Question

Compare the following numbers.
(1) −7, −2

(2) 0, $\frac{-9}{5}$

(3) $\frac{8}{7}$, 0

(4) $\frac{-5}{4}$, $\frac{1}{4}$

(5) $\frac{40}{29}$, $\frac{141}{29}$

(6) −$\frac{17}{20}$, $\frac{-13}{20}$

(7) $\frac{15}{12}$, $\frac{7}{16}$

(8) $\frac{-25}{8}$, $\frac{-9}{4}$

(9) $\frac{12}{15}$, $\frac{3}{5}$

(10) $\frac{-7}{11}$, $\frac{-3}{4}$

Answer 1

(1) We know that, 7 > 2

∴ −7 < −2.

(2) We know that, a negative number is always less than 0.

∴ $0>-\frac{9}{5}$.

(3) We know that, a positive number is always greater than 0.

∴ $\frac{8}{7}>0$

(4) We know that, −5 < 1.

∴ $-\frac{5}{4}<\frac{1}{4}$.

(5) We know that, 40 < 141.

∴ $\frac{40}{29}<\frac{141}{29}$.

(6) We know that, −17 < −13.

∴$-\frac{17}{20}<-\frac{13}{20}$.

$\left(7\right)\frac{15}{12}=\frac{15\times 4}{12\times 4}=\frac{60}{48};\frac{7}{16}=\frac{7\times 3}{16\times 3}=\frac{21}{48}$
Now, $\frac{60}{48}>\frac{21}{48}$
∴ $\frac{15}{12}>\frac{7}{16}$.

(8) Let us first compare $\frac{25}{8}$ and $\frac{9}{4}$.
$\frac{25}{8}=\frac{25\times 1}{8\times 1}=\frac{25}{8};\frac{9}{4}=\frac{9\times 2}{4\times 2}=\frac{18}{8}$
Now, $\frac{25}{8}>\frac{18}{8}$
∴ $\frac{25}{8}>\frac{9}{4}$
∴ $-\frac{25}{8}<-\frac{9}{4}$.

$\left(9\right)\frac{12}{15}=\frac{12\times 1}{15\times 1}=\frac{12}{15};\frac{3}{5}=\frac{3\times 3}{5\times 3}=\frac{9}{15}$
Now, $\frac{12}{15}>\frac{9}{15}$
∴ $\frac{12}{15}>\frac{3}{5}$.

(10) Let us first compare $\frac{7}{11}$ and $\frac{3}{4}$.
$\frac{7}{11}=\frac{7\times 4}{11\times 4}=\frac{28}{44};\frac{3}{4}=\frac{3\times 11}{4\times 11}=\frac{33}{44}$
Now, $\frac{28}{44}<\frac{33}{44}$
∴ $\frac{7}{11}<\frac{3}{4}$
∴ $-\frac{7}{11}>-\frac{3}{4}$.