If you colored one tooth on each cog, which pairs of cogs let the colored tooth go into every ‘gap' on the other cog?
Which pairs do not let this happen? Why?
Can you explain how to determine which pairs will work, and why?
Record and show your reasoning, conjectures, explanations and any
generalizations on your own paper or right here in Kami.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional