6) (4)/(19)cdot (-3)/(7)-(3)/(7)cdot (15)/(19)+(5)/(7) 9) (53)/(101)cdot (-13)/(97)+(53)/(101)cdot (-84)/(97)+(13)/(101)

**6) $\frac{4}{19} \cdot \frac{-3}{7} - \frac{3}{7} \cdot \frac{15}{19} + \frac{5}{7}$**<br /><br />We can factor out $\frac{-3}{7}$ from the first two terms:<br /><br />$= \frac{-3}{7} \left( \frac{4}{19} + \frac{15}{19} \right) + \frac{5}{7}$<br /><br />$= \frac{-3}{7} \left( \frac{19}{19} \right) + \frac{5}{7}$<br /><br />$= \frac{-3}{7} (1) + \frac{5}{7}$<br /><br />$= \frac{-3 + 5}{7}$<br /><br />$= \frac{2}{7}$<br /><br /><br />**9) $\frac{53}{101} \cdot \frac{-13}{97} + \frac{53}{101} \cdot \frac{-84}{97} + \frac{13}{101}$**<br /><br />We can factor out $\frac{53}{101}$ from the first two terms:<br /><br />$= \frac{53}{101} \left( \frac{-13}{97} + \frac{-84}{97} \right) + \frac{13}{101}$<br /><br />$= \frac{53}{101} \left( \frac{-97}{97} \right) + \frac{13}{101}$<br /><br />$= \frac{53}{101} (-1) + \frac{13}{101}$<br /><br />$= \frac{-53 + 13}{101}$<br /><br />$= \frac{-40}{101}$<br /><br />Therefore:<br /><br />6) $\frac{2}{7}$<br />9) $\frac{-40}{101}$<br />