Question

Find ten rational numbers between-
1) -2/5 and 1/2
2) 2/3 and 4/5
3) -3/2 and 5/3​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\red{\underline \bold{To \: Find:}}$

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• Find ten rational numbers between

1. -2/5 and 1/2
2. 2/3 and 4/5
3. -3/2 and 5/3

$\large{\orange{\underline{\tt{Solution :-}}}}$

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$\tt \longmapsto \frac { -2} { 5} \& \frac { 1} { 2}$

Firstly we need to have a same denominator.

Taking LCM = 10

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$\sf \implies \frac { -4 } { 10 } \& \frac { 5 } { 10 }$

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Let us multiply the fraction by $\rm \frac { 11 } { 11 }$

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$\sf \implies \frac { -4×11 } { 10×11 } \& \frac { 5×11 } { 10×11}$

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$\sf \implies \frac { -44 } { 110 } \& \frac { 55 } { 110}$

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$\underline{\bold{\texttt{Hence 10 rational numbers are }}}$

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$\rm \frac { -43 } { 55 } , \frac { -42 } { 55 } , \frac { -41 } { 55 } , \frac { -40 } { 55 } , \frac { -39 } { 55 } </p><p>, \frac { -38 } { 55 } ,\frac { -37 } { 55 } , \frac { -36 } { 55 } , \frac { -35 } { 55 } , \frac { -34 } { 55 }$

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$\rule{200}2$

$\tt \longmapsto \frac { 2} { 3 } \& \frac { 4} { 5}$

Firstly we need to have a same denominator.

Taking LCM = 15

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$\sf \implies \frac { 10} { 15 } \& \frac { 12} { 10 }$

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Let us multiply the fraction by $\rm \frac { 11 } { 11 }$

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$\sf \implies \frac { 10×11 } { 15×11 } \& \frac { 12×11 } { 15×11}$

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$\sf \implies \frac { 110 } { 165} \& \frac { 132} { 165}$

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$\underline{\bold{\texttt{Hence 10 rational numbers are }}}$

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$\rm \frac { 111 } { 165 } , \frac { 112} { 165 } , \frac { 113 } { 165 } , \frac { 114} { 165 } , \frac { 115 } { 165 } , \frac { 116} { 165 } , \frac { 117 } { 165 } , \frac { 118 } { 165 } , \frac { 119 } { 165 } , \frac { 120 } { 165 }$

$\rule{200}2$

$\tt \longmapsto \frac { -3} { 2 } \& \frac { 5} { 3}$

Firstly we need to have a same denominator.

Taking LCM = 6

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$\sf \implies \frac { -9 } { 6 } \& \frac { 10 } { 6 }$

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Let us multiply the fraction by $\rm \frac { 11 } { 11 }$

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$\sf \implies \frac { -9×11 } { 6×11 } \& \frac { 10×11 } { 6×11}$

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$\sf \implies \frac { -99} { 66} \& \frac { 110 } { 66}$

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$\underline{\bold{\texttt{Hence 10 rational numbers are }}}$

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$\rm \frac { -98 } { 66 } , \frac { -97 } { 66 } ,\frac { -96 } { 66 } ,\frac { -95 } { 66 } , \frac { -94} { 66 } , \frac { -93 } { 66 } , \frac { -92 } { 66 } , \frac { -91 } { 66 } , \frac { -90} { 66 } , \frac { -89 } { 66 }$

$\rule{200}5$