I want to know if there is a way to simplify a fraction by the press of a button on my ti-31xIIs

Refer to page no 13 of user manual of calculator. (TI-30XS / TI-30XB MultiView™ Guidebook - Texas Instruments - US and Canada) It will solve your problem.

0.32=32/100. But 32=4*8 and 100=4*25. Simplifying by the common factor 4, yields 0.32=8/25
On the TI 83Plus, enter the number, then press the MATH key. Select 1:>Frac. Press ENTER.

You do not simplify fractions on the calculator. If the calculator is able to display fraction results, be sure that the form it gives you is the simplest. If the fraction is a mixed one there is usually a key to switch from mixed to improper, and from improper to mixed the keys are [a b/c] and [d/c]

you press the a b/c button say a=4 b=6 c=9 then it would be 4 6/9 you click enter and it simplifies it.

Two ways:

1) hit the equal sign

2) hit 2nd and [d/c] (you can do this multiple times to see it as the most reduced improper fraction or as a mixed fraction)

for my 82 i put my fraction in parentheses then press MATH and scroll to >FRAC

Enter the fraction for example: enter 8/12.
The answer will be .666666
Then click Math (which is located under the Alpha button).
Click the ->Frac button (the first one).
It should come up as Ans->Frac.
Click Enter.
It should now read 2/3 which is 8/12 reduced.
Note: I have a TI-84 Plus Silver Edition, and the TI-84 Plus might not have this function, but that is how I do it on my TI-84 Plus Silver Edition

Yeah, there isn't a fraction button on an 84. You have to enter it manually as 4/9 or if simplifying a decimal, use the Ans>Frac under the MATH menu

a quart is one fourth of a gallon. Dan drank half a quart of milk. What fraction of a gallon did Dan drink

Theres an A b/c button. Pretend its 90/100 Do 90 then press A b/c then type 100 and =.