Answer:
(-4)/3
Step-by-step explanation:
Simplify the following:
16/(5 (-(2 + 2/5)))
Put 2 + 2/5 over the common denominator 5. 2 + 2/5 = (5×2)/5 + 2/5:
16/(5 (-(5×2)/5 + 2/5))
5×2 = 10:
16/(5 (-(10/5 + 2/5)))
10/5 + 2/5 = (10 + 2)/5:
16/(5 (-(10 + 2)/5))
10 + 2 = 12:
(16/5)/(-12/5)
(16/5)/((12 (-1))/5) = 16/(-12/5×5):
16/(-12/5×5)
-12×5 = -60:
16/((-60)/5)
Multiply the numerator of 16/((-60)/5) by the reciprocal of the denominator. 16/((-60)/5) = (16×5)/(-60):
(16×5)/(-60)
5/(-60) = 5/(5 (-12)) = 1/(-12):
16/(-12)
The gcd of 16 and -12 is 4, so 16/(-12) = (4×4)/(4 (-3)) = 4/4×4/(-3) = 4/(-3):
4/(-3)
Multiply numerator and denominator of 4/(-3) by -1:
Answer: (-4)/3
