Adding and Subtracting Simple Fractions With Variables
Need some basic practice with adding and subtracting fractions first? Adding and Subtracting Fractions
Examples
Question:
Combine into a single fraction:
$\displaystyle\,\frac{2x}{5} + \frac{1}{3}$
Solution:
Notice that the least common denominator is $\,15\,.$
$\displaystyle
\begin{align}
\cssId{s10}{\,\frac{2x}{5} + \frac{1}{3}}
&\cssId{s11}{\ \ =\ \ \frac{2x}{5}\cdot\frac{3}{3} + \frac{1}{3}\cdot\frac{5}{5}}\cr\cr
&\cssId{s12}{\ \ =\ \ \frac{6x}{15} + \frac{5}{15}}
\cssId{s13}{\ \ =\ \ \frac{6x+5}{15}}
\end{align}
$
Question:
Combine into a single fraction:
$\displaystyle\,\frac{2}{9t} - \frac{1}{6}$
Solution:
Notice that the least common denominator is $\,18t\,.$
$\displaystyle
\begin{align}
\cssId{s19}{\,\frac{2}{9t} - \frac{1}{6}}
&\cssId{s20}{\ \ =\ \ \frac{2}{9t}\cdot\frac{2}{2} - \frac{1}{6}\cdot\frac{3t}{3t}}\cr\cr
&\cssId{s21}{\ \ =\ \ \frac{4}{18t} - \frac{3t}{18t}}
\cssId{s22}{\ \ =\ \ \frac{4-3t}{18t}}
\end{align}
$