How can I simplify a fraction after adding two fractions?

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.

Put the integer part on the same denominator as the fraction part. Combine the two numerators, and simplify if possible.

When you enter a fraction using the fraction key, the displayed fraction is always reduced (simplified). By hand, you look for common factors in the numerator and denominator then simplify by them. Keep looking for common factors and simplifying until there are no more common factors.

If you enter the ratios using the fraction entry key ( [a b/c] the results will be displayed as fractions. And when the calculator displays fractions they are always in their reduced form.
In general, when you are manipulating fractions ( Pi/2 is no a fraction even if you write it as one) you can try to simplify them by looking for the greatest common factor (GCF) of the numerator and denominator. When you simplify by the GCF the fraction that is left is in its reduced form.

If you enter the ratios using the fraction entry key ( [a b/c] the results will be displayed as fractions. And when the calculator displays fractions they are always in their reduced form.
In general, when you are manipulating fractions ( Pi/2 is no a fraction even if you write it as one) you can try to simplify them by looking for the greatest common factor (GCF) of the numerator and denominator. When you simplify by the GCF the fraction that is left is in its reduced form.

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]

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

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