Răspuns :
1.
0,8 ( 2/3 + 0,75 ) + 3 : ( 7,5 - 3 ) - 1/6
= 8/10 ( 2/3 + 75/100 ) + 3 : ( 75/10 - 3 ) - 1/6
= 4/5 ( 2/3 + 3/4 ) + 3 : ( 15/2 - 3 ) - 1/6
= 4/5 ( 8/12 + 9/12 ) + 3 : ( 15/2 - 6/2 ) - 1/6
= 4/5 * 17/12 + 3 * 2/9 - 1/6
= 17/15 + 2/3 - 1/6
= 34/30 + 20/30 - 5/30
= 49/30
2.
( 0,2 + 1/2 + 0,02 * 10 ) : [(0,37 + 8/20 ) * 10 - 65 : 10 ]
= ( 2/10 + 1/2 + 2/10 ) : [( 37/100 + 8/20 ) * 10 - 65 : 10
= ( 2/10 + 5/2 + 2/10 ) : [( 37/100 + 40/100 ) * 10 - 65/10 ]
= 9/10 : ( 77/100 * 10 - 13/2 )
= 9/10 : ( 77/10 - 13/2 )
= 9/10 : ( 77/10 - 65/10 )
= 9/10 * 10/12
= 3/4
3.
3,75 + ( 0,5 - 1/5 + 0,35 ) * 10
= 375/100 + ( 5/10 - 1/5 + 35/100 ) * 10
= 15/4 + ( 1/2 - 1/5 + 7/20 ) * 10
= 15/4 + ( 10/20 - 4/20 + 7/20 ) * 10
= 15/4 + 13/20 * 10
= 15/4 + 13/2 = 15/4 + 26/4 = 41/4
4.
14/5 + 0,7 * 10 : ( 3 + 0,2 * 2 1/2 )
= 14/5 + 7 : ( 3 + 2/10 * 5/2 )
= 14/5 + 7 : ( 3 + 1/2 )
= 14/5 + 7 : 7/2
= 14/5 + 7 * 2/7
= 14/5 + 2
= 14/5 + 10/5
= 24/5
5.
[0,(6) + 5/6 ] * ( 3/4 - 0,4 ) + 1,5 * 5 * ( 0,8 : 37 )
= ( 6/9 + 5/6 ) * ( 3/4 - 4/10 ) + 15/10 * 5 ( 8/10 * 1/37 )
= ( 2/3 + 5/6 ) * ( 15/20 - 8/20 ) + 15/2 * 4/(5*37)
= 9/6 * 7/20 + 6/37
= 63/120 + 6/37
= 2331/4440 + 720/4440
= 3051/4440 ( se simplifica cu 3 )
= 1017/1480
0,8 ( 2/3 + 0,75 ) + 3 : ( 7,5 - 3 ) - 1/6
= 8/10 ( 2/3 + 75/100 ) + 3 : ( 75/10 - 3 ) - 1/6
= 4/5 ( 2/3 + 3/4 ) + 3 : ( 15/2 - 3 ) - 1/6
= 4/5 ( 8/12 + 9/12 ) + 3 : ( 15/2 - 6/2 ) - 1/6
= 4/5 * 17/12 + 3 * 2/9 - 1/6
= 17/15 + 2/3 - 1/6
= 34/30 + 20/30 - 5/30
= 49/30
2.
( 0,2 + 1/2 + 0,02 * 10 ) : [(0,37 + 8/20 ) * 10 - 65 : 10 ]
= ( 2/10 + 1/2 + 2/10 ) : [( 37/100 + 8/20 ) * 10 - 65 : 10
= ( 2/10 + 5/2 + 2/10 ) : [( 37/100 + 40/100 ) * 10 - 65/10 ]
= 9/10 : ( 77/100 * 10 - 13/2 )
= 9/10 : ( 77/10 - 13/2 )
= 9/10 : ( 77/10 - 65/10 )
= 9/10 * 10/12
= 3/4
3.
3,75 + ( 0,5 - 1/5 + 0,35 ) * 10
= 375/100 + ( 5/10 - 1/5 + 35/100 ) * 10
= 15/4 + ( 1/2 - 1/5 + 7/20 ) * 10
= 15/4 + ( 10/20 - 4/20 + 7/20 ) * 10
= 15/4 + 13/20 * 10
= 15/4 + 13/2 = 15/4 + 26/4 = 41/4
4.
14/5 + 0,7 * 10 : ( 3 + 0,2 * 2 1/2 )
= 14/5 + 7 : ( 3 + 2/10 * 5/2 )
= 14/5 + 7 : ( 3 + 1/2 )
= 14/5 + 7 : 7/2
= 14/5 + 7 * 2/7
= 14/5 + 2
= 14/5 + 10/5
= 24/5
5.
