Adding Rational Numbers: Positive and Negative Fractions

If the denominators are already the same, simply add the numerators and simplify

 $\frac{3}{8}+\frac{2}{8}=\frac{5}{8}$               or            $-\frac{11}{24}+\left(-\frac{9}{24}\right)=-\frac{20}{24}=\frac{5}{6}$  

If the denominators are not the same, you must find common denominators. The GREATEST common multiple is best.

 $\frac{1}{6}+\frac{2}{5}\ \ \ \ =\ \ \ \ \frac{5}{30}+\frac{12}{30}\ \ \ \ =\ \ \ \ \frac{17}{30}$  

 $\frac{2}{7}+\left(-\frac{2}{3}\right)=\$  ...

 $\frac{2}{7}+\left(-\frac{2}{3}\right)=$  

First, find a common denomintor and write two equivalent fractions

 $\frac{6}{21}+\left(-\frac{14}{21}\right)\ \ \ \$  

Next, find the difference of their absolute values

 $\left|\frac{14}{21}\right|-\left|\frac{6}{21}\right|=\frac{8}{21}$  

Give the difference the sign of the greater fraction

 $-\frac{8}{21}$  This is the sum of the original problem and the final answer