To add the fractions \(-1 \frac{3}{10}\) and \(-4 \frac{2}{15}\), we can first convert these mixed numbers into improper fractions and then find a common denominator.
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Convert the mixed numbers to improper fractions:
\[ -1 \frac{3}{10} = -\left(1 \times 10 + 3\right)/10 = -\frac{13}{10} \]
\[ -4 \frac{2}{15} = -\left(4 \times 15 + 2\right)/15 = -\frac{62}{15} \]
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Now we want to add these two improper fractions:
\[ -\frac{13}{10} + \left(-\frac{62}{15}\right) \]
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Find a common denominator. The least common multiple of 10 and 15 is 30.
Convert the fractions:
\[ -\frac{13}{10} = -\frac{13 \times 3}{10 \times 3} = -\frac{39}{30} \]
\[ -\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30} \]
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Now add the two fractions:
\[ -\frac{39}{30} + -\frac{124}{30} = -\frac{39 + 124}{30} = -\frac{163}{30} \]
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Convert \(-\frac{163}{30}\) back into a mixed number:
\(-\frac{163}{30}\) means that \(163\) divided by \(30\) is \(5\) with a remainder of \(13\):
\[ -\frac{163}{30} = -5 \frac{13}{30} \]
So the answer is:
\(-5 \frac{13}{30}\)
Thus the correct response is \(-5 \frac{13}{30}\).