Question

FIND FIVE RATIONAL NUMBERS BETWEEN 2/3 AND 4/5

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Answer 1

Answer:

$\frac{2}{3} = \frac{2 \times 15}{3 \times 15} = \frac{30}{45} \\ \frac{4}{5} = \frac{4 \times 9}{5 \times 9} = \frac{36}{45} \\ hence \: 5 \: rational \: numbers \: are \\ \\ \frac{31}{45} \\ \frac{32}{45} \\ \frac{33}{45} \\ \frac{34}{45} \\ \frac{35}{4}$

Answer 2

$\huge\frak{\underline{\underline{\red{Solution:-}}}}$

$\orange{\bigstar\:}$ $\small{\underline{\sf{\green{Step\:1:-}}}}$

${\bullet\:}$ Make the denominator same.

$\purple{\hookrightarrow\:}$ $\sf{\dfrac{2}{3} \times \dfrac{5}{5} = \dfrac{10}{15} }$

$\purple{\hookrightarrow\:}$ $\sf{\dfrac{4}{5} \times \dfrac{5}{3} = \dfrac{12}{15} }$

$\orange{\bigstar\:}$ $\small{\underline{\sf{\green{Step\:2:-}}}}$

${\bullet\:}$ As we need to find 5 rational numbers, multiply and divide above rational number by 6.

$\purple{\hookrightarrow\:}$ $\sf{\dfrac{10}{15} \times \dfrac{6}{6} = \dfrac{60}{90} }$

$\purple{\hookrightarrow\:}$ $\sf{\dfrac{12}{15} \times \dfrac{6}{6} = \dfrac{73}{90} }$

$\large\boxed{\underline{{\sf \therefore\:5\:Rational\:numbers\:are\:\dfrac{61}{90} ,\dfrac{62}{90},\dfrac{63}{90}, \dfrac{64}{90},}\dfrac{65}{90}}}$

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