Converting Fractions

A. Converting mixed numbers to improper fractions

Example 1:

$$\begin{array}{rl}5\frac{3}{4}& =5\times \frac{4}{4}+\frac{3}{4}\\ \\ 5\frac{3}{4}& =\frac{20}{4}+\frac{3}{4}\\ \\ 5\frac{3}{4}& =\frac{23}{4}\end{array}$$

Example 2:

$$\begin{array}{rl}2\frac{5}{12}& =2\times \frac{12}{12}+\frac{5}{12}\\ \\ 2\frac{5}{12}& =\frac{24}{12}+\frac{5}{12}\\ \\ 2\frac{5}{12}& =\frac{29}{12}\end{array}$$

B. Converting improper fractions to mixed fractions

Example 1:

$$\begin{array}{rl}\frac{5}{4}& =\frac{4}{4}+\frac{1}{4}\\ \\ \frac{5}{4}& =1+\frac{1}{4}\\ \\ \frac{5}{4}& =1\frac{1}{4}\end{array}$$

Example 2:

$$\begin{array}{rl}\frac{7}{2}& =\frac{2}{2}+\frac{2}{2}+\frac{2}{2}+\frac{1}{2}\\ \\ \frac{7}{2}& =1+1+1+\frac{1}{2}\\ \\ \frac{7}{2}& =3+\frac{1}{2}\\ \\ \frac{7}{2}& =3\frac{1}{2}\end{array}$$

C. Converting percent and permille to fractions

Example 1:

$$\begin{array}{rl}1.4\mathrm{\%}& =1.4÷100\\ \\ 1.4\mathrm{\%}& =\frac{1.4}{100}\\ \\ 1.4\mathrm{\%}& =\frac{1.4\times 10}{100\times 10}\\ \\ 1.4\mathrm{\%}& =\frac{14}{1000}\\ \\ 1.4\mathrm{\%}& =\frac{14÷2}{1000÷2}\\ \\ 1.4\mathrm{\%}& =\frac{7}{500}\end{array}$$

Example 2:

$$\begin{array}{rl}20‰& =\frac{20}{1000}\\ \\ 20‰& =\frac{20÷20}{1000÷20}\\ \\ 20‰& =\frac{1}{50}\end{array}$$

D. Converting Decimals to fractions

Example 1:

$$\begin{array}{rl}0.045& =\frac{45}{1000}\\ \\ 0.045& =\frac{45÷5}{1000÷5}\\ \\ 0.045& =\frac{9}{200}\end{array}$$

Example 2:

$$\begin{array}{rl}12.85& =\frac{1285}{100}\\ \\ 12.85& =\frac{1285÷5}{100÷5}\\ \\ 12.85& =\frac{257}{20}\\ \\ 12.85& =\frac{240}{20}+\frac{17}{20}\\ \\ 12.85& =12+\frac{17}{20}\\ \\ 12.85& =12\frac{17}{20}\end{array}$$