Question

find the five rational numbers between given number. 1) 2/3 & 5/3 2) 8/7 & 3/7​

Answer 1

Step-by-step explanation:

$\rm \: 1) \: \: \frac{2}{3} \: and \: \frac{5}{3}$

$\scriptsize \rm On \: multiplying \: the \: numerator \: and \: denominator \: of \: \frac{2}{3} \: and \: \frac{5}{3} \: by \: 2.$

$\rm \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \: , \: \frac{5 \times 2}{3 \times 2} = \frac{10}{6}$

$\frac{4}{6} , \frac{5}{6} , \frac{6}{6} , \frac{7}{6} , \frac{8}{6} , \frac{9}{6} , \frac{10}{6}$

$\scriptsize \rm Hence \: there \: are \: five \: rational \: numbers \: between \: \frac{2}{3} \: and \: \frac{5}{3} \: is -</p><p>$

$\frac{5}{6} , \frac{6}{6} , \frac{7}{6} , \frac{8}{6} , \frac{9}{6}$

$\rm 2) \: \: \frac{8}{7} \: and \: \frac{3}{7}$

$\scriptsize \rm On \: multiplying \: the \: numerator \: and \: denominator \: of \: \frac{3}{7} \: and \: \frac{8}{7} \: by \: 2.$

$\rm \frac{3 \times 2}{7 \times 2} = \frac{6}{14} \: , \: \frac{8 \times 2}{7 \times 2} = \frac{16}{14} </p><p>$

$\rm \frac{6}{14} , \frac{7}{14}, \frac{8}{14} , \frac{9}{14} , \frac{10}{14} , \frac{11}{14} , \frac{12}{14} , \frac{13}{14} , \frac{14}{14} ,\frac{15}{14} , \frac{16}{14}$

$\scriptsize \rm Hence \: there \: are \: five \: rational \: numbers \: between \: \frac{3}{7} \: and \: \frac{8}{7} \: is -</p><p>$

$\rm\frac{7}{14}, \frac{8}{14} , \frac{9}{14} , \frac{10}{14} ,... ,\frac{15}{14}$

I hope it is helpful

Answer 2

Step-by-step explanation:

$\rm \: 1) \: \: \frac{2}{3} \: and \: \frac{5}{3}$

$\scriptsize \rm On \: multiplying \: the \: numerator \: and \: denominator \: of \: \frac{2}{3} \: and \: \frac{5}{3} \: by \: 2.$

$\rm \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \: , \: \frac{5 \times 2}{3 \times 2} = \frac{10}{6}$

$\frac{4}{6} , \frac{5}{6} , \frac{6}{6} , \frac{7}{6} , \frac{8}{6} , \frac{9}{6} , \frac{10}{6}$

$\scriptsize \rm Hence \: there \: are \: five \: rational \: numbers \: between \: \frac{2}{3} \: and \: \frac{5}{3} \: is -</p><p>$

$\frac{5}{6} , \frac{6}{6} , \frac{7}{6} , \frac{8}{6} , \frac{9}{6}$

$\rm 2) \: \: \frac{8}{7} \: and \: \frac{3}{7}$

$\scriptsize \rm On \: multiplying \: the \: numerator \: and \: denominator \: of \: \frac{3}{7} \: and \: \frac{8}{7} \: by \: 2.$

$\rm \frac{3 \times 2}{7 \times 2} = \frac{6}{14} \: , \: \frac{8 \times 2}{7 \times 2} = \frac{16}{14} </p><p>$

$\rm \frac{6}{14} , \frac{7}{14}, \frac{8}{14} , \frac{9}{14} , \frac{10}{14} , \frac{11}{14} , \frac{12}{14} , \frac{13}{14} , \frac{14}{14} ,\frac{15}{14} , \frac{16}{14}$

$\scriptsize \rm Hence \: there \: are \: five \: rational \: numbers \: between \: \frac{3}{7} \: and \: \frac{8}{7} \: is -</p><p>$

$\rm\frac{7}{14}, \frac{8}{14} , \frac{9}{14} , \frac{10}{14} ,... ,\frac{15}{14}$

