Question

Daca a pe b = 0,(7) , aflati 3a-2b pe a+b = ...
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Answer 1

a/b=0,(7)⇔a/b=7/9⇔9a=7b⇒a=7b/9
3a-2b=3×7b/9-2b=21b/9-2b (aduc la acelasi numitor)=21b/9-2b×9/9=21b/9-18b/9=3b/9 (se simplifica cu 3)=b/3
a+b=7b/9+b (aduc la acelasi numitor)=7b/9+9b/9=16b/9
acum 3a02b supra a+b=b/3supra16b/9=b/3:16b/9=b/3×9/16b=9b/48b (se simplifica b)=9/48 (se simplifica cu 3)=3/16

Answer 2

0,(7)=7/9
a/b=7/9
9a=7b
a=7b/9
(3a-2b)/(a+b)=[(3x7b/9)-2b]/[(7b/9)+b]=(7b/3-2b)/[(7b+9b)/9=
=[(7b-6b)/3]/(16b/9)=(b/3):(16b/9)=(b/3)x(9/16b)=simplificam=3/16=0,1875