Can rational numbers be expressed as a fraction of two integers

Yes this is the exact definition of what it means to be a rational number. A rational number is one that is a fraction of two whole numbers (or integers). The denominator, or the number in the bottom of the fraction, cannot be 0.

Some examples:

7 = 7/1

2/3

8/10

0.5 (since this equals 1/2)

the square root of 64 (since it equals 8 = 8/1)

any repeating decimal

any terminating decimal

Non-examples are things like ...

sqrt (7)

pi

log (3)

any decimal where there isn't a clear pattern that repeats

Yes, this is what a rational number is.