1 5/9÷(−2/3)+(−2 3/5)

(-74)/15

Step-by-step explanation:

Simplify the following:

(1 + 5/9)/((-2)/3) - (2 + 3/5)

Multiply the numerator of (1 + 5/9)/((-2)/3) by the reciprocal of the denominator. (1 + 5/9)/((-2)/3) = ((1 + 5/9)×3)/(-2):

((5/9 + 1) 3)/(-2) - (2 + 3/5)

Put 1 + 5/9 over the common denominator 9. 1 + 5/9 = 9/9 + 5/9:

(9/9 + 5/9 3)/(-2) - (2 + 3/5)

9/9 + 5/9 = (9 + 5)/9:

((9 + 5)/9×3)/(-2) - (2 + 3/5)

9 + 5 = 14:

(14/9×3)/(-2) - (2 + 3/5)

14/9×3 = (14×3)/9:

((14×3)/9)/(-2) - (2 + 3/5)

((14×3)/9)/(-2) = (14×3)/(9 (-2)):

(14×3)/(9 (-2)) - (2 + 3/5)

3/9 = 3/(3×3) = 1/3:

14/(3 (-2)) - (2 + 3/5)

The gcd of 14 and -2 is 2, so 14/(3 (-2)) = (2×7)/(3 (2 (-1))) = 2/2×7/(3 (-1)) = 7/(3 (-1)):

7/(3×-1) - (2 + 3/5)

Put 2 + 3/5 over the common denominator 5. 2 + 3/5 = (5×2)/5 + 3/5:

7/(-3) - (5×2)/5 + 3/5

5×2 = 10:

7/(-3) - (10/5 + 3/5)

10/5 + 3/5 = (10 + 3)/5:

7/(-3) - (10 + 3)/5

10 + 3 = 13:

7/(-3) - 13/5

Multiply numerator and denominator of 7/(-3) by -1:

(-7)/3 - 13/5

Put (-7)/3 - 13/5 over the common denominator 15. (-7)/3 - 13/5 = (5 (-7))/15 + (3 (-13))/15:

(5 (-7))/15 + (3 (-13))/15

5 (-7) = -35:

(-35)/15 + (3 (-13))/15

3 (-13) = -39:

(-35)/15 + (-39)/15

-35/15 - 39/15 = (-35 - 39)/15:

(-35 - 39)/15

-35 - 39 = -(35 + 39):

(-(35 + 39))/15

| 1 |  

| 3 | 9

+ | 3 | 5

| 7 | 4:

(-74)/15