Question

13.
Find five rational number between.
(a) 2/3 and 4/5 ​

Answer 1

Answer:

The rational numbers between 2/3 and 4/5 are 61/90 62/90 63/90 64/90 65/90 66/90 67/90.

Answer 2

AnswEr-:

$\underline {\mathrm {\pink { \therefore { Five\:Rational \:numbers\:are\:-: \dfrac{61}{90}\:, \dfrac{62}{90}\:,\dfrac{63}{90}\:,\dfrac{64}{90}\:\:and\:\dfrac{65}{90}}}}}$

Explanation-:

• Find five rational number between-:

• $\sf{\dfrac{ 2}{3}\: and\: \dfrac{4}{5}}$

$\mathrm {\bf{ \dag{ Solution \:of\:Question -:}}}$

• $\underbrace { \mathrm { Understanding \:The\:Concept \:-:}}$

• We have to find five rational numbers between -: $\sf{\dfrac{ 2}{3}\: and\: \dfrac{4}{5}}$

• Firstly Convert Both Fractions in like fraction and then ,

• We have to find five rational numbers Multiply the Obtained Fraction [ Numerator and Denominator ] by 6 .

• And , By doing this we can get the Five rational numbers between them .

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$\sf{\bf{\underline{ Converting\:both\:Fractions\:in\:like\:terms\:-:}}}$

• Find five rational number between-:

• $\quad \qquad \longmapsto{\sf{\dfrac{ 2}{3}\: and\: \dfrac{4}{5}}}$

• As , We know that ,

• $\star{\mathrm { L.C.M\:of\:3\:and\:5\:are\:15\:.}}$

• $\quad \qquad \longmapsto{\sf{\dfrac{ 2}{3}\: and\: \dfrac{4}{5}}}$

• $\quad \qquad \longmapsto{\sf{\dfrac{ 10 \:and \:12 }{15}\: }}$

• $\quad \qquad \longmapsto{\sf{\dfrac{ 10 }{15}\:and\:\dfrac{12}{15} }}$

$\sf{\bf{\underline{ Now\:Multiplying \:\:both\:Obtained \:fraction\:[Numerator \:and\;Denominator]\:by\:6\:-:}}}$

• $\quad \qquad \longmapsto{\sf{\dfrac{ 10 }{15}\:and\:\dfrac{12}{15} }}$

• $\quad \qquad \longmapsto{\sf{\dfrac{ 10\times 6 }{15\times 6 }\:and\:\dfrac{12\times 6 }{15\times 6 } }}$

• $\quad \qquad \longmapsto{\sf{\dfrac{ 60 }{90 }\:and\:\dfrac{ 72}{90 } }}$

Then ,

• $\quad \qquad \longmapsto{\sf{Five\:Rational\:between\:-:\dfrac{ 60 }{90 }\:and\:\dfrac{ 72}{90 }\:or \:\dfrac{ 2}{3}\: and\: \dfrac{4}{5} \:are-: }}$

• $\quad \qquad \longmapsto{\sf{ \dfrac{61}{90}\:, \dfrac{62}{90}\:,\dfrac{63}{90}\:,\dfrac{64}{90}\:\:and\:\dfrac{65}{90}}}$

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• $\underline {\mathrm {\pink { \therefore { Five\:Rational \:numbers\:are\:-: \dfrac{61}{90}\:, \dfrac{62}{90}\:,\dfrac{63}{90}\:,\dfrac{64}{90}\:\:and\:\dfrac{65}{90}}}}}$

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