# Fractions

### Converting Fractions

#### Converting Fractions

##### $$\color{purple}\text{Proper Fraction}$$

$$\color{gray}\Large \dfrac{3}{4}$$

A fraction with a numerator that is less than the denominator

##### $$\color{purple}\text{Improper Fraction}$$

$$\color{gray}\Large\dfrac{4}{3}$$

A fraction with a numerator is greater than the denominator

##### $$\color{purple}\text{Mixed Fraction}$$

$$\color{gray}\Large 1\dfrac{1}{3}$$

A combination of a whole number and a fraction

##### A. Converting mixed numbers to improper fractions

Example 1:

\begin{equation*} \begin{split} 5\frac{3}{4}&= 5\times \frac{4}{4} + \frac{3}{4}\\\\ 5\frac{3}{4}&= \frac{20}{4} + \frac{3}{4}\\\\ 5\frac{3}{4}&=\frac{23}{4} \end{split} \end{equation*}

Example 2:

\begin{equation*} \begin{split} 2\frac{5}{12}&= 2\times \frac{12}{12} + \frac{5}{12}\\\\ 2\frac{5}{12}&= \frac{24}{12} + \frac{5}{12}\\\\ 2\frac{5}{12}&=\frac{29}{12} \end{split} \end{equation*}

##### B. Converting improper fractions to mixed fractions

Example 1:

\begin{equation*} \begin{split} \frac{5}{4}&= \frac{4}{4} + \frac{1}{4}\\\\ \frac{5}{4}& = 1 + \frac{1}{4}\\\\ \frac{5}{4}& =1\frac{1}{4} \end{split} \end{equation*}

Example 2:

\begin{equation*} \begin{split} \frac{7}{2}&= \frac{2}{2} + \frac{2}{2} + \frac{2}{2} + \frac{1}{2}\\\\ \frac{7}{2}& = 1 + 1 + 1 + \frac{1}{2}\\\\ \frac{7}{2}& =3 + \frac{1}{2}\\\\ \frac{7}{2}& = 3\frac{1}{2} \end{split} \end{equation*}

##### C. Converting percent and permille to fractions

Example 1:

\begin{equation*} \begin{split} 1.4\% & = 1.4 \div 100\\\\ 1.4\%& = \frac{1.4}{100}\\\\ 1.4\%& = \frac{1.4 \times \color{red}10 }{100 \times \color{red}10 }\\\\ 1.4\%& = \frac{14}{1000}\\\\ 1.4\%& = \frac{14 \div \color{red}2 }{1000 \div \color{red}2}\\\\ 1.4\%& = \frac{7}{500} \end{split} \end{equation*}

Example 2:

\begin{equation*} \begin{split} 20‰& = \frac{20}{1000}\\\\ 20‰& = \frac{20  \div \color{red}20}{1000 \div \color{red}20}\\\\ 20‰& = \frac{1}{50} \end{split} \end{equation*}

##### D. Converting Decimals to fractions

Example 1:

\begin{equation*} \begin{split} 0.045& = \frac{45}{1000}\\\\ 0.045& = \frac{45 \div \color {red} 5}{1000 \div \color {red} 5}\\\\ 0.045& = \frac{9}{200} \end{split} \end{equation*}

Example 2:

\begin{equation*} \begin{split} 12.85& = \frac{1285}{100}\\\\ 12.85& = \frac{1285\div \color {red} 5}{100 \div \color {red} 5}\\\\ 12.85& = \frac{257}{20}\\\\ 12.85& = \frac{240}{20} + \frac{17}{20}\\\\ 12.85& = 12 + \frac{17}{20}\\\\ 12.85& = 12\frac{17}{20} \end{split} \end{equation*}