Question

Fill in the boxes with the correct symbol out of >, <, and =.
(i) $\frac{-5}{7}\frac{2}{3}$
(ii) $\frac{-8}{5}\frac{-7}{4}$
(iii) $\frac{1}{-3}\frac{-1}{4}$

Answer 1

(i) $\frac{-5}{7}\frac{2}{3}$
Since, one of the numbers is negative and the other is positive, we can straightaway say that the negative number is lesser than the postive number.
So, $\frac{-5}{7}<\frac{2}{3}$

(ii) $\frac{-8}{5}\frac{-7}{4}$
Making the denominators equal,
$\frac{-8\times 4}{5\times 4}\frac{-7\times 5}{4\times 5}$
$\frac{-32}{20}\frac{-35}{20}$
Now, we can compare the numerators.
$\frac{-32}{20}>\frac{-35}{20}$
So, $\frac{-8}{5}>\frac{-7}{4}$

(iii) $\frac{1}{-3}\frac{-1}{4}$
First, making all denominators positive, we get,
$\frac{-1}{3}\frac{-1}{4}$
Making the denominators equal,
$\frac{-1\times 4}{3\times 4}\frac{-1\times 3}{4\times 3}$
$\frac{-4}{12}\frac{-3}{12}$
Now, we can compare the numerators.
$\frac{-4}{12}<\frac{-3}{12}$
So, $\frac{1}{-3}<\frac{-1}{4}$