When there are fractions in equations, the standard procedure is to remove the fractions by multiplying both sides of the equation by an appropriate whole number. The next step is to remove the brackets.

\begin{examplebox}
    \begin{questions}
        \questionpoints[2] Solve:
        \begin{parts}
            \part \(2 x+\frac{1}{2}=\frac{2}{3}\)
            \begin{solutionordottedlines}[1in]
                \[
                2 x+\frac{1}{2}=\frac{2}{3}
                \]

                \[
                6\left(2 x+\frac{1}{2}\right)=6 \times \frac{2}{3} \quad \begin{gathered}
                \text { (Multiply both sides by } 6, \text { the lowest common multiple of the } \\
                \text { denominators. })
                \end{gathered}
                \]

                \[
                12 x+3=4
                \]

                \[
                \begin{aligned}
                12 x & =1 \\
                x & =\frac{1}{12}
                \end{aligned}
                \]
            \end{solutionordottedlines}
            \part \(3 x-\frac{1}{4}=\frac{4}{5}\)
            \begin{solutionordottedlines}[1in]
                \(\quad 3 x-\frac{1}{4}=\frac{4}{5}\)

                \[
                \begin{aligned}
                20\left(3 x-\frac{1}{4}\right) & =20 \times \frac{4}{5} \\
                60 x-5 & =16 \\
                60 x & =21 \quad \text { (Multiply both sides by 20.) } \\
                x & =\frac{21}{60} \\
                & =\frac{7}{20}
                \end{aligned}
                \]
            \end{solutionordottedlines}
        \end{parts}
        \questionpoints[2] Solve:
        \begin{parts}
            \part \(\frac{2 x}{3}+\frac{1}{5}=4\)
            \begin{solutionordottedlines}[1in]
            \end{solutionordottedlines}
            \part \(10-\frac{a+3}{4}=6\)
            \begin{solutionordottedlines}[1in]
            \end{solutionordottedlines}
        \end{parts}
        \questionpoints[1] Solve \(2.1 x+3.5=9.4\)
        \begin{solutionordottedlines}[1in]
            \[
            \begin{aligned}
            2.1 x+3.5 & =9.4 \\
            21 x+35 & =94 \quad \text { (Multiply both sides by 10.) } \\
            21 x & =59 \\
            x & =\frac{59}{21}
            \end{aligned}
            \]
        \end{solutionordottedlines}
        \questionpoints[1] Solve \(\frac{2 x}{3}-3=x+\frac{3}{4}\)
        \begin{solutionordottedlines}[1in]
            \[
            \begin{aligned}
            \frac{2 x}{3}-3 & =x+\frac{3}{4} \\
            8 x-36 & =12 x+9 \quad \text { (Multiply both sides by 12.) } \\
            -4 x & =45 \\
            x & =-\frac{45}{4}
            \end{aligned}
            \]
        \end{solutionordottedlines}
        \questionpoints[1] Solve \(\frac{a+5}{4}=\frac{a+3}{3}\)
        \begin{solutionordottedlines}[1in]
            \[
            \begin{aligned}
            \frac{a+5}{4} & =\frac{a+3}{3} \\
            3(a+5) & =4(a+3) \quad \text { (Multiply both sides by 12.) } \\
            3 a+15 & =4 a+12 \\
            15 & =a+12 \\
            3 & =a \\
            a & =3
            \end{aligned}
            \]
        \end{solutionordottedlines}
    \end{questions}
\end{examplebox}

\fbox{\parbox{\linewidth}{
\large{\textbf{Crash Course:}}
\begin{itemize}
  \item Remove all fractions by multiplying both sides of the equation by the lowest common multiple of the denominators.
  \item Remove all brackets.
  \item Collect like terms and solve the equation.
\end{itemize}
}
}

\begin{exercisebox}
    \subsection{Exercises:}
    \begin{questions}
        \questionpoints[9] Solve for the unknown pronumeral:
        \begin{parts}\begin{multicols}{2}
            \part \(2 x-\frac{1}{2}=\frac{1}{4}\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{7}{2}-3 y=\frac{2}{3}\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(-2 x+\frac{1}{3}=\frac{1}{5}\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{a}{3}+5=3\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{3 b}{7}+6=2\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{2}{3}(m-3)=1\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{2 y+1}{3}+4=7\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{3 y-1}{2}+2=9\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(2+\frac{2 x-1}{5}=5\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(e+1.8=2.9\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(1.2 u=15.6\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(1.2 x+4=10\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{3 x}{4}-1=\frac{x}{2}+3\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{x}{3}-4=6-\frac{2 x}{5}\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
        \begin{parts}\begin{multicols}{2}
            \part \(1.6 x+10=0.9 x+12\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(4.8-1.3 x=23+1.3 x\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{a+3}{2}=\frac{a+1}{5}\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{2 a+1}{3}=\frac{3 a+1}{4}\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{3 a+2}{4}+2=a\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{3 a-2}{4}=\frac{a-5}{2}\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{4 a-1}{3}+a=2\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(5 a+9=24\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{c}{3}-2=4\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{4 e}{3}+\frac{1}{2}=2\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(2 g+5=7 g-6\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(2(i-1)=5(i+6)\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(2(k+1)-3(k-2)=7\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{m+1}{3}=\frac{m-2}{5}\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
            \part \(\frac{2 q-2}{5}+1=4 q\)
            \begin{solutionordottedlines}[2cm]
            \end{solutionordottedlines}
        \end{multicols}\end{parts}
    \end{questions}
\end{exercisebox}
