Add the reciprocal of 1 1/5 to the sum of the numbers (+1.25) and (-1 3/4).

To find the reciprocal of a mixed number, we first convert it to an improper fraction. 1 1/5 = 5/5 + 1/5 (remember that 1 whole would have the same numerator and denominator) = 6/5.

The reciprocal is this number flipped, so 5/6.

To find the sum of 1.25 and - 1 3/4, we will convert the decimal to a fraction. 0.25 is read as "twenty-five hundredths," so the fraction would be 25/100. This will simplify to 1/4, so 1.25 = 1 1/4.

1 1/4 + - 1 3/4 = - 2/4 = - 1/2.

Now we add 5/6 + - 1/2:

Find the least common denominator (LCD). 6 is the first number that both 6 and 2 will divide into evenly. This gives us 5/6 + - 3/6 (we multiply 2 by 3 to get 6, so we multiply the numerator, - 1, by 3 as well). This equals 2/6 which simplifies to 1/3.