Answer:
Rational numbers are integer fractions.
Now if the denominator is the same adding or subtracting fractions is the same as adding or subtracting their numerators:
ac±bc=a±bc
Now if the denominators differ you can find a common denominator (usually the least) and use this trick:
ab±cd=a⋆±c⋆lcm(b,d)
Note
a⋆=a×lcm(b,d)b
and
c⋆=c×lcm(b,d)d
Integers are these rational numbers where in the most simplified version of the integer fraction the denominator is 1.