Question

Find five rational numbers between:
a) 3/5 and 2/3
b) -2 and -1 1/2
c) -3 and -2

Plzz answer.​

Answer 1

Here is your answer.

ATQ,

To find five rational number between

$= \frac{3}{5} \:and \: \frac{2}{3} \\ now \\ = lcm \: of \: 5 \: and \: 3 \: is \: 15 \\ so \\ = \frac{9 \: and \: 10}{15} \\ now \\ = \frac{9 \times 6}{15 \times 6} = \frac{54}{90} \\ \frac{10 \times 6}{15 \times 6} = \frac{60}{90} \\ hence \: the \: required \: the \: fractions \: are \\ = \frac{55}{90} \: and \: \frac{56}{90} \: and \: \frac{57}{90} \: and \: \frac{58}{90} \: and \: \frac{59}{90}$

and,

$as \: done \: in \: first \: part \: \\ five \: rational \: number \: between \: \frac{ - 2}{1} \: and \: \frac{ - 11}{2} \: will \: be \\ lcm \: of \: 2 \: and \: 1 \: is \: 2 \: \\ so \\ \frac{ - 4 \: and \: - 11}{2} \\ hence \: the \: rational \: numbers \: are \: \\ \frac{ - 5}{11} \: and \: \frac{ - 6}{11} \: and \: \frac{ - 7}{11} and \: \frac{ - 8}{11} and \: \frac{ - 9}{11}$

$now \: five \: rational \: number \: between \: \frac{ - 2}{1} \: and \: \frac{ - 3}{1} \: is \: \\ lcm \: of \: 1 \: is \: 1 \\ so \\ \frac{ - 2 \: and \: - 3}{1} \:now \: as \: there \: are \: no \: rational \: between \: these \: numbers \: they \: will \: be \: multiplied \: by \: 6 \\ so \\ = \frac{ - 2 \times 6}{1 \times 6} = \frac{ - 12}{6} \: and \: \frac{ - 3 \times 6}{1 \times 6} = \frac{ - 18}{6} \\ hence \: the \: required \: rational \: numbers \: are \: \frac{ - 13}{6} \: and \: \frac{ - 14}{6} \: and \: \frac{ - 15}{6} \: and \: \frac{ - 16}{6} \: and \: \frac{ - 17}{6}$

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