To add the numbers \(-1 \frac{3}{10}\) and \(-4 \frac{2}{15}\), let's first convert them to improper fractions:
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Convert \(-1 \frac{3}{10}\): \[ -1 \frac{3}{10} = -\left(1 \times 10 + 3\right) / 10 = -\frac{10 + 3}{10} = -\frac{13}{10} \]
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Convert \(-4 \frac{2}{15}\): \[ -4 \frac{2}{15} = -\left(4 \times 15 + 2\right) / 15 = -\frac{60 + 2}{15} = -\frac{62}{15} \]
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 the fractions to have the common denominator of 30: \[ -\frac{13}{10} = -\frac{13 \times 3}{10 \times 3} = -\frac{39}{30} \] \[ -\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30} \]
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Now, add the two fractions: \[ -\frac{39}{30} + -\frac{124}{30} = -\frac{39 + 124}{30} = -\frac{163}{30} \]
Finally, we can convert \(-\frac{163}{30}\) to a mixed number: \[ -\frac{163}{30} = -5 \frac{13}{30} \]
Thus, the answer is: \[ \text{negative 5 } \frac{13}{30} \]
Based on the responses provided, none of them match \(-5 \frac{13}{30}\), but if we're looking for the closest option, we have:
- \(-5 \frac{1}{6}\) is close but doesn’t match our result.
Please double-check to see if the options provided are different. If modifying fractions is acceptable, \(-5 \frac{1}{5}\) could be rounded, but it's not equivalent.
None of the provided options are correct based on the calculations made.