Răspuns:
Explicație pas cu pas:
a/b = 0,(4)
0,(4) = 4/9
a/b = 4/9 => 9 a = 4 b => a/4 = b/9 = k -> coeficient de proportionalitate
=> a = 4 k si b = 9 k
( 2 a + 3 b ) / ( 3 a + 5 b ) = 35/57 -> valoarea raportului
= ( 2×4k + 3×9k) / ( 3×4k + 5×9k) =
= ( 8k+27k)/(12k+45k) =
= 35 k/57k =
= 35/57
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b)
a/b = 2/5 => 5 a = 2 b => a/2 = b/5 = k -> coeficient de proportionalitate
=> a = 2 k si b = 5 k
( 8 a + 3 b ) / ( 6 b - 2 a ) = 31/26 -> valoarea raportului
= ( 8×2k + 3×5k) /( 6×5k - 2× 2k) =
= ( 16 k + 15 k ) / ( 30 k - 4 k ) =
= 31 k / 26 k =
= 31/26
