First, we need to convert the mixed numbers to improper fractions.
-1 3/10 can be written as -(10/10 + 3/10) = -(13/10)
Similarly, -4 2/15 can be written as (-4 * 15 + 2)/15 = (-58/15)
Now we can add the fractions:
-(13/10) + (-58/15)
To find a common denominator for 10 and 15, we can multiply them together: 10 * 15 = 150.
Now we can rewrite the fractions with the common denominator of 150:
-(13/10) = -(13/10 * 15/15) = -(195/150)
-(58/15) = -(58/15 * 10/10) = -(580/150)
Now we can add the fractions:
-(195/150) + -(580/150) = (-195 - 580)/150 = -775/150
However, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 25:
-775/150 = (-31 * 25)/(6 * 25) = -31/6
Therefore, -1 3/10 + (-4 2/15) = -31/6.