1) \( \frac{16}{5}-\frac{13}{15}+\frac{29}{30}-\frac{16}{9} \)

To solve \( \frac{16}{5}-\frac{13}{15}+\frac{29}{30}-\frac{16}{9} \), we first find a common denominator, which is 90. - Convert \( \frac{16}{5} \) to \( \frac{288}{90} \) (by multiplying numerator and denominator by 18). - Convert \( \frac{13}{15} \) to \( \frac{78}{90} \) (by multiplying numerator and denominator by 6). - Convert \( \frac{29}{30} \) to \( \frac{87}{90} \) (by multiplying numerator and denominator by 3). - Convert \( \frac{16}{9} \) to \( \frac{160}{90} \) (by multiplying numerator and denominator by 10). Now combine: \[ \frac{288}{90} - \frac{78}{90} + \frac{87}{90} - \frac{160}{90} = \frac{288 - 78 + 87 - 160}{90} = \frac{137}{90} \] Thus, the final answer is: \[ \frac{137}{90} \]