Răspuns
Explicație pas cu pas:
5)
a × 4 / 9 = 32 / 81
a = ( 32 / 81 ) : ( 4 / 9 )
a = ( 32 / 4 ) x ( 9 / 81 )
a = 8 x 1 / 9
a = 8 / 9 → fractia
Verific; 8 / 9 × 4 / 9 = ( 8 x 4 ) / ( 9 x 9 ) = 32 / 81
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b)
b × 9 / 5 = 4 / 3
b = ( 4 / 3 ) : ( 9 / 5 )
b = ( 4 / 3 ) × ( 5 / 9 )
b = 20 / 27
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6)
a) → introduc intregii in fractie
3 intregi si 1 / 5 = ( 3 x 5 + 1 ) / 5 = 16 / 5
2 intregi si 1 / 6 = ( 2 x 6 + 1 ) / 6 = 13 / 6
( 31 / 12 ) : ( 16 / 5 - 13 / 6 ) =
= ( 31 / 12 ) : ( 96 / 30 - 65 / 30 ) =
= ( 31 / 12 ) × ( 30 / 31 ) =
= ( 30 : 6 ) / ( 12 : 6 ) =
= 5 / 2 =
= 2 intregi si 1 / 2
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b)
( 7 / 34 + 1 / 17 ) : 72 / 17 =
= ( 7 / 34 + 2 / 34 ) × 17 / 72 =
= ( 9 / 34 ) × 17 / 72 =
= 1 / ( 2 × 8 ) =
= 1 / 16
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c)
( 16 / 5 - 5 / 2 ) : ( 7 / 6 + 7 / 3 ) =
= ( 32 / 10 - 25 / 10 ) : ( 7 / 6 + 14 / 6 ) =
= ( 7 / 10 ) × ( 6 / 21 ) =
= 3 / ( 5 × 3 ) =
= 1 / 5
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7)
2 intregi si 3 / 10 = ( 2 x 10 + 3 ) / 10 = 23 / 10 → cablu de sarma
3 / 5 = ( 3 x 2 ) / ( 5 x 2 ) = 6 / 10
23 / 10 : 6 / 10 = 23 / 10 × 10 / 6 = 23 / 6 = 3 bucati intregi de cablu si rest 5 / 6
23 / 10 - 3 × 6 / 10 = 5 / 10 → lungimea portiunii ramase
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8) 26 ecusoane
7 intregi si 1 / 2 = ( 7 x 2 + 1 ) / 2 = 15 / 2 = 7,5 cm → lungimea ecusonului
200 cm : 7, 5 = 26 ecusoane si un rest de 0,(6)
sau: 200 : 15 / 2 = 200 × 2 / 15 = 80 / 3 = 26 intregi si 2 / 3 ( restul )
26 intregi → reprezinta numarul ecusoanelor
2 / 3 → restul
