Idon't quite get this.

jan has 35 teaspoons of chocolate cocoa mix and 45 teaspoons of french vanilla cocoa mix. she wants to put the same amount of mix into each jar. she want to fill as many as jars as possible. how many jars of french vanilla cocoa mix will jan fill?

should i use distributive property? if not then what do i use and how?

Psh, I dont even get this a bit.. 
but imma do what I usually do and go with my instinct..

35 teaspoons of chocolate cocoa mix
45 teaspoons of french vanilla cocoa mix

(some excess way of finding it out aka my way :p)
35 x 1 = 35
35 x 2 = 70 
35 x 3 = 105
35 x 4 = 140
35 x 5 = 175
35 x 6 = 210
35 x 7 = 245
35 x 8 = 280
35 x 9 = 315 <=
35 x 10 = 350 

45 x 1 = 45
45 x 2 = 90
45 x 3 = 135
45 x 4 = 180
45 x 5 = 225
45 x 6 = 270
45 x 7 = 315 <=
45 x 8 = 360
45 x 9 = 405
45 x 10 = 450

As you can see, 315 is the first to go into them both! 

35 x 9 = 315
45 x 7 = 315

therefore..
you add 9 teaspoons of chocolate cocoa mix and 7 teaspoons of french vanilla cocoa mix to get the same amount of mix into each jar..