Fractions

Example 1:

$\frac{2}{5}$ means $2÷5$

The whole has been divided into $5$ parts and $2$ are being considered.

The fraction $\frac{2}{5}$ can be represented by a shape divided into $5$ pieces of equal size, with $2$ of them shaded.

Example 2:

$\frac{3}{7}$ is a proper fraction . It can be represented by a shape divided into $7$ pieces of equal size, with $3$ of them shaded.

$\frac{14}{5}$ is an improper fracti on . It is greater than $1$ , so to draw it, you'll need more than $1$ shape. In fact it needs $3$ equal shapes, each divided into $5$ pieces of equal size, and $14$ of them shaded.

Example 3:

Write $7\frac{2}{5}$ as an improper fraction.

$7\frac{2}{5}=\frac{7}{1}+\frac{2}{5}$

$=\frac{7\cdot 5}{1\cdot 5}+\frac{2}{5}$

$=\frac{35}{5}+\frac{2}{5}$

$=\frac{37}{5}$

Example 4:

Write $\frac{11}{7}$ as a mixed number in simple form.

$\frac{11}{7}=11÷7=1\text{ R }4$

Therefore, $\frac{11}{7}=1\frac{4}{7}$ .

Example 5:

Write $\frac{45}{75}$ in lowest terms.

$45$ and $75$ have a common factor of $15$ .

$\frac{45}{75}=\frac{45÷15}{75÷15}=\frac{3}{5}$