Question

Compare the following numbers.
$-\frac{17}{20},-\frac{13}{20}$
$\frac{15}{12},\frac{7}{16}$

Answer 1

1) Here, the denominators of the given numbers are the same.
Since, $17<13$
$$\begin{array}{cc}& \therefore -17<-13\\ & \therefore -\frac{17}{20}<-\frac{13}{20}\end{array}$$

2) Here, the denominators of the given numbers are not the same.
LCM of 12 and $16=48$
$$\begin{array}{cc}& \frac{15}{12}=\frac{15\times 4}{12\times 4}=\frac{60}{48},\\ & \frac{7}{16}=\frac{7\times 3}{16\times 3}=\frac{21}{48}\end{array}$$
Since, $60>21$
$$\begin{array}{cccc}& \therefore & \frac{60}{48}& >\frac{21}{48}\\ \therefore & \frac{15}{12}& >\frac{7}{16}& \end{array}$$