To solve the expression (-\frac{3}{10} + \left(-1 \frac{1}{2}\right) + \left(-\frac{4}{5}\right)), let's first convert the mixed number into an improper fraction:
[
-1 \frac{1}{2} = -\frac{3}{2}
]
Now we can rewrite the expression:
[
-\frac{3}{10} - \frac{3}{2} - \frac{4}{5}
]
Next, we need to find a common denominator. The denominators are 10, 2, and 5. The least common multiple (LCM) of these numbers is 10.
Now, we will convert each term to have a denominator of 10:
- The first term is already (-\frac{3}{10}).
- For (-\frac{3}{2}), multiply the numerator and denominator by 5:
[
-\frac{3}{2} = -\frac{3 \times 5}{2 \times 5} = -\frac{15}{10}
]
- For (-\frac{4}{5}), multiply the numerator and denominator by 2:
[
-\frac{4}{5} = -\frac{4 \times 2}{5 \times 2} = -\frac{8}{10}
]
Now we can add all the fractions together:
[
-\frac{3}{10} - \frac{15}{10} - \frac{8}{10} = -\frac{3 + 15 + 8}{10} = -\frac{26}{10}
]
Finally, we can simplify (-\frac{26}{10}):
[
-\frac{26}{10} = -\frac{13}{5}
]
Thus, the final result is:
[
-\frac{13}{5}
]
