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Compare the following 2/-3, -4/5, 21/-32, -15/24

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

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: