Question 1209284
Answer: <font color=red>1/3</font>


Explanation


The other tutors have great responses. 
I'll offer another approach.


Let's compare the fractions A and B
For now assume they are equal. 
We can use the cross multiplication rule like so
3/7 = 1/3
3*3 = 7*1
9 = 7
The last equation is false since the two sides don't agree on the same number.
To fix the error, change each equal sign to a greater than sign.
3/7 > 1/3
3*3 > 7*1
9 > 7
We determine that 3/7 is larger than 1/3.
Cross choice A off the list.
So far 1/3 is the smallest value. 
But there could be another fraction in this list that's smaller.


Now let's compare B and C. 
Like before we assume they are equal, and use the cross multiplication rule to get,
1/3 = 5/6
1*6 = 3*5
6 = 15
This is false, so let's fix the errors.
1/3 < 5/6
1*6 < 3*5
6 < 15
The fraction 1/3 is still the smallest so far. 
Cross choice C off the list.


The last comparison is to look at B and D.
1/3 = 9/14
1*14 = 3*9
14 = 27
Let's fix the errors
1/3 < 9/14
1*14 < 3*9
14 < 27
Cross choice D off the list since D is larger than B.


Therefore 1/3 is the smallest fraction in the list.
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