Question

Daca a supra b=2,(6),determinati numarul rational pozitiv b in cazurile:
a) a=0,8
b) a=1,(3)
c) a=0,(6)
d) a=3,2
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Answer 1

a) 2,(6)=(26-2)/9=24/9=8/3
0,8=8/10=4/5
4/5:b=8/3
b=4/5×3/8
b=3/10

b) 1,(3)=(13-1)/9=12/9=4/3
4/3:b=8/3
b=4/3×3/8
b=1/2

c) 0,(6)=6/9=2/3
2/3:b=8/3
b=2/3×3/8
b=1/4

d) 3,2=32/10=16/5
16/5:b=8/3
b=16/5×3/8
b=6/5

Answer 2

$\frac{a}{b} = 2.(6) = \frac{26 - 2}{9} = \frac{24}{9} = \frac{8}{3}$

$a)a = 0.8 = \frac{8}{10} = \frac{4}{5}$

$\frac{a}{b} = \frac{8}{3}$

$3a = 8b$

$3 \times \frac{4}{5} = 8b$

$\frac{3 \times 4}{5} = 8b$

$\frac{12}{5} = 8b$

$5 \times 8b = 12$

$40b = 12$

$b = \frac{12}{40}$

$b = \frac{3}{10}$

$b)a = 1.(3) = \frac{13 - 1}{9} = \frac{12}{9} = \frac{4}{3}$

$\frac{a}{b} = \frac{8}{3}$

$3a = 8b$

$3 \times \frac{4}{3} = 8b$

$8b = 4$

$b = \frac{4}{8}$

$b = \frac{1}{2}$

$c)a = 0.(6) = \frac{6}{9} = \frac{2}{3}$

$\frac{a}{b} = \frac{8}{3}$

$3a = 8b$

$3 \times \frac{2}{3} = 8b$

$8b = 2$

$b = \frac{2}{8}$

$b = \frac{1}{4}$

$d)a = 3.2 = \frac{32}{10} = \frac{16}{5}$

$\frac{a}{b} = \frac{8}{3}$

$3a = 8b$

$3 \times \frac{16}{5} = 8b$

$\frac{3 \times 16}{5} = 8b$

$\frac{48}{5} = 8b$

$5 \times 8b = 48$

$40b = 48$

$b = \frac{48}{40}$

$b = \frac{6}{5}$