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1. a
\(\dfrac{8}{5}-\dfrac{5}{6}\cdot\dfrac{3}{4}\)
\(=\dfrac{8}{5}-\dfrac{5\cdot3}{3\cdot2\cdot4}\)
\(=\dfrac{8}{5}-\dfrac{5}{8}=\dfrac{39}{40}\)
1.b
\(=\dfrac{7}{8}+\dfrac{5}{6}\cdot\dfrac{3}{2}\)
\(=\dfrac{7}{8}+\dfrac{5\cdot3}{3\cdot2\cdot2}\)
\(=\dfrac{7}{8}+\dfrac{5}{4}=\dfrac{17}{8}\)
2.a
\(\dfrac{4}{5}+x=\dfrac{11}{10}\)
\(x=\dfrac{11}{10}-\dfrac{4}{5}=\dfrac{3}{10}\)
2.b
\(x-\dfrac{3}{4}=\dfrac{5}{7}\)
\(x=\dfrac{5}{7}+\dfrac{3}{4}=\dfrac{41}{28}\)
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\(\left(x+9\right)+\left(x-8\right)+\left(x+7\right)+\left(x-6\right)+\left(x+5\right)+\left(x-4\right)+\left(x+3\right)+\left(x-2\right)+\left(x+1\right)=95.9\\ =>x+9+x-8+x+7+x-6+x+5+x-4+x+3+x-2+x+1=855\\ =>\left(x+x+x+x+x+x+x+x+x\right)+\left(9-8+7-6+5-4+3-2+1\right)=855\\ =>9x+5=855\\ =>9x=855-5\\ =>9x=850\\ =>x=\dfrac{850}{9}\)
\(\left(x+9\right)+\left(x-8\right)+...+\left(x-2\right)+\left(x+1\right)\)
\(=x+9+x-8+...+x-2+x+1\)
\(=\left(x+9+x-8\right)+...+\left(x+5\right)+...+\left(x-2+x+1\right)\)
(Ta gộp 4 số vào 1 tổng, riêng (x+5) là ta giữ nguyên)
\(=\left(2x-1\right)+...+\left(x+5\right)+...+\left(2x-1\right)\)
\(=4\left(2x-1\right)+\left(x+5\right)\)
\(=8x-4+x-5\)
\(=9x-9\) (1)
Từ bài toán trên, ta có:
\(\left(x+9\right)+\left(x-8\right)+...+\left(x-2\right)+\left(x+1\right)=95,9\)
Từ (1)
\(\Leftrightarrow9x-9=95,9\)
\(9x=95,9-9\)
\(x=86,9:9\)
\(x=9,6\left(5\right)\)
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a) ( 1/2-1/3-1/6).(1/2+2/3+3/4+...+2017/2018) + 3/4.x = 9/10
0.(1/2+2/3+3/4+...+2017/2018) + 3/4.x = 9/10
0+3/4.x = 9/10
3/4.x = 9/10
x = 9/10: 3/4
x = 6/5
b) x + ( 3/1.3+3/3.5+...+3/13.15) = 11/5
x + 3/2. ( 1-1/3 + 1/3 - 1/5 + ...+ 1/13 - 1/15) = 11/5
x + 3/2. ( 1-1/15) = 11/5
x + 3/2.14/15 = 11/5
x + 7/5 = 11/5
x = 11/5 - 7/5
x = 4/5
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\(\left(x-\dfrac{1}{2}\right).\dfrac{5}{2}=\dfrac{7}{4}-\dfrac{1}{2}\)
\(\Rightarrow\left(x-\dfrac{1}{2}\right).\dfrac{5}{2}=\dfrac{5}{4}\)
\(\Rightarrow x-\dfrac{1}{2}=\dfrac{1}{2}\)
=> x = 1
Ta có: \(\left(x-\dfrac{1}{2}\right)\cdot\dfrac{5}{2}=\dfrac{7}{4}-\dfrac{1}{2}\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)\cdot\dfrac{5}{2}=\dfrac{5}{4}\)
\(\Leftrightarrow x-\dfrac{1}{2}=\dfrac{1}{2}\)
hay x=1
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3 1/2 = 7/2...
5 3/4 = ...23/4
2 1/5 = ...11/5
2. TÌm x
x + 17,67 = 100 - 63,2
x + 17,67 = 36,8
x = 36,8 - 17,67
x = 11,13
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a) 1+2+3+...+2018
=[(2018-1):1+1].(2018+1):2
=2018.2019:2
=2037171
b) 4+7+10+13+...+2017
=[(2017-4):3+1].(2017+4):2
=672.2021:2
=679056
c) 1+2-3-4+5+6-7-8+9+10-11-12+13+14
=(1+2-3-4)+(5+6-7-8)+(9+10-11-12)+13+14
=-4+(-4)+(-4)+13+14
=-12+27
=15
d) 23 x 75 + 25 x 23 + 180
=23 x (75+25) +180
=23 x 100 +180
=2300+180
2480
chúc ban hoc tốt nha
a) Số số hạng: ( 2018 - 1 ) : 1 + 1 = 2018
Tổng: 2018 x ( 2018 + 1 ) : 2 = 2 037 171
4/5 + x : 1/3 = 2
= x : 1/3 = 2 - 4/5
= x : 1/3 = 6/5
= x = 6/5 x 1/3
= x = 2/5
4/5 + x : 1/3 = 2
x : 1/3 = 2 - 4/5
x : 1/3 = 6/5
x = 6/5 . 1/3
x = 2/5