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a)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{98.99}+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
b)\(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\)
\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+....+\frac{1}{61}-\frac{1}{66}\)
\(=\frac{1}{11}-\frac{1}{66}\)
\(=\frac{5}{66}\)
a,\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\)
ta có:
\(\frac{1}{1.2}=\frac{2-1}{1.2}=\frac{2}{1.2}-\frac{1}{1.2}=1-\frac{1}{2}\)
\(\frac{1}{2.3}=\frac{3-2}{2.3}=\frac{3}{2.3}-\frac{2}{2.3}=\frac{1}{2}-\frac{1}{3}\)
...
\(\frac{1}{99.100}=\frac{1}{99}-\frac{1}{100}\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
=\(1-\frac{1}{100}=\frac{99}{100}\)
b,
\(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.16}+...+\frac{5}{61.66}\)
ta có:
\(\frac{5}{11.16}=\frac{16-11}{11.16}=\frac{16}{11.16}-\frac{11}{11.16}=\frac{1}{11}-\frac{1}{16}\)
\(\frac{5}{16.21}=\frac{21-16}{16.21}=\frac{21}{16.21}-\frac{16}{16.21}=\frac{1}{16}-\frac{1}{21}\)
...
\(\frac{5}{61.66}=\frac{66-61}{61.66}=\frac{66}{61.66}-\frac{61}{61.66}=\frac{1}{61}-\frac{1}{66}\)
= \(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
=\(\frac{1}{11}-\frac{1}{66}\)=\(\frac{5}{66}\)
a, \(\frac{5}{11.16}+\frac{5}{11.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)
=\(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)
=\(\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)
a, A=1/11-1/16+1/16-1/21+1/21-1/26+...+1/61-1/66
= 1/11-1/66=5/66 ( A chính là biểu thức ở phần a)
b, 1/12+1/20+1/30+...+1/110
=1/3.4+1/4.5+1/5.6+..+1/10.11
=1/3-1/4+1/4-1/5+1/5-1/6+...+1/10-1/11
=1/3-1/11=8/33
a,Ta có :
1/3 + 1/16 + 1/19 + 1/21 + 1/61 + 1/72 + 1/83 + 1/94 = 0,54
3/4 = 0,6
=>b < 3/4
Bài 6:
\(21,251+6,058+0,749+1,042\)
\(=\left(21,251+0,749\right)+\left(6,058+1,042\right)\)
\(=22+7,1\)
\(=29,1\)
___________________
\(1,53+5,309+12,47+5,691\)
\(=\left(1,53+12,47\right)+\left(5,309+5,691\right)\)
\(=14+11\)
\(=25\)
5:
a: =>x/17=5/17
=>x=5
b; =>6+x=7/11*33=21
=>x=15
c: \(\dfrac{12+x}{43-x}=\dfrac{2}{3}\)
=>3x+36=86-2x
=>5x=50
=>x=10
d: \(\dfrac{x}{5}< \dfrac{3}{7}\)
=>x<3/7*5
=>x<15/7
f: 15/26+x/16=46/52
=>x/16=23/26-15/26=8/26=4/13
=>x=4/13*16=64/13
Bài 1: Ta chỉ cần bỏ ngoặc rồi cộng hai phân số để ra kết quả là số tự nhiên là xong
Bài 2:
A = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+............+\frac{1}{2003.2004}\)
A = \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-.............-\frac{1}{2003}+\frac{1}{2003}-\frac{1}{2004}\)
A = \(1-\frac{1}{2004}\)
A = \(\frac{2004}{2004}-\frac{1}{2004}=\frac{2003}{2004}\)
Mk làm mẫu 1 bài nha
Bài 1 :
a, = (1/4+3/4) - (5/13+8/13)+2/11
= 1 - 1 + 2/11
= 2/11
Tk mk nha
1)\(\dfrac{2}{9}+\dfrac{-3}{4}+\dfrac{5}{30}\)
\(=\dfrac{2.20}{9.20}+\dfrac{-3.45}{4.45}+\dfrac{5.6}{30.6}\)
\(=\dfrac{40}{180}+\dfrac{-135}{180}+\dfrac{30}{180}\)
\(=\dfrac{40+\left(-135\right)+30}{180}\)
\(=\dfrac{-65}{180}\)
\(=\dfrac{-13}{36}\)
2)\(\dfrac{-7}{12}-\dfrac{11}{18}\)
\(=\dfrac{-7.3}{12.3}-\dfrac{11.2}{18.2}\)
\(=\dfrac{-21}{36}-\dfrac{22}{36}\)
\(=\dfrac{-21-22}{36}\)
\(=\dfrac{-43}{36}\)
3)\(\dfrac{7}{8}-\dfrac{-5}{16}\)
\(=\dfrac{7.2}{8.2}-\dfrac{-5}{16}\)
\(=\dfrac{14}{16}-\dfrac{-5}{16}\)
\(=\dfrac{14-\left(-5\right)}{16}\)
\(=\dfrac{19}{16}\)
4)\(\dfrac{3}{8}-\dfrac{-9}{10}-\dfrac{5}{16}\)
\(=\dfrac{3.10}{8.10}-\dfrac{-9.8}{10.8}-\dfrac{5.5}{16.5}\)
\(=\dfrac{30}{80}-\dfrac{-72}{80}-\dfrac{25}{80}\)
\(=\dfrac{30-\left(-72\right)-25}{80}\)
\(=\dfrac{77}{80}\)
a) \(\frac{2}{5x7}+\frac{2}{7x9}+...+\frac{2}{35x37}+\frac{2}{37x39}\)
\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{35}-\frac{1}{37}+\frac{1}{37}-\frac{1}{39}\)
\(=\frac{1}{5}-\frac{1}{39}\)
\(=\frac{34}{195}\)
c)đề sai ở phân số cuối
D ) 1/11×16 +1/16×21+...+1/61×66
Đặt Thắng=1/11×16 +1/16×21+...+1/61×66
5Thắng=5(1/11×16 +1/16×21+...+1/61×66)
5Thắng=1/11-1/16+1/16-1/21+...+1/61-1/66
5Thắng=1/11-1/66
Thắng=5/176:5=1/176
D) Đặt D=1/11×16 +1/16×21+...+1/61×66
=>5D=5.(1/11x16+1/16x21+...+1/61x66)
=>5D=5/11x16+5/16x21+...+5/61x66
=>5D=1/11-1/16+1/16-1/21+...+1/61-1/66
=>5D=1/11-1/66
=>5D=5/66
=>D=1/66