I hope it is helpful

Answer 3

Step-by-step explanation:

$\rm \: 1) \: \: \frac{2}{3} \: and \: \frac{5}{3}$

$\scriptsize \rm On \: multiplying \: the \: numerator \: and \: denominator \: of \: \frac{2}{3} \: and \: \frac{5}{3} \: by \: 2.$

$\rm \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \: , \: \frac{5 \times 2}{3 \times 2} = \frac{10}{6}$

$\frac{4}{6} , \frac{5}{6} , \frac{6}{6} , \frac{7}{6} , \frac{8}{6} , \frac{9}{6} , \frac{10}{6}$

$\scriptsize \rm Hence \: there \: are \: five \: rational \: numbers \: between \: \frac{2}{3} \: and \: \frac{5}{3} \: is -</p><p>$

$\frac{5}{6} , \frac{6}{6} , \frac{7}{6} , \frac{8}{6} , \frac{9}{6}$

$\rm 2) \: \: \frac{8}{7} \: and \: \frac{3}{7}$

$\scriptsize \rm On \: multiplying \: the \: numerator \: and \: denominator \: of \: \frac{3}{7} \: and \: \frac{8}{7} \: by \: 2.$

$\rm \frac{3 \times 2}{7 \times 2} = \frac{6}{14} \: , \: \frac{8 \times 2}{7 \times 2} = \frac{16}{14} </p><p>$

$\rm \frac{6}{14} , \frac{7}{14}, \frac{8}{14} , \frac{9}{14} , \frac{10}{14} , \frac{11}{14} , \frac{12}{14} , \frac{13}{14} , \frac{14}{14} ,\frac{15}{14} , \frac{16}{14}$

$\scriptsize \rm Hence \: there \: are \: five \: rational \: numbers \: between \: \frac{3}{7} \: and \: \frac{8}{7} \: is -</p><p>$

$\rm\frac{7}{14}, \frac{8}{14} , \frac{9}{14} , \frac{10}{14} ,... ,\frac{15}{14}$

I hope it is helpful

Answer 4

Step-by-step explanation:

$\rm \: 1) \: \: \frac{2}{3} \: and \: \frac{5}{3}$

$\scriptsize \rm On \: multiplying \: the \: numerator \: and \: denominator \: of \: \frac{2}{3} \: and \: \frac{5}{3} \: by \: 2.$

$\rm \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \: , \: \frac{5 \times 2}{3 \times 2} = \frac{10}{6}$

$\frac{4}{6} , \frac{5}{6} , \frac{6}{6} , \frac{7}{6} , \frac{8}{6} , \frac{9}{6} , \frac{10}{6}$

$\scriptsize \rm Hence \: there \: are \: five \: rational \: numbers \: between \: \frac{2}{3} \: and \: \frac{5}{3} \: is -</p><p>$

$\frac{5}{6} , \frac{6}{6} , \frac{7}{6} , \frac{8}{6} , \frac{9}{6}$

$\rm 2) \: \: \frac{8}{7} \: and \: \frac{3}{7}$

$\scriptsize \rm On \: multiplying \: the \: numerator \: and \: denominator \: of \: \frac{3}{7} \: and \: \frac{8}{7} \: by \: 2.$

$\rm \frac{3 \times 2}{7 \times 2} = \frac{6}{14} \: , \: \frac{8 \times 2}{7 \times 2} = \frac{16}{14} </p><p>$

$\rm \frac{6}{14} , \frac{7}{14}, \frac{8}{14} , \frac{9}{14} , \frac{10}{14} , \frac{11}{14} , \frac{12}{14} , \frac{13}{14} , \frac{14}{14} ,\frac{15}{14} , \frac{16}{14}$

$\scriptsize \rm Hence \: there \: are \: five \: rational \: numbers \: between \: \frac{3}{7} \: and \: \frac{8}{7} \: is -</p><p>$

$\rm\frac{7}{14}, \frac{8}{14} , \frac{9}{14} , \frac{10}{14} ,... ,\frac{15}{14}$

I hope it is helpful