Question

Which ratio is smaller:
(i) $\frac{9}{17}\text{or}\frac{8}{15}$

Answer 1

LCM of $17,15$
Factors of $17=17\times 1$
Factors of $15=3\times 5$
Thus, LCM of $17,15=5\times 3\times 17=255$
Multiplying the numerator and denominator of the first fraction by $15$.
we get,
$\frac{9}{17}=\frac{9\times 15}{17\times 15}$
$=\frac{135}{255}$
Multiplying the numerator and denominator of the second factors by 17.
$\frac{8}{15}=\frac{17\times 8}{17\times 15}$
$=\frac{136}{255}$
We know,
$135<136$
Thus,
$\frac{135}{255}<\frac{136}{255}$
$\frac{9}{17}<\frac{8}{15}$
$\therefore \frac{9}{17}$ is smaller between given ratios.