Question

−1 3/10 +(−4 2/15)

Answer 1

To add the fractions \(-1 \frac{3}{10}\) and \(-4 \frac{2}{15}\), we can first convert the mixed numbers into improper fractions.

1. **Convert \(-1 \frac{3}{10}\) to an improper fraction:**
\[
-1 \frac{3}{10} = -\left(1 \times 10 + 3\right)/10 = -\frac{13}{10}
\]

2. **Convert \(-4 \frac{2}{15}\) to an improper fraction:**
\[
-4 \frac{2}{15} = -\left(4 \times 15 + 2\right)/15 = -\frac{62}{15}
\]

Now we have:
\[
-\frac{13}{10} + -\frac{62}{15}
\]

Next, we need a common denominator to add these fractions. The least common multiple (LCM) of 10 and 15 is 30.

3. **Convert the fractions to have a common denominator:**
- For \(-\frac{13}{10}\):
\[
-\frac{13}{10} = -\frac{13 \times 3}{10 \times 3} = -\frac{39}{30}
\]
- For \(-\frac{62}{15}\):
\[
-\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30}
\]

Now we can add the fractions:
\[
-\frac{39}{30} + -\frac{124}{30} = -\frac{39 + 124}{30} = -\frac{163}{30}
\]

4. **Convert the improper fraction back to a mixed number (if desired):**
- Divide 163 by 30, which goes 5 times remainder 13.
\[
-\frac{163}{30} = -5 \frac{13}{30}
\]

Thus, the result of \(-1 \frac{3}{10} + (-4 \frac{2}{15})\) is:
\[
\boxed{-5 \frac{13}{30}}
\]