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a. ( x - 1/2 ) x 5/3= 7/4 - 1/2
(x -1/2 ) x 5/3 = 5/4
x - 1/2 = 5/4 : 5/3
x - 1/2 = 3/4
x = 3/4 + 1/2
x = 5/4
b . 6/13 : ( 1/2 + x ) = 15/39
1/2 + x = 6/13- 15/39
1/2 + x = 1/13
x = 1/13 - 1/2
x = -11/26
c. 16/3 : (1/2+ x ) = 15/39
1/2 + x = 16/3 - 15/69
1/2 + x = 353/69
x = 353/69 - 1/2
x = 637/138
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(1-1/2) x (1-1/3) x .... x (1-1/100)
= 1/2 x 2/3 x ... x 99/100
= 1x2x...x99/2x3x..x100
= 1/ 100
a, \(\frac{3}{5}+25-\frac{1}{5}\)
\(=\left(\frac{3}{5}-\frac{1}{5}\right)+25\)
\(=\frac{2}{5}+25\)
\(=25\frac{2}{5}\)
\(=25,4\)
b, \(13.3.32,27+67,63.39\)
\(=39.32,27+67,63.39\)
\(=39\left(32,37+67,63\right)\)
\(=39.100\)
\(=3900\)
c, \(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{100}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}......\frac{99}{100}\)
\(=\frac{1}{100}\)
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Bài 1:
\(A=\frac{1}{\left(1+2\right)}+\frac{1}{\left(1+2+3\right)}+\frac{1}{\left(1+2+3+4\right)}\)\(+\frac{1}{\left(1+2+3+4+5\right)}+...+\)\(\frac{1}{\left(1+2+3+...+10\right)}\)
\(A=\frac{1}{3}+\frac{1}{6}+....+\frac{1}{55}\)
\(A=2\left(\frac{1}{6}+\frac{1}{12}+....+\frac{1}{110}\right)\)
\(A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{10}-\frac{1}{11}\right)\)
\(A=2.\left(\frac{1}{2}-\frac{1}{11}\right)\)
\(A=\frac{9}{11}\)
Bài 2 :
2) Tử số = 11 x 13 x 15 + 3 x 3 x 3 x 11 x 13 x 15 + 5 x 5 x 5 x 11 x 13 x 15 + 9 x 9 x 9 x 11 x 13 x 15
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) x 11 x 13 x 15 = (1+27+125+ 729) x 11 x 13 x 15
Mẫu số = 11 x 13 x 17 + 3 x 3 x 3 x 13 x 15 x 19 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17 lớn hơn 11 x 13 x 15 + 3 x 3 x 3 x 13 x 15 x 17 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) 13 x 15 x 17 = (1+27+125+729) x 13 x 15 x 17
\(\Rightarrow A< \frac{\left(1+27+125+729\right)\times11\times13\times15}{\left(1+27+125+729\right)\times13\times15\times17}\)
\(=\frac{11}{17}\)
\(=\frac{1111}{1717}=B\)
Vậy \(A=B\)
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1)\(A=\frac{1}{3}+\frac{1}{6}+...+\frac{1}{55}=2\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)=2.\left(\frac{1}{2}-\frac{1}{11}\right)=\frac{9}{11}\)
2) Tử số = 11 x 13 x 15 + 3 x 3 x 3 x 11 x 13 x 15 + 5 x 5 x 5 x 11 x 13 x 15 + 9 x 9 x 9 x 11 x 13 x 15
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) x 11 x 13 x 15 = (1+27+125+ 729) x 11 x 13 x 15
Mẫu số = 11 x 13 x 17 + 3 x 3 x 3 x 13 x 15 x 19 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17
lớn hơn 11 x 13 x 15 + 3 x 3 x 3 x 13 x 15 x 17 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) 13 x 15 x 17 = (1+27+125+729) x 13 x 15 x 17
=> \(A<\frac{\left(1+27+125+729\right)\times11\times13\times15}{\left(1+27+125+729\right)\times13\times15\times17}=\frac{11}{17}=\frac{1111}{1717}=B\)
Vậy A < B
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0,225 x 840 + 22,5 x 0,6 + 2,25 : 0,01
=0,225 x 100 x 8,4 + 22,5 x 0,6 + 2,25 x 10 : 0,1
=22,5 x 8,4 + 22,5 x 0,6 + 22,5 x 1/10
=22,5 x 8,4 + 22,5 x 0,6 + 22,5 x 10
=22,5 x (8,4 + 0,6 + 10)
=22,5 x 19
=427,5
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1 .
a . ta có : 2,34 . 1.3 + 23, 4 . 0,87
=2,34 . 10. 0.13 + 23, 4 . 0,87
=23,4. 0,13 + 23,4 . 0,8
=23,4(0,13+0,87)
=23,4 . 0,1
=2,34
b . 0,417 . 840 - 41,7 . 7,4
=0,417 . 840 - 0,417. 100. 7,4
=0,417 . 840 - 0,417 . 740
=0,417(840-740)
=0,417. 100
=41,7
bai 2 :
khối lượng của lượng đầu trong thùng là :
25 . 0,8=20 (kg)
khối lượng của thùng dầu là :
20 + 5, 28=25,28(kg)
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