Question

Find 5 rational numbers between 3/5 and 2/3

Answer 1

Hey friend,
Here is the answer you were looking for:
$to \: find \: rational \: number \: between \: \frac{3}{5} \: and \: \frac{2}{3} \\ \\ = ( \frac{3}{5} + \frac{2}{3} ) \div 2 \\ \\ = ( \frac{3 \times 3 + 2 \times 5}{15} ) \times \frac{1}{2} \\ \\ = \frac{19}{15} \times \frac{1}{2} \\ \\ = \frac{19}{30} \\ \\ = \frac{3}{10} \\ to \: find \: a \: rational \: number \: \\ between \: \frac{3}{5} \: and \: \frac{3}{10} \\ \\ ( \frac{3}{5} + \frac{3}{10} ) \div 2 \\ \\ = ( \frac{3 \times 2 + 3 \times 1}{10} ) \times \frac{1}{2} \\ \\ = ( \frac{6 + 3}{10} ) \times \frac{1}{2} \\ \\ = \frac{9}{10} \times \frac{1}{2} \\ \\ = \frac{9}{20} \\ \\ to \: find \: a \: rational \: number \: \\ between \: \frac{3}{10} \: and \: \frac{2}{3} \\ \\ ( \frac{3}{10} + \frac{2}{3} ) \div 2 \\ \\ = ( \frac{3 \times 3 + 2 \times 10}{30} ) \times \frac{1}{2} \\ \\ = \frac{29}{30} \times \frac{1}{2} \\ \\ = \frac{29}{60} \\ \\ to \: find \: a \: rational \: number \: \\ between \: \frac{3}{5} \: and \: \frac{9}{20} \\ \\ ( \frac{3}{5} + \frac{9}{20} ) \div 2 \\ \\ = (\frac{3 \times 4 + 9 \times 1}{20} ) \times \frac{1}{2} \\ \\ = ( \frac{12 + 9}{20} ) \times \frac{1}{2} \\ \\ = \frac{21}{20} \times \frac{1}{2} \\ \\ = \frac{21}{40} \\ \\ to \: find \: a \: rational \: number \: \\ between \: \frac{29}{60} \: and \: \frac{2}{3} \\ \\ =( \frac{29}{60} + \frac{2}{3} ) \div 2 \\ \\ = ( \frac{29 \times 1 + 2 \times 20}{60} ) \times \frac{1}{2} \\ \\ = ( \frac{29 + 40}{60} ) \times \frac{1}{2} \\ \\ = \frac{69}{60} \times \frac{1}{2} \\ \\ = \frac{23}{20} \times \frac{1}{2} \\ \\ = \frac{23}{40} \\ \\ so \: the \: 5 \: rational \: numbers \: between \: \frac{3}{5} \: and \: \frac{2}{3} \: are \: \\ \\ \frac{19}{30}, \: \frac{9}{20} ,\: \frac{29}{60}, \: \frac{21}{40} ,\: \frac{23}{40}$

Hope this helps!!!

@Mahak24

Thanks...
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