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Đặt \(A=\)\(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{143}\)
\(=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{11.13}\)
\(2A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}\)
\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)
\(2A=\frac{1}{3}-\frac{1}{13}=\frac{10}{39}\)
\(A=\frac{5}{39}\)
Câu còn lại cx dựa như vậy nhé bn !
Chúc bn hc tốt <3
2,
a) \(315-\left(135-x\right)=215\)
\(\Rightarrow135-x=315-215\)
\(\Rightarrow135-x=100\)
\(\Rightarrow x=135-100\)
\(\Rightarrow x=35\)
b) \(x-320:32=25\cdot16\)
\(\Rightarrow x-10=5^2\cdot4^2\)
\(\Rightarrow x-10=20^2\)
\(\Rightarrow x-10=400\)
\(\Rightarrow x=410\)
c) \(3\cdot x-2018:2=23\)
\(=3\cdot x-1009=23\)
\(\Rightarrow3\cdot x=1032\)
\(\Rightarrow x=1032:3\)
\(\Rightarrow x=344\)
d) \(280-9\cdot x-x=80\)
\(\Rightarrow280-x\cdot\left(9+1\right)=80\)
\(\Rightarrow280-10\cdot x=80\)
\(\Rightarrow10\cdot x=280-80\)
\(\Rightarrow10\cdot x=200\)
\(\Rightarrow x=20\)
e) \(38\cdot x-12\cdot x-x\cdot16=40\)
\(\Rightarrow x\cdot\left(38-12-16\right)=40\)
\(\Rightarrow x\cdot10=40\)
\(\Rightarrow x=40:10\)
\(\Rightarrow x=4\)
bài 1
a) 155 - 10.(x+1) = 55
=>10 .(x+1) = 100
=>x + 1 = 10
=>x = 9
còn lại tương tự
a) (-370) + 114 + 236 + 370
= (-370 + 370) + 114 + 236
= 114 + 236
= 350
b, (-120) + (-130) + 360 + (-110)
= (-120 - 130 - 110) + 360
= -360 + 360
= 0
c, 25 + 37 - 48 - 25 - 37
= (25 - 25) + (37 - 37) - 48
= -48
d, (-125) - (19 - 125)
= -125 - 19 + 125
= (-125 + 125) - 19
= -19
e, 100 - [ 25 - (-19 - 11)]
= 100 - (25 + 19 + 11)
= 100 - (25 + 30)
= 100 - 55
= 45
f, 271 - [( -43) + 271 - (-17)]
= 271 - (-43 + 271 + 17)
= 271 + 43 - 271 + 17
= (271 - 271) + (43 + 17)
= 60
g, 35 . (-29) + (-29) . 65
= (-29)(35 + 65)
= (-29) . 100
= -2900
h, 22 . (-8) . (-25) . 125 . 18
= 4 . (-8) . (-25) . 125 . 18
= [4 . (-25)] . [(-8) . 125] . 18
= -100 . (-1000) . 18
= 100000 . 18
= 1800000
i, 48 : (-6 . 4 + 8)
= 48 : (-24 + 8)
= 48 : (-16)
= -3
j, -3 . 7 - 4 . (-5) + 1
= -21 + 20 + 1
= 0
k, 16 + (102 -7.6) - ( 94 . 17 - 27 . 94)
= 16 + (102 - 42) - 94(17 - 27)
= 16 + 102 - 42 - 94 . (-10)
= 16 + 102 - 42 + 940
= 16 + 60 + 940
= 16 + (60 + 940)
= 16 + 1000
= 1016
Chúc bn học tốt (Đây là cách của mình, mình nghĩ còn nhiều cách nữa, bạn có thể tham khảo bài mình)
Bài 1:
Ta có: \(x-35\%\cdot x=\dfrac{1}{25}\)
\(\Leftrightarrow65\%\cdot x=\dfrac{1}{25}\)
\(\Leftrightarrow x=\dfrac{1}{25}:\dfrac{13}{20}=\dfrac{1}{25}\cdot\dfrac{20}{13}=\dfrac{4}{65}\)
Vậy: \(x=\dfrac{4}{65}\)
Bài 2:
a) Ta có: \(17\dfrac{2}{31}-\left(\dfrac{15}{17}+6\dfrac{2}{31}\right)\)
\(=17\dfrac{2}{31}-\dfrac{15}{17}-6\dfrac{2}{31}\)
\(=11+\dfrac{2}{31}-\dfrac{15}{17}\)
\(=\dfrac{5366}{527}\)
a) \(48.19+48.15+134.52\)
\(=48\left(19+15\right)+6968\)
\(=48.34+6968\)
\(=1632+6968\)
\(=8600.\)
b) \(27.121-87.27+73.34\)
\(=27\left(121-87\right)+73.34\)
\(=27.34+73.34\)
\(=34\left(27+73\right)\)
\(=34.100\)
\(=3400.\)
c) \(125.98-125.46-52-25\)
\(=125\left(98-46\right)-52-25\)
\(=125.52-52-25\)
\(=52\left(125-1\right)-25\)
\(=52.124-25\)
\(=6448-25\)
\(=6423.\)
d) \(136.23+136.17-40.36\)
\(=136\left(23+17\right)-40.36\)
\(=136.40-40.36\)
\(=40\left(136-36\right)\)
\(=40.100\)
\(=4000.\)
e) \(66.25+5.66+66.14+33.94\)
\(=33\left(2.50+5.2+14.2+94\right)\)
\(=33\left(50+10+28+94\right)\)
\(=33.182\)
\(=6006.\)
\(A=\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{83.85}\)
\(\Rightarrow2A=\frac{2}{25.27}+\frac{2}{27.29}+\frac{2}{29.31}+...+\frac{2}{83.85}\)
\(2A=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{83}-\frac{1}{85}\)
\(2A=\frac{1}{25}-\frac{1}{85}\)
\(2A=\frac{12}{425}\)
\(A=\frac{12}{425}:2\)
\(A=\frac{6}{425}\)
\(C=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)
\(C=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)
\(C=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
\(C=\frac{1}{3}-\frac{1}{21}\)
\(C=\frac{2}{7}\)
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