To add the fractions \(-1 \frac{3}{10}\) and \(-4 \frac{2}{15}\), let's follow these steps:
-
First, convert the mixed numbers to improper fractions.
For \(-1 \frac{3}{10}\): \[ -1 \frac{3}{10} = -\left(1 \times 10 + 3\right) / 10 = -\left(10 + 3\right) / 10 = -13/10 \]
For \(-4 \frac{2}{15}\): \[ -4 \frac{2}{15} = -\left(4 \times 15 + 2\right) / 15 = -\left(60 + 2\right) / 15 = -62/15 \]
-
Now we need to add the two improper fractions: \[ -\frac{13}{10} + -\frac{62}{15} \]
-
To add these fractions, we need a common denominator. The least common multiple (LCM) of 10 and 15 is 30.
-
Convert each fraction: \[ -\frac{13}{10} = -\frac{13 \times 3}{10 \times 3} = -\frac{39}{30} \] \[ -\frac{62}{15} = -\frac{62 \times 2}{15 \times 2} = -\frac{124}{30} \]
-
Now, add the fractions: \[ -\frac{39}{30} + -\frac{124}{30} = -\frac{39 + 124}{30} = -\frac{163}{30} \]
-
Convert the improper fraction back to a mixed number: \(-\frac{163}{30}\) can be converted by dividing \(163\) by \(30\): \[ 163 \div 30 = 5 \text{ remainder } 13 \] So, \[ -\frac{163}{30} = -5 \frac{13}{30} \]
Therefore, the final answer is: \[ -5 \frac{13}{30} \]
1 answer