which of the following inequalities is true?

a. 3/4 < 5/7

b. 2/3> 5/6

c. 5/8 > 6/10

d. 4/5 < 2/9

Let's go through each answer choice one at a time.

Choice A
3/4 < 5/7 
3*7 < 4*5 ... cross multiply
21 < 20
The last inequality is false, so the original inequality is false
Choice A is false

Choice B
2/3 > 5/6
2*6 > 3*5 ... cross multiply
12 > 15
The last inequality is false, so the original inequality is false
Choice B is false

Choice C
5/8 > 6/10
5*10 > 8*6  ... cross multiply
50 > 48
The last inequality is true, so the original inequality is true
Choice C is true

Choice D
4/5 < 2/9
4*9 < 5*2  ... cross multiply
36 < 10
The last inequality is false, so the original inequality is false
Choice D is false

In summary, we have
A. False
B. False
C. True
D. False
So the final answer is choice C