Converting Fractions
\(\color{gray}\Large \dfrac{3}{4}\) A fraction with a numerator that is less than the denominator\(\color{purple}\text{Proper Fraction}\)
\(\color{gray}\Large\dfrac{4}{3}\) A fraction with a numerator is greater than the denominator\(\color{purple}\text{Improper Fraction}\)
\(\color{gray}\Large 1\dfrac{1}{3}\) A combination of a whole number and a fraction Example 1: \begin{equation*} Example 2: \begin{equation*} Example 1: \begin{equation*} Example 2: \begin{equation*} Example 1: \begin{equation*} Example 2: \begin{equation*} Example 1: \begin{equation*} Example 2: \begin{equation*} \(\color{purple}\text{Mixed Fraction}\)
A. Converting mixed numbers to improper fractions
\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*}
\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
\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*}
\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
\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*}
\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
\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*}
\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*}