Question

varianta 2 exercițiul 8 ​

Answer 1

Răspuns:

0,(3)=(3/9)⁽³=1/3

1,(3)=(13-1)/9=(12/9)⁽³=4/3

1 intreg 7/9=(1·9+7)/9=16/9

(1/3+4/3 :16/9) :13/12=

(1/3+4/3·9/16) ·12/13=

(⁴⁾1/3+³⁾3/4)·12/13=

(4+9)/12·12/13=

13/12·12/13= 1

Answer 2

Răspuns:

$\bf \bigg[0,(3)+1,(3):1\dfrac{7}{9}\bigg] :\bigg(1+\dfrac{1}{12}\bigg)=$

$\bf \bigg[\dfrac{3}{9}+\dfrac{13-1}{9} :\dfrac{9\cdot1+7}{9}\bigg] :\bigg(\dfrac{^{^{12)}}1~}{1}+\dfrac{1}{12}\bigg)=$

$\bf \bigg[\dfrac{3^{(3}~}{9}+\dfrac{12}{9} :\dfrac{16}{9}\bigg] :\bigg(\dfrac{12}{12}+\dfrac{1}{12}\bigg)=$

$\bf \bigg(\dfrac{1}{3}+\dfrac{\not12}{\not9} \cdot\dfrac{\not9}{\not16}\bigg) :\dfrac{13}{12}=$

$\bf \bigg(\dfrac{1}{3}+\dfrac{3}{1} \cdot\dfrac{1}{4}\bigg) :\dfrac{13}{12}=$

$\bf \bigg(\dfrac{^{^{4)}} 1~}{3}+\dfrac{^{^{3)}} 3~}{4} \bigg)\cdot\dfrac{12}{13}=$  

$\bf \bigg(\dfrac{4}{12}+\dfrac{9}{12} \bigg)\cdot\dfrac{12}{13}=$

$\bf \dfrac{\not13}{\not12} \cdot\dfrac{\not12}{\not13}= \red{\boxed{\bf ~1~}}$