﻿ Adding and Subtracting Simple Fractions With Variables

# 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}

## Concept Practice

Combine into a single fraction (use the least common denominator):