Question

Which ratio is smaller:
(ii) $\frac{7}{15}\text{or}\frac{15}{32}$

Answer 1

LCM of $15,9$
Factors of $15=3\times 5$
Factors of $32=2\times 2\times 2\times 2\times 2$
Thus, LCM of $15,32=5\times 3\times 2\times 2\times 2\times 2\times 2=480$
Multiplying the numerator and denominator of the first fraction by $32$.
we get,
$\frac{7}{15}=\frac{7\times 32}{15\times 32}$
$=\frac{224}{480}$
Multiplying the numerator and denominator with 15.
$\frac{15}{32}=\frac{15\times 15}{15\times 32}$
$=\frac{225}{480}$
We know,
$224<225$
Thus,
$\frac{224}{480}<\frac{225}{480}$
$\frac{7}{15}<\frac{15}{32}$
$\therefore \frac{7}{15}$ is smaller between given ratios.