To add the fractions \(-1 \frac{3}{10} + (-4 \frac{2}{15})\), we can first convert both mixed numbers into improper fractions.
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Convert \(-1 \frac{3}{10}\) to an improper fraction: \[ -1 \frac{3}{10} = -\left(1 \cdot 10 + 3\right)/10 = -\frac{10 + 3}{10} = -\frac{13}{10} \]
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Convert \(-4 \frac{2}{15}\) to an improper fraction: \[ -4 \frac{2}{15} = -\left(4 \cdot 15 + 2\right)/15 = -\frac{60 + 2}{15} = -\frac{62}{15} \]
Now we need to add \(-\frac{13}{10}\) and \(-\frac{62}{15}\). To do this, we need a common denominator. The least common multiple of 10 and 15 is 30.
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Convert \(-\frac{13}{10}\) to have a denominator of 30: \[ -\frac{13}{10} = -\frac{13 \times 3}{10 \times 3} = -\frac{39}{30} \]
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Convert \(-\frac{62}{15}\) to have a denominator of 30: \[ -\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30} \]
Now we can add the two fractions: \[ -\frac{39}{30} + -\frac{124}{30} = -\frac{39 + 124}{30} = -\frac{163}{30} \]
Now, to express \(-\frac{163}{30}\) as a mixed number:
- Divide 163 by 30.
- 30 goes into 163 five times (since \(30 \times 5 = 150\)), and we have a remainder of \(163 - 150 = 13\).
So, \(-\frac{163}{30} = -5 \frac{13}{30}\).
Thus, the answer is: \[ \boxed{-5 \frac{13}{30}} \]
This corresponds to option C.