6. Find the sum or difference. a. (2)/(3)+(2)/(4) b. (7)/(4)-(5)/(6) C (25)/(3)-(10)/(6) d. (7)/(9)+(3)/(4) e. (1)/(12)+(1)/(8)

## Step 1: Finding the Least Common Denominator (LCD) for (a)<br />### To add fractions, we need a common denominator. The LCD of 3 and 4 is 12.<br /><br />## Step 2: Converting Fractions to Equivalent Fractions with the LCD (a)<br />### Convert both fractions to have a denominator of 12: $\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$ and $\frac{2}{4} = \frac{2 \times 3}{4 \times 3} = \frac{6}{12}$.<br /><br />## Step 3: Adding the Fractions (a)<br />### Now, add the numerators: $\frac{8}{12} + \frac{6}{12} = \frac{14}{12}$.<br /><br />## Step 4: Simplifying the Result (a)<br />### Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 2: $\frac{14}{12} = \frac{7}{6}$.<br /><br /><br />## Step 5: Repeating the Process for (b)<br />### LCD of 4 and 6 is 12. $\frac{7}{4} = \frac{21}{12}$ and $\frac{5}{6} = \frac{10}{12}$. $\frac{21}{12} - \frac{10}{12} = \frac{11}{12}$.<br /><br />## Step 6: Repeating the Process for (c)<br />### LCD of 3 and 6 is 6. $\frac{25}{3} = \frac{50}{6}$ and $\frac{10}{6}$ remains as is. $\frac{50}{6} - \frac{10}{6} = \frac{40}{6} = \frac{20}{3}$.<br /><br />## Step 7: Repeating the Process for (d)<br />### LCD of 9 and 4 is 36. $\frac{7}{9} = \frac{28}{36}$ and $\frac{3}{4} = \frac{27}{36}$. $\frac{28}{36} + \frac{27}{36} = \frac{55}{36}$.<br /><br />## Step 8: Repeating the Process for (e)<br />### LCD of 12 and 8 is 24. $\frac{1}{12} = \frac{2}{24}$ and $\frac{1}{8} = \frac{3}{24}$. $\frac{2}{24} + \frac{3}{24} = \frac{5}{24}$.