Question

aratati ca exista o singura fractie cu numitorul 15 cuprinsa intre 11/13 si 12/13

Answer 1

• Notam cu x numaratorul, x∈N

$\frac{11}{13} <\frac{x}{15} <\frac{12}{13} \\\\\frac{11\times15}{13\times15} <\frac{13\times x}{13\times 15} <\frac{12 \times15}{13\times15}$

• Dupa ce am adus la acelasi numitor,l-am eliminat si am obtinut:

   165<13x<180 |:13  

• Dupa ce am impartit inecuatia la 13 vom obtine:

    $\frac{165}{13} </p><p>Facem impartirea cu 2 zecimale si obtinem:</p><p></p><p>12,69<x<13,84</p><p></p><p>x ∈N ⇒ x=13</p><p>Deci fractia noastra va fi [tex]\frac{13}{15}$