Question

Which of the two rational numbers is greater in the given pair ?

(i) $\frac{3}{8}$ or 0 (ii) $\frac{-2}{9}$ or 0 (iii) $\frac{-3}{4}$ or $\frac{1}{4}$

(iv) $\frac{-5}{7}$ or $\frac{-4}{7}$ (v) $\frac{2}{3}$ or $\frac{3}{4}$ (vi) $\frac{-1}{2}$ or -1

Answer 1

(i) $\frac{3}{8}$ or 0

We know that every positive rational number is greater than 0.

$\therefore \frac{3}{8}$ is greater.

(ii) $\frac{-2}{9}$ or 0

We know that every negative rational number is less than 0

$\therefore 0$ is greater.

(iii) $\frac{-3}{4}or\frac{1}{4}$

We know that every negative rational number is less than every positive rational number

$\therefore \frac{1}{4}$ is greater.

(iv) $\frac{-5}{7}or\frac{-4}{7}$

Here, denominator is same i.e., it is 7. and (-4) > (-5)

$\therefore \frac{-4}{7}$ is greater.

(v) $\frac{2}{3}or\frac{3}{4}$

Here, denominators are different.

$\therefore$ Making denominator same LCM of 3 and 4 = 12

$\therefore \frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12}$ and $\frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12}$

$\therefore$ Between $\frac{8}{12}$ and $\frac{9}{12}$ and clearly $\frac{9}{12}$ is greater or $\frac{3}{4}$ is greater.

(vi) $\frac{-1}{2}$ or -1

Here, denominators are different

$\therefore$ Making denominator same, LCM of 2, 1 = 2

$\therefore \frac{-1}{2}=\frac{-1}{2}$

$-1=\frac{-1\times 2}{1\times 2}=\frac{-2}{2}$

and clearly $\frac{-1}{2}$ is greater.