Adding \& Subtracting Fractions Bertha Songolo \( \begin{array}{ll}\text { a. } \frac{5}{8}+\frac{1}{4}= & \text { b. } \frac{6}{10}-\frac{2}{5}= \\ \text { c. } \frac{8}{12}-\frac{3}{6}= & \text { d. } \frac{2}{3}+\frac{4}{9}= \\ \text { e. } \frac{4}{5}+\frac{8}{10}= & \text { f. } \frac{3}{4}-\frac{2}{3}= \\ \text { g. } \frac{4}{9}-\frac{1}{3}= & \text { h. } \frac{1}{4}+\frac{4}{12}= \\ \text { i. } \frac{3}{5}+\frac{1}{3}= & \text { j. } \frac{1}{2}-\frac{1}{5}= \\ \text { k. } \frac{5}{6}-\frac{1}{2}= & \text { I. } \frac{1}{2}+\frac{1}{3}=\end{array} \)

Sure, let's solve each of the addition and subtraction fraction problems step by step. ### a. \(\frac{5}{8} + \frac{1}{4}\) **Step 1:** Find a common denominator. The least common denominator (LCD) of 8 and 4 is 8. \[ \frac{1}{4} = \frac{2}{8} \] **Step 2:** Add the fractions. \[ \frac{5}{8} + \frac{2}{8} = \frac{7}{8} \] **Answer:** \(\frac{7}{8}\) --- ### b. \(\frac{6}{10} - \frac{2}{5}\) **Step 1:** Find a common denominator. The LCD of 10 and 5 is 10. \[ \frac{2}{5} = \frac{4}{10} \] **Step 2:** Subtract the fractions. \[ \frac{6}{10} - \frac{4}{10} = \frac{2}{10} = \frac{1}{5} \] **Answer:** \(\frac{1}{5}\) --- ### c. \(\frac{8}{12} - \frac{3}{6}\) **Step 1:** Simplify the fractions. \[ \frac{8}{12} = \frac{2}{3}, \quad \frac{3}{6} = \frac{1}{2} \] **Step 2:** Find a common denominator. The LCD of 3 and 2 is 6. \[ \frac{2}{3} = \frac{4}{6}, \quad \frac{1}{2} = \frac{3}{6} \] **Step 3:** Subtract the fractions. \[ \frac{4}{6} - \frac{3}{6} = \frac{1}{6} \] **Answer:** \(\frac{1}{6}\) --- ### d. \(\frac{2}{3} + \frac{4}{9}\) **Step 1:** Find a common denominator. The LCD of 3 and 9 is 9. \[ \frac{2}{3} = \frac{6}{9} \] **Step 2:** Add the fractions. \[ \frac{6}{9} + \frac{4}{9} = \frac{10}{9} = 1 \frac{1}{9} \] **Answer:** \(1 \frac{1}{9}\) or \(\frac{10}{9}\) --- ### e. \(\frac{4}{5} + \frac{8}{10}\) **Step 1:** Simplify \(\frac{8}{10}\). \[ \frac{8}{10} = \frac{4}{5} \] **Step 2:** Add the fractions. \[ \frac{4}{5} + \frac{4}{5} = \frac{8}{5} = 1 \frac{3}{5} \] **Answer:** \(1 \frac{3}{5}\) or \(\frac{8}{5}\) --- ### f. \(\frac{3}{4} - \frac{2}{3}\) **Step 1:** Find a common denominator. The LCD of 4 and 3 is 12. \[ \frac{3}{4} = \frac{9}{12}, \quad \frac{2}{3} = \frac{8}{12} \] **Step 2:** Subtract the fractions. \[ \frac{9}{12} - \frac{8}{12} = \frac{1}{12} \] **Answer:** \(\frac{1}{12}\) --- ### g. \(\frac{4}{9} - \frac{1}{3}\) **Step 1:** Find a common denominator. The LCD of 9 and 3 is 9. \[ \frac{1}{3} = \frac{3}{9} \] **Step 2:** Subtract the fractions. \[ \frac{4}{9} - \frac{3}{9} = \frac{1}{9} \] **Answer:** \(\frac{1}{9}\) --- ### h. \(\frac{1}{4} + \frac{4}{12}\) **Step 1:** Simplify \(\frac{4}{12}\). \[ \frac{4}{12} = \frac{1}{3} \] **Step 2:** Find a common denominator. The LCD of 4 and 3 is 12. \[ \frac{1}{4} = \frac{3}{12}, \quad \frac{1}{3} = \frac{4}{12} \] **Step 3:** Add the fractions. \[ \frac{3}{12} + \frac{4}{12} = \frac{7}{12} \] **Answer:** \(\frac{7}{12}\) --- ### i. \(\frac{3}{5} + \frac{1}{3}\) **Step 1:** Find a common denominator. The LCD of 5 and 3 is 15. \[ \frac{3}{5} = \frac{9}{15}, \quad \frac{1}{3} = \frac{5}{15} \] **Step 2:** Add the fractions. \[ \frac{9}{15} + \frac{5}{15} = \frac{14}{15} \] **Answer:** \(\frac{14}{15}\) --- ### j. \(\frac{1}{2} - \frac{1}{5}\) **Step 1:** Find a common denominator. The LCD of 2 and 5 is 10. \[ \frac{1}{2} = \frac{5}{10}, \quad \frac{1}{5} = \frac{2}{10} \] **Step 2:** Subtract the fractions. \[ \frac{5}{10} - \frac{2}{10} = \frac{3}{10} \] **Answer:** \(\frac{3}{10}\) --- ### k. \(\frac{5}{6} - \frac{1}{2}\) **Step 1:** Find a common denominator. The LCD of 6 and 2 is 6. \[ \frac{1}{2} = \frac{3}{6} \] **Step 2:** Subtract the fractions. \[ \frac{5}{6} - \frac{3}{6} = \frac{2}{6} = \frac{1}{3} \] **Answer:** \(\frac{1}{3}\) --- ### l. \(\frac{1}{2} + \frac{1}{3}\) **Step 1:** Find a common denominator. The LCD of 2 and 3 is 6. \[ \frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6} \] **Step 2:** Add the fractions. \[ \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \] **Answer:** \(\frac{5}{6}\) --- If you need further explanations or assistance with any of these problems, feel free to ask!