Question

Find six rational number between
1) -1/3 and -2/3
(2) -1/4 and -1/2

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Answer 1

$\large \fbox \red{A}\large \fbox \orange{n}\large \fbox \purple{S}\large \fbox \green{w}\large \fbox \pink{E}\large \fbox \purple{r}$

$\bf{\large{ \frac{ - 1}{3} \: and \: \frac{ - 2}{3}}}$

$\bf{\blue{ = > \frac{ - 1}{3} \times \frac{10}{10}}} \: and \: {\bf{\purple{ \frac{ - 2}{3} \times \frac{10}{10} }}}$

$\bf{\blue{ = > \frac{ - 10}{30}}} \: and \:{\bf{\purple{\frac{ - 20}{30}}}}$

Hence, the six rational number between -10/30 and -20/30 is -11/30, -12/30, -13/30, -14/30, -15/30, -16/30.

$\bf{\large{ \frac{ - 1}{4} \: and \: \frac{ - 1}{2}}}$

• The LCM of 4 and 2 is 4.

$\mathtt{{\red{So,}}}$

$\bf{\blue{ = > \frac{ - 1}{4} \times \frac{1}{1} \: and \: {\bf{\purple{ \frac{ - 1}{2} \times \frac{2}{2}}}}}}$

$\bf{\blue{ = > \frac{ - 1}{4} }} \: and \: {\bf{\purple{ \frac{ - 2}{4} }}}$

Here, the six rational number are not come.

$\mathtt{{\red{So,}}}$

$\bf{\blue{ = > \frac{ - 1}{4} \times \frac{10}{10}}} \: and \: {\bf{\purple{ \frac{2}{4} \times \frac{10}{10} }}}$

$\bf{\blue{ = > \frac{ - 10}{40}}} \: and \: {\bf{\purple{ \frac{ - 20}{40} }}}$

Hence, the six rational number between -10/40 and -20/40 is -11/40, -12/40, -13/40, -14/40, -15/40, -16/40.