Question

Which ratio is greater:
(i) $\frac{8}{15}\text{or}\frac{5}{9}$

Answer 1

LCM of $15,9$
Factors of $15=3\times 5$
Factors of $9=3\times 3$
Thus, LCM of $15,9=5\times 3\times 3=45$
Multiplying the numerator and denominator of the first fraction by 3, we get
$\frac{8}{15}=\frac{8\times 3}{15\times 3}$
$=\frac{24}{45}$
Multiplying the numerator and denominator of the second fraction by 5.
$\frac{5}{9}=\frac{5\times 5}{9\times 5}$
$=\frac{25}{45}$
We know,
$24<25$
Thus,
$\frac{24}{45}<\frac{25}{45}$
$\frac{8}{15}<\frac{5}{9}$
$\therefore \frac{5}{9}$ is greater between gives ratios.