# Which is greater in each of the following:$(i)$. $\frac{2}{3},\ \frac{5}{2}$$(ii). -\frac{5}{6},\ -\frac{4}{3}$$(iii)$. $-\frac{3}{4},\ \frac{2}{-3}$$(iv). -\frac{1}{4},\ \frac{1}{4}$$(v)$. $-3\frac{2}{7\ },\ -3\frac{4}{5}$

Given:

$(i)$. $\frac{2}{3},\ \frac{5}{2}$

$(ii)$. $-\frac{5}{6},\ -\frac{4}{3}$

$(iii)$. $-\frac{3}{4},\ \frac{2}{-3}$

$(iv)$. $-\frac{1}{4},\ \frac{1}{4}$

$(v)$. $-3\frac{2}{7\ },\ -3\frac{4}{5}$

To do: To find the greater rational number in each of the given pairs.

Solution:

$(i)$. $\frac{2}{3},\ \frac{5}{2}$

Taking the LCM of the denominators $3$ and $2$ of both the rational numbers, we get $6$.

So, $\frac{2}{3}=\frac{2}{3}\times\frac{2}{2}$

$=\frac{4}{6}$

And $\frac{5}{2}=\frac{5}{2}\times\frac{3}{3}$

$=\frac{15}{6}$

On comparing both the rational numbers we have:

$\frac{4}{6}<\frac{15}{6}$

Therefore, $\frac{2}{3}$< $\frac{5}{2}$

$(ii)$. $-\frac{5}{6},\ -\frac{4}{3}$

Taking the LCM of the denominators $6$ and $3$ of both the rational numbers, we get $6$.

So, $-\frac{5}{6}=-\frac{5}{6}\times\frac{1}{1}$

$=-\frac{5}{6}$

And $-\frac{4}{3}=\frac{-4}{3}\times\frac{2}{2}$

$=\frac{-8}{6}$

On comparing both the fractions we have: $-\frac{5}{6}$> $-\frac{8}{6}$

Therefore, $-\frac{5}{6}$>$-\frac{4}{3}$

$(iii)$. $-\frac{3}{4},\ \frac{2}{-3}$

Taking the LCM of the denominators $4$ and $3$ of both the rational numbers, we get $12$.

So, $-\frac{3}{4}=-\frac{3}{4}\times\frac{3}{3}$

$=-\frac{9}{12}$

And $\frac{2}{-3}=\frac{2}{-3}\times\frac{4}{4}$

$= \frac{8}{-12}$

On comparing both fractions we have,

$-\frac{9}{12}$<$\frac{8}{-12}$

Or $-\frac{3}{4}$ < $\frac{2}{-3}$

$(iv)$. $-\frac{1}{4},\ \frac{1}{4}$

It is known that all the negative integers are less than $0$ and all the positive integers are greater than $0$.

Here, $\frac{-1}{4}$<$0$

And $\frac{1}{4}$>$0$

Therefore, $\frac{-1}{4}$ < $\frac{1}{4}$

$(v)$. $-3\frac{2}{7},\ -3\frac{4}{5}$

$-3\frac{2}{7}=-\frac{21+2}{7}$

$=-\frac{23}{7}$

And $-3\frac{4}{5}=-\frac{15+4}{5}$

$=-\frac{19}{5}$

Taking the LCM of the denominators $7$ and $5$ of both the rational numbers, we get $35$.

$-\frac{23}{7}=-\frac{23}{7}\times\frac{5}{5}$

$=\frac{-115}{35}$

And $-\frac{19}{5}=-\frac{19}{5}\times\frac{7}{7}$

$=\frac{-133}{35}$

On comparing both the fractions we have:

$-\frac{115}{35}$>$-\frac{133}{35}$

Or $-3\frac{2}{7}\ >\ -3\frac{4}{5}$

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Updated on: 10-Oct-2022

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