tinh nhanh:
a)1/3×5+1/5×7+1/7×9+.....+1/2015×2017+1/2017×2019
b)1/1×4+1/4×7+1/7×10+....+1/313×319
c)7256×4375-725/7255×4375+3650
d)(315+372)×3+(372+315)×7/28×13+74×14
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A= 1+5+9+.....+2001
Số số hạng: (2001-1):4+1=501
Tổng là: (2001+1)x501:2=501501
a) B = [ ( 315 + 372 ) . 3 + ( 372 + 315 . 7 ] : ( 26 . 13 + 74 . 14 )
= [687.3+687.7]:1374=6870:1374=5
\(\dfrac{\left(315+372\right).3+\left(372+315\right).7}{26.13+74.14}\)
\(=\dfrac{\left(315+372\right)\left(3+7\right)}{2.13.13+74.2.7}\)
\(=\dfrac{687.10}{2\left(169+518\right)}\)
\(=\dfrac{6870}{2.687}=\dfrac{6870}{1374}=5\)
a, [ (315+372) .3 +(372+315).7] /26.13 +74.14
=[ (315+372) .(3+7) ] /26 .13 + 74 .13 +74
= [(315+372).10 ] / (26+74).13 +74
= 687 .10 / 100.13 +74
= 6870 /1374
den day ban tu rut gon
\(27.332+93.43+57.61+69.57\\ =27.332+93.43+57.\left(61+69\right)\\ =27.332+93.43+57.130\\ =8964+3999+7410=20373\\ 34.75+75.66-65.100\\ =\left(34+66\right).75-65.100\\ =100.75-65.100\\ =100.\left(75-65\right)\\ =100.10=1000\\ \left(456.11+912\right).37:13:74\\ =5928:13:\left(74:37\right)\\ =456:2=228\\ 6^2:4.3+2.5^2\\ =36:4.3+2.25\\ =9.3+50=27+50=77\\ 5.4^2-18:3^2\\ =5.16-18:9\\ =80-2=78\\\left[\left(315+372\right).3+\left(372+315\right).7\right]:\left(26.13+74.14\right)\\ =687.\left(3+7\right):\left(338+1036\right)\\ 687.10:1374\\ =6870:1374=5\\ 12:\left\{390:\left[500-\left(125+35.7\right)\right]\right\}\\ =12:\left[390:\left(500-370\right)\right]\\ =12:\left(390:130\right)=12:3=4\\ 192000-\left(1500.2+1800.3+1800.2:3\right)\\ =192000-\left(3000+5400+1200\right)\\ =192000-9600=182400\)
\(\dfrac{7256.4375-725}{3650+4375.7255}\)
\(=\dfrac{\left(7255+1\right).4375-725}{3650+4375.7255}\)
\(=\dfrac{7255.4375+1.4375-725}{3650+4375.7255}\)
\(=\dfrac{7255.4375+3650}{3650+4375.7255}=1\)
\(\dfrac{7256.4375-725}{3650+4375.7255}=\dfrac{\left(7255+1\right).4375-725}{3650+4375.7255}\)
\(=\dfrac{7255.4375+4375-725}{3650+4372.7255}=\dfrac{7255.4375+3650}{3650+4375.7255}=1\)
\(\frac{315}{316}\cdot\frac{316}{314}\cdot\frac{316}{315}\cdot\frac{317}{313}=\frac{315.316.316.317}{316.314.315.313}=\frac{1.1.316.317}{1.314.1.313}=\frac{100172}{98282}\)
Ta có : \(\frac{3}{2}\times\frac{4}{5}\times\frac{2}{3}\)
\(=\frac{3}{2}\times\frac{2}{3}\times\frac{4}{5}=1\times\frac{4}{5}\)
\(=\frac{4}{5}\)