Division of Fractions - Examples, Exercises and Solutions

According to the rules of the order of operations, we should first solve the exercise from left to right since there are only multiplication and division operations present:

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

$\frac{1}{2}:2=\frac{1}{4}$

Let's convert the decimal fraction to a simple fraction:

$\frac{0.5}{4}=\frac{\frac{1}{2}}{4}$

Let's convert the division problem to a multiplication problem.

We'll multiply $\frac{1}{2}$ by the reciprocal of 4 as follows:

$\frac{1}{2}\times\frac{1}{4}$

We'll solve it as follows:

$\frac{1\times1}{2\times4}=\frac{1}{8}$

Let's convert the decimal fraction to a simple fraction:

$0.5=\frac{5}{10}$

We'll write the division problem as follows:

$\frac{\frac{5}{10}}{2}$

Let's convert the division problem to a multiplication problem.

We'll multiply $\frac{5}{10}$ by the reciprocal of $2$ as follows:

$\frac{5}{10}\times\frac{1}{2}$

We'll solve it this way:

$\frac{5\times1}{10\times2}=\frac{5}{20}$

We'll reduce both the numerator and denominator by 5 and get:

$\frac{5:5}{20:5}=\frac{1}{4}$

Let's convert the decimal fractions to simple fractions:

$0.3=\frac{3}{10}$

$0.5=\frac{5}{10}$

We'll write the division problem as follows:

$\frac{\frac{3}{10}}{\frac{5}{10}}$

Let's convert the division problem to a multiplication problem.

We'll multiply $\frac{3}{10}$ by the reciprocal of $\frac{5}{10}$ as follows:

$\frac{3}{10}\times\frac{10}{5}$

We'll solve it this way:

$\frac{3\times10}{10\times5}$

We'll cancel out the 10 in the numerator with the 10 in the denominator and get:

$\frac{3}{5}$