**Which fraction is smaller? **$\displaystyle \frac{3}{5}$ or $\displaystyle \frac{7}{9}$

Since the fractions have different denominators we find the least common denominator.

5 = 1 x 5

9 = 3 x 3

LCD(5, 9) = 1 x 3 x 3 x 5 = 45

We convert our fractions into equivalent one´s with the denominator 45

$\displaystyle \frac{3}{5}\times \frac{9}{9}=\frac{{27}}{{45}}$

$\displaystyle \frac{7}{9}\times \frac{5}{5}=\frac{{35}}{{45}}$

Since the fractions have same denominator then we compare the numerators.

Since 27 < 35 then $\displaystyle \frac{{27}}{{45}}<\frac{{35}}{{45}}$ or $\displaystyle \frac{3}{5}<\frac{7}{9}$