What is the value of 1 - ((1)/(30) + (4)/(15))?

To add the fractions $\frac{1}{30}$ and $\frac{4}{15}$, find a common denominator. The least common multiple of 30 and 15 is 30.
Convert $\frac{4}{15}$ to an equivalent fraction with a denominator of 30:

$$\frac{4}{15} = \frac{4 \times 2}{15 \times 2} = \frac{8}{30}$$

$$1 - \frac{3}{10}$$

To subtract, express 1 as a fraction with a denominator of 10:

$$\frac{10}{10} - \frac{3}{10} = \frac{10-3}{10} = \frac{7}{10}$$

The final answer is $\frac{7}{10}$.