Step-by-step explanation:
for such problems it is always the best approach to being both fractions to the same denominator.
that means for one or both of them we need to multiply them with the same factor on the top and the bottom (so that the fraction value remains unchanged), so that we get 2 fractions with the same denominators (bottom part).
the the least common multiple for 4 and 5 is 20.
so, we need to bring both fractions to .../20 :
7/4 × 5/5 = 35/20
9/5 × 4/4 = 36/20
now, to find a fraction between them, we need to actually refine the denominator even further, as 35 and 36 are consecutive integers.
in such a case I suggest doubling things.
35/20 × 2/2 = 70/40
36/20 × 2/2 = 72/40
now we see, a fraction between 7/4 and 9/5 would be
71/40
as 7/4 = 70/40 is smaller, and 9/5 = 72/40 is larger.
