Step-by-step explanation:
to compare them, we should all bring to the same denominator.
the lcm (lowest common multiplier) is the that denominator.
let's use the approach of the prime factors :
3 : 3
5 : 5
32 : 2×2×2×2×2
24 : 2×2×2×3
the lcm is the combination of the longest "streaks" of the prime factors.
so,
2×2×2×2×2 × 3 × 5 = 32×15 = 480
2/-3 = -2/3 = -320/480 (as 3×160 = 480)
-4/5 = -4×96 / 5×96 = -384/480 (as 5×96 = 480)
21/-32 = -21/32 = -315/480 (as 32×15 = 480)
-15/24 = -15×20 / 24×20 = -300/480 (24×20 = 480)
as
-384/480 < -320/480 < -315/480 < -300/480
we can say
-4/5 < -2/3 < -21/32 < -15/24
