Question

5/7 × {1/12+11/15:[1/60+162×(1/270+1/450+1/360)]}

Answer 1

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

_________________

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

_____________________________________________

= 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

Answer 2

Răspuns

3835/8988 ;

Explicație pas cu pas:

5/7x{1/12+11/15:[1/60+162x(1/270+1/450+1/360)]} ; in paranteza rotunda numitor comun 5400 ;

5/7x{1/12+11/15:[1/60+162x(20+12+15)/5400]} =

5/7x[1/12+11/15:(1/60+162x47/5400)] =

5/7x[1/12+11/15:(1/60+7614/5400) =  (7614/5400 ;simplificat prin 54 = 141/100)

5/7x[1/12+11/15:(1/60+141/100) = (in paranteza rotunda numitor comun 300)

5/7x[1/12+11/15:(5+141x3)/300 =

5/7x(1/12+11/15x300/428) =

5/7x(1/12+3300/6420) =

5/7x(535+3300/6420) =

5/7x3835/6420 =

3835/(7x1284)  =

3835/8988 ;