5}$:

$\frac{1}{2} \times \frac{3}{5} = \frac{1 \times 3}{2 \times 5}.$

This results in

$\frac{3}{10}.$

Thus, the solution to $\frac{1}{2}:\frac{5}{3}$ is $\frac{3}{10}$.