[0,(6) + 5/6 ] * ( 3/4 - 0,4 ) + 1,5 * 5 * ( 0,8 : 37 )
= ( 6/9 + 5/6 ) * ( 3/4 - 4/10 ) + 15/10 * 5 ( 8/10 * 1/37 )
= ( 2/3 + 5/6 ) * ( 15/20 - 8/20 ) + 15/2 * 4/(5*37)
= 9/6 * 7/20 + 6/37
= 63/120 + 6/37
= 2331/4440 + 720/4440
= 3051/4440 ( se simplifica cu 3 )
= 1017/1480
1. 0,8(2/3+0,75)+3:(7,5-3)-1/6=
8/10x(2/3+75/100)+3:4,5-1/6= se observa ca 75/100 se simplifica cu 25 deci vom avea 3/4
ex.devine 8/10x(2/3+3/4)+3/1:45/10-1/6=
8/10x(2x4+3x3)/12+3/1x10/45-1/6
=8/10x(8+9)/12+30/45-1/6
=8/10x17/12+30/45-1/6 se simplifica ce se poate
=1/5x17/3+2/5-1/6
=17/15+2/5-1/6
=(17x2+2x6-1x5)/30
=(34+12-5)/30=41/30=1,3(6)
2.(0,2+1/2+0,02x10):[(0,37+8/20)x10-65:10]=
(2/10+1/2+0,2):[(37/100+8/20)x10-65/10]=simplificam ce se poate
(2/10+1/2+2/10):[(37+8x5)/100x10-65/10]=
(2+1x5+2)/10:[77/100x10-65/10]=
9/10:(77/10-65/10]=
9/10:12/10=9/10x10/12=9/12=3/4
3.3,75+(0,5-1/5+0,35)x10=
3,75+(5/10-1/5-35/100)x100=
3,75+(5x10-1x20-35)/100x100=
3,75+(50-20-35)/100x100=
3,75+5/100x100/1=3,75+5=8,75
4.14/5+0,7x10:(3+0,2x2 1/2)=
14/5+7:(3+2/10x5/2)=
14/5+7:(3+1/2)=
14/5+7:(3x2+1)/2=
14/5+7:7/2=
14/5+7/1x2/7=
14/5+2=(14+2x5)/5=24/5
5,[0,(6)+5/6]x(3/4-0,4)+1,5x5x(0,8:37)=
[6/9+5/6]x(3/4-4/10)+15/10x5/1x(8/10:37/1)=
(2/3+5/6)x(3/4-2/5)+15/2x(4/5x1/37)=
(2x2+5)/6x(3x5-2x4)/20+15/2x4/185=
9/6x7/20+3/1x2/37=
3/2x7/20+6/37=
21/40+6/37=
(21x37+6x40)/1480=
(777+240)/1480=1017/1480=0,687(162)
8/10x(2/3+75/100)+3:4,5-1/6= se observa ca 75/100 se simplifica cu 25 deci vom avea 3/4
ex.devine 8/10x(2/3+3/4)+3/1:45/10-1/6=
8/10x(2x4+3x3)/12+3/1x10/45-1/6
=8/10x(8+9)/12+30/45-1/6
=8/10x17/12+30/45-1/6 se simplifica ce se poate
=1/5x17/3+2/5-1/6
=17/15+2/5-1/6
=(17x2+2x6-1x5)/30
=(34+12-5)/30=41/30=1,3(6)
2.(0,2+1/2+0,02x10):[(0,37+8/20)x10-65:10]=
(2/10+1/2+0,2):[(37/100+8/20)x10-65/10]=simplificam ce se poate
(2/10+1/2+2/10):[(37+8x5)/100x10-65/10]=
(2+1x5+2)/10:[77/100x10-65/10]=
9/10:(77/10-65/10]=
9/10:12/10=9/10x10/12=9/12=3/4
3.3,75+(0,5-1/5+0,35)x10=
3,75+(5/10-1/5-35/100)x100=
3,75+(5x10-1x20-35)/100x100=
3,75+(50-20-35)/100x100=
3,75+5/100x100/1=3,75+5=8,75
4.14/5+0,7x10:(3+0,2x2 1/2)=
14/5+7:(3+2/10x5/2)=
14/5+7:(3+1/2)=
14/5+7:(3x2+1)/2=
14/5+7:7/2=
14/5+7/1x2/7=
14/5+2=(14+2x5)/5=24/5
5,[0,(6)+5/6]x(3/4-0,4)+1,5x5x(0,8:37)=
[6/9+5/6]x(3/4-4/10)+15/10x5/1x(8/10:37/1)=
(2/3+5/6)x(3/4-2/5)+15/2x(4/5x1/37)=
(2x2+5)/6x(3x5-2x4)/20+15/2x4/185=
9/6x7/20+3/1x2/37=
3/2x7/20+6/37=
21/40+6/37=
(21x37+6x40)/1480=
(777+240)/1480=1017/1480=0,687(162)
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