Задача 72524 ...
Условие
номер 1.
1) 2/3=0,(6)
2) 8/11=0,(7)
3) 3/5=0,6
4) -3/4=-0,75
5) -8 2/7≈-8,29
6) 13/99=0,(13)
номер 2.
1) 2/11 (×9) +1/9 (×11) =18/99+11/99=29/99=0,(29)
2) 8/13 (×3) +2/3 (×13) =24/39+26/39=50/39=1 11/39≈1,29
3) 1/3+1,25=1/3+125/100=1/3 (×4) +5/4 (×3) =4/12+15/12=19/12=1 7/12≈1,59
4) 1/6+0,33=1/6 (×50) +33/100 (×3) = 50/300+99/300=149/300=0,49(6)
5) 3/14×1,05=3/14×105/100=3/14×21/20=3/2×3/20=9/40=0,225
6) 7/9×1,7=7/9×17/10=119/90=1 29/90=1,3(2)
Решение
2) 8/11 = 72/99 = 0,(72)
0,(7) = 7/9
2 номер.
2) 8/13 + 2/3 = 24/39 + 26/39 = 50/39 = 1 11/39 = 1,(282051)
3) 1/3 + 1,25 = 1/3 + 5/4 = 4/12 + 15/12 = 19/12 = 1 7/12 = 1,58(3)
3 номер.
1) 0,(6) = 2/3
2) 1,(55) = 1 55/99 = 1 5/9 = 14/9
3) 0,1(2) = 1/10 + 2/90 = 9/90 + 2/90 = 11/90
4) -0,(8) = -8/9
5) -3,(27) = -3 27/99 = -3 3/11 = -36/11
6) -2,3(82) = -(2 + 3/10 + 82/99) = -(2*10*99 + 3*99 + 82*10)/(99*10) =
= -(1980 + 297 + 820)/990 = -3297/990
4 номер.
1) (20,88 : 18 + 45 : 0,36) : (19,59 + 11,95) =
= (2*9*1,16 : 18 + 9*5*100 : 36) : 31,54 = (1,16 + 5*25) : 31,54 =
= (1,16 + 125) : 31,54 = 126,16 : 31,54 = 12616 : 3154 = 4
2) 7/36*9 + 8*11/32 + 9/10*5/18 = 7*9/(4*9) + 8*11/(8*4) + 9/18*5/10 =
= 7/4 + 11/4 + 1/2*1/2 = 18/4 + 1/4 = 19/4 = 4 3/4 = 4,75
5 номер.
1) (3 4/25 + 0,24)*2,15 + (5,1625 - 2 3/16)*2/5 =
= (79/25 + 24/100)*215/100 + (5 13/80 - 2 15/80)*2/5 =
= (79/25 + 6/25)*43/20 + (413 - 175)/80*2/5 =
= 85/25*43/20 + 238/400 = 17*43/100 + 119/200 = 1581/200 = 7,905
2) 0,364 : 7/25 + 5/16 : 0,125 + (2 1/2)*0,8 =
= 364/1000*25/7 + 5/16 : 1/8 + 5/2*4/5 =
= 7*52/7*25/(25*40) + 5/16*8 + 2 = 52/40 + 5/2 + 2 =
= 4*13/(4*10) + 2,5 + 2 = 13/10 + 4,5 = 1,3 + 4,5 = 5,8