To solve the problem of adding \(-1 \frac{3}{10}\) and \(-4 \frac{2}{15}\), we first convert both mixed numbers into improper fractions.
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Convert \(-1 \frac{3}{10}\): \[ -1 \frac{3}{10} = -\left(1 \times 10 + 3\right)/10 = -\frac{13}{10} \]
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Convert \(-4 \frac{2}{15}\): \[ -4 \frac{2}{15} = -\left(4 \times 15 + 2\right)/15 = -\frac{62}{15} \]
Now, we need to add these two fractions: \[ -\frac{13}{10} + (-\frac{62}{15}) \] This simplifies to: \[ -\frac{13}{10} - \frac{62}{15} \]
Next, we need a common denominator to add these fractions. The least common multiple of 10 and 15 is 30.
- Convert both fractions to have a denominator of 30:
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For \(-\frac{13}{10}\): \[ -\frac{13}{10} = -\frac{13 \times 3}{10 \times 3} = -\frac{39}{30} \]
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For \(-\frac{62}{15}\): \[ -\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30} \]
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Now we can add the two fractions: \[ -\frac{39}{30} - \frac{124}{30} = -\frac{39 + 124}{30} = -\frac{163}{30} \]
Now we can convert \(-\frac{163}{30}\) back into a mixed number:
- 30 goes into 163 five times (since \(30 \times 5 = 150\)), leaving a remainder of 13.
- Therefore: \[ -\frac{163}{30} = -5 \frac{13}{30} \]
Thus, the final result is: \[ \boxed{-5 \frac{13}{30}} \]
The answer is \(d. -5 \frac{13}{30}\).