Question

Numărul rațional 8,(6) -7,(7) are partea întreaga egală cu:

a) 0
b) 1
c) 6
d)7
e)8

Answer 1

$8.(6) = 8 \frac{6}{9} = \frac{8 \times 9 + 6}{9} = \frac{72 + 6}{9} = \frac{78}{9} = \frac{26}{3}$

$7.(7) = 7\frac{7}{9} = \frac{7 \times 9 + 7}{9} = \frac{63 + 7}{9} = \frac{70}{9}$

$8.(6) - 7.(7) = \frac{26}{3} - \frac{70}{9} = \frac{78}{9} - \frac{70}{9} = \frac{78 - 70}{9} = \frac{8}{9} = 0.(8)$

$[0.(8)] = 0$

$=>a)\:0$