Find five rational numbers between:
(i) $\tfrac{2}{3}$ and $\tfrac{4}{5}$
(ii) $-\tfrac{3}{2}$ and $\tfrac{5}{3}$
(iii) $\tfrac{1}{4}$ and $\tfrac{1}{2}$
(i) Convert to common denominator $15$: $\tfrac{2}{3} = \tfrac{10}{15},\; \tfrac{4}{5} = \tfrac{12}{15}$
Five rational numbers between $\tfrac{2}{3}$ and $\tfrac{4}{5}$: $\tfrac{11}{15},\; \tfrac{21}{30},\; \tfrac{7}{10},\; \tfrac{23}{30},\; \tfrac{11}{15}$
(ii) Convert to common denominator $6$: $-\tfrac{3}{2} = -\tfrac{9}{6},\; \tfrac{5}{3} = \tfrac{10}{6}$
Five rational numbers between $-\tfrac{3}{2}$ and $\tfrac{5}{3}$: $-\tfrac{8}{6},\; -\tfrac{1}{1},\; -\tfrac{1}{6},\; \tfrac{1}{2},\; \tfrac{5}{6}$
(iii) Convert to common denominator $4$: $\tfrac{1}{4} = \tfrac{1}{4},\; \tfrac{1}{2} = \tfrac{2}{4}$
Five rational numbers between $\tfrac{1}{4}$ and $\tfrac{1}{2}$: $\tfrac{3}{12},\; \tfrac{4}{12},\; \tfrac{5}{12},\; \tfrac{1}{3},\; \tfrac{6}{12}$
निम्न के बीच पाँच परिमेय संख्याएँ ज्ञात कीजिए:
(i) $\tfrac{2}{3}$ और $\tfrac{4}{5}$
(ii) $-\tfrac{3}{2}$ और $\tfrac{5}{3}$
(iii) $\tfrac{1}{4}$ और $\tfrac{1}{2}$
(i) समान हर $15$ में: $\tfrac{2}{3} = \tfrac{10}{15},\; \tfrac{4}{5} = \tfrac{12}{15}$
$\tfrac{2}{3}$ और $\tfrac{4}{5}$ के बीच पाँच परिमेय संख्याएँ: $\tfrac{11}{15},\; \tfrac{21}{30},\; \tfrac{7}{10},\; \tfrac{23}{30},\; \tfrac{11}{15}$
(ii) समान हर $6$ में: $-\tfrac{3}{2} = -\tfrac{9}{6},\; \tfrac{5}{3} = \tfrac{10}{6}$
$-\tfrac{3}{2}$ और $\tfrac{5}{3}$ के बीच पाँच परिमेय संख्याएँ: $-\tfrac{8}{6},\; -1,\; -\tfrac{1}{6},\; \tfrac{1}{2},\; \tfrac{5}{6}$
(iii) समान हर $12$ में: $\tfrac{1}{4} = \tfrac{3}{12},\; \tfrac{1}{2} = \tfrac{6}{12}$
$\tfrac{1}{4}$ और $\tfrac{1}{2}$ के बीच पाँच परिमेय संख्याएँ: $\tfrac{4}{12},\; \tfrac{5}{12},\; \tfrac{1}{3},\; \tfrac{7}{12},\; \tfrac{5}{12}$