−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: \[ \boxed{-5 \frac{13}{30}} \]