EXAMPLES:
Question:
Combine into a single fraction:
$\displaystyle\,\frac{2x}{5} + \frac{1}{3}$
Solution:
Notice that the least common denominator is $\,15\,$.
$\displaystyle
\cssId{s10}{\,\frac{2x}{5} + \frac{1}{3}}
\cssId{s11}{\ \ =\ \ \frac{2x}{5}\cdot\frac{3}{3} + \frac{1}{3}\cdot\frac{5}{5}}
\cssId{s12}{\ \ =\ \ \frac{6x}{15} + \frac{5}{15}}
\cssId{s13}{\ \ =\ \ \frac{6x+5}{15}}
$
Question:
Combine into a single fraction:
$\displaystyle\,\frac{2}{9t} - \frac{1}{6}$
Solution:
Notice that the least common denominator is $\,18t\,$.
$\displaystyle
\cssId{s19}{\,\frac{2}{9t} - \frac{1}{6}}
\cssId{s20}{\ \ =\ \ \frac{2}{9t}\cdot\frac{2}{2} - \frac{1}{6}\cdot\frac{3t}{3t}}
\cssId{s21}{\ \ =\ \ \frac{4}{18t} - \frac{3t}{18t}}
\cssId{s22}{\ \ =\ \ \frac{4-3t}{18t}}
$
Master the ideas from this section
by practicing the exercise at the bottom of this page.
When you're done practicing, move on to:
Divisibility Equivalences