Question

DETERMINATI FRACTIA A SUPRA B , STIIND CA ESR EGALA CU FRACTIA 2 SUPRA 3 SI CA B -A =11!!!! VA ROG ESTE UNGENT . CU EXPLICATIE VA ROG​

Answer 1

$\frac{A}{B} =\frac{2}{3}$

$A=\frac{2B}{3}$

$B-A=11$

$\frac{3B}{3} -\frac{2B}{3} =11$

$\frac{B}{3} =11$

$B=3*11=33$

$A=\frac{2*33}{3} =2*11=22$

Answer 2

$\it b-a=11 \Rightarrow a=b-11\ \ \ \ \ (1)\\ \\ \\ \dfrac{a}{b}=\dfrac{2}{3}\ \stackrel{(1)}{\Longrightarrow}\ \dfrac{b-11}{b}=\dfrac{2}{3} \Rightarrow \dfrac{b}{b}-\dfrac{11}{b}=\dfrac{2}{3} \Rightarrow 1-\dfrac{11}{b}=\dfrac{2}{3} \Rightarrow \dfrac{11}{b}=1-\dfrac{2}{3} \Rightarrow\\ \\ \Rightarrow \dfrac{1}{3}=\dfrac{11}{b} \Rightarrow \dfrac{11}{b} = \dfrac{^{11)}1}{\ \ 3} \Rightarrow \dfrac{11}{b}=\dfrac{11}{33} \Rightarrow b=33\ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow a=33-11=22$

$\it Frac\c{\it t}ia\ \ cerut\breve a\ \ este\ \ \dfrac{22}{33}$