Răspuns
Explicație pas cu pas:
5 / 7 × { 1 / 12 + 11 / 15 : [ 1 / 60 + 162 × ( 1 / 270 + 1 / 450 + 1 / 360 ) ] } =
→ aflu c.m.m.m.c al numitorilor 270; 450 si 360 din paranteza rotunda
270 = 3³ x 10
450 = 3² x 5 x 10
360 = 2² x 3² x 10
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c.m.m.m.c al numitorilor 270, 450 si 360 = 27 × 4 × 5 × 10 = 5 400
→ amplific fractiile aducandu-le la acelasi numitor comun, prima cu 20 , a doua fractie cu 12, iar a treia fractie cu 15
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= 5 / 7 × { 1 / 12 + 11 / 15 : [ 1 / 60 + 162 × ( 20 + 12 + 15 ) / 5 400 ] } =
= 5 / 7 × [ 1 / 12 + 11 / 15 : ( 1 / 60 + 162 × 47 / 5400 ) ] =
= 5 / 7 × [ 1 / 12 + 11 / 15 : ( 1 / 60 + 3×47 / 100 )] =
= 5 / 7 × [ 1 / 12 + 11 / 15 : ( 5 / 300 + 3 ×141 / 300 ) ] =
= 5 / 7 × ( 1 / 12 + 11 / 15 : 428 / 300 ) =
428 / 300 = 107 / 75 → am simplificat fractia cu 4
= 5 / 7 × ( 1 / 12 + 11 / 15 × 75 / 107 )
= 5 / 7 × ( 1 / 12 + 55 / 107 )
= 5 / 7 × ( 107 / 1 284 + 12 × 55 / 1 284 )
= 5 / 7 × 767 / 1284 =
= 3835 / 8988
