Adding Rational Numbers: Positive and Negative Fractions

Adding Rational Numbers: Positive and Negative Fractions

7.NS.1d

Apply properties of operations as strategies to add and subtract rational numbers.

To add fractions, apply the same rules for adding integers...

When adding fractions with the SAME sign, the sum will be the same as the sign of the fractions

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

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

When adding fractions with the SAME sign, the sum will be the same as the sign of the fractions

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

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

To add fractions with different signs, find the difference of their absolute values. Then use the sign of the fraction with the greater absolute value

•  $\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

Open Ended

 $\frac{2}{3}+\left(-\frac{1}{6}\right)=$  

 

 $\frac{4}{15}+\frac{7}{15}=$