Explanation:
since a ratio is a fraction with all calculation and comparison rules (but with a special overall meaning), we need to observe the main rule for transforming fractions : when multiplying one part of the fraction by a factor, we also need to multiply the other part by the same factor to keep the value of the fraction unchanged.
the basic ratio is here
145/52 (or written 145:52 - it has the same meaning)
290/104 is just (145×2)/(52×2)
435/156 is just (145×3)/(52×3)
to complete the table we simply have to keep following that structure :
580 = 145×4
so, 52×4 = 208
and the ratio is
580/208
725 = 145×5
52×5 = 260
and the ratio is
725/260