Brenda is finding 1/4 + 3/5. she used this reasoning to come up with 4/9 = 1/4 + 3/5. is she correct? if not correct it and explain my answer

No she's not correct. To add fractions you have to have common denominators. Since 4 and 5 are different, you can't just add the tops. You would have to think of equivalent fractions to give you  the same denominator before adding the numerators. 

No, she can't just add the bottoms
the botoms have to be the same, then she can add the tops

so

1/4+3/5
a fraction times 1 remains the same
x/x=1 where x=x

1/4 times 5/5=5/20

3/5 times 4/4=12/20

we have
1/4+3/5=5/20+12/20=(5+12)/20=17/20