cenng ((3)/(14)+(13)/(21))cdot 9 __

To solve the expression \((\frac{3}{14} + \frac{13}{21}) \cdot 9\), follow these steps:<br /><br />1. **Find a common denominator for the fractions**:<br /> The denominators are 14 and 21. The least common multiple (LCM) of 14 and 21 is 42.<br /><br />2. **Convert each fraction to have the common denominator**:<br /> \[<br /> \frac{3}{14} = \frac{3 \times 3}{14 \times 3} = \frac{9}{42}<br /> \]<br /> \[<br /> \frac{13}{21} = \frac{13 \times 2}{21 \times 2} = \frac{26}{42}<br /> \]<br /><br />3. **Add the fractions**:<br /> \[<br /> \frac{9}{42} + \frac{26}{42} = \frac{9 + 26}{42} = \frac{35}{42}<br /> \]<br /><br />4. **Simplify the fraction**:<br /> \[<br /> \frac{35}{42} = \frac{5}{6} \quad \text{(since 35 and 42 have a common factor of 7)}<br /> \]<br /><br />5. **Multiply the result by 9**:<br /> \[<br /> \frac{5}{6} \cdot 9 = \frac{5 \times 9}{6} = \frac{45}{6} = 7.5<br /> \]<br /><br />So, the final answer is:<br />\[<br />(\frac{3}{14} + \frac{13}{21}) \cdot 9 = 7.5<br />\]