\(B=\dfrac{14}{38\cdot31}+\dfrac{10}{38\cdot43}+\dfrac{6}{43\cdot46}+\dfrac{22}{46\cdot57}\)

=2(7/31*38+5/38*43+3/43*46+11/46*57)

=2(1/31-1/38+1/38-1/43+...+1/46-1/57)

=>A/B=5/2

5/2 nhé

23x57+23x43

=23x(57+43)

=23x100

=2300

=23x(57+43)

=23x100

=2300

23 x 57 +23 x 43=2300

d)\(\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{97.99}\) 

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{97}-\frac{1}{99}\)

\(=\frac{1}{3}-\frac{1}{99}\)

\(=\frac{32}{99}\)

a)   11/4x(-0,4)x-1,6x11/4

     = -1,1 x-1,6x11/4

    = 1,76x11/4

    = 4,48

b)    6/19x-7/11+6/19x-4/19x-4/11+13/19

     = -42/209+96/3971+13/19

     = -702/3971+13/19

     = 2015/3971

c)     2/5x3/7+-3/7x3/5+3/7

      = 3/7x(2/5+3/5+1)

      = 3/7x(1+1)

      = 3/7x2

      = 6/7

d)      2/3x5+2x5/7+2/7x9+....+2/97x99

      = 1/3-1/5+1/5-1/7+1/7-1/9+......+1/97-1/99

      = 1/3-1/99

      = 32/99

d)=1/3-1/5+1/5-1/7+....+1/97-1/99

=1/3-1/99

=32/99

a: \(\dfrac{1}{7}+\dfrac{1}{91}+\dfrac{1}{247}+\dfrac{1}{475}+\dfrac{1}{775}+\dfrac{1}{1147}\)

\(=\dfrac{1}{1\cdot7}+\dfrac{1}{7\cdot13}+\dfrac{1}{13\cdot19}+\dfrac{1}{19\cdot25}+\dfrac{1}{25\cdot31}+\dfrac{1}{31\cdot37}\)

\(=\dfrac{1}{6}\left(\dfrac{6}{1\cdot7}+\dfrac{6}{7\cdot13}+\dfrac{6}{13\cdot19}+\dfrac{6}{19\cdot25}+\dfrac{6}{25\cdot31}+\dfrac{6}{31\cdot37}\right)\)

\(=\dfrac{1}{6}\left(1-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{13}+...+\dfrac{1}{31}-\dfrac{1}{37}\right)\)

\(=\dfrac{1}{6}\left(1-\dfrac{1}{37}\right)=\dfrac{1}{6}\cdot\dfrac{36}{37}=\dfrac{6}{37}\)

b: Sửa đề:\(\dfrac{3}{5\cdot8}+\dfrac{11}{8\cdot19}+\dfrac{12}{19\cdot31}+\dfrac{80}{31\cdot101}+\dfrac{99}{101\cdot200}\)

\(=\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{31}+\dfrac{1}{31}-\dfrac{1}{101}+\dfrac{1}{101}-\dfrac{1}{200}\)

\(=\dfrac{1}{5}-\dfrac{1}{200}=\dfrac{39}{200}\)

1.

\(a,\dfrac{3}{4}+\dfrac{5}{2}=\dfrac{3}{4}+\dfrac{10}{4}=\dfrac{13}{4}\)

\(b,3+\dfrac{6}{11}+\dfrac{33}{11}+\dfrac{6}{11}=\dfrac{39}{11}\)

\(c,2-\dfrac{5}{7}=\dfrac{14}{7}-\dfrac{5}{7}=\dfrac{9}{7}\)

\(\dfrac{11}{3}-2=\dfrac{11}{3}-\dfrac{6}{3}=\dfrac{5}{3}\)

2.

\(a,\dfrac{13}{19}+\dfrac{18}{19}+\dfrac{17}{19}=\dfrac{13}{19}+\dfrac{17}{19}+\dfrac{18}{19}=\dfrac{30}{19}+\dfrac{18}{19}=\dfrac{48}{19}\)

\(b,\dfrac{3}{5}+\dfrac{3}{16}+13+16=\dfrac{63}{80}+29=\dfrac{2383}{80}\)

3.

Nửa chu vi :

\(4:2=2\left(m\right)\)

Chiều rộng :

\(2-\dfrac{5}{6}=\dfrac{7}{6}\left(m\right)\)

1)

a) 3/4+10/4= 13/4

b) 3/1+6/11= 33/11+6/11= 39/11

c) 2/1-5/7= 14/7-5/7= 9/7

d) 11/3-2/1= 11/3-6/3= 5/3

3) Nữa chu vi là

4:2= 2 (m)

Chiều rộng là

2-5/6= 7/6(m)

\(1,\\ a,\dfrac{3}{4}+\dfrac{5}{2}=\dfrac{3}{4}+\dfrac{10}{4}=\dfrac{13}{4}\\ b,3+\dfrac{6}{11}=\dfrac{33}{11}+\dfrac{6}{11}=\dfrac{39}{11}\\ c,2-\dfrac{5}{7}=\dfrac{14}{7}-\dfrac{5}{7}=\dfrac{9}{7}\\ d,\dfrac{11}{3}-2=\dfrac{11}{3}-\dfrac{6}{3}=\dfrac{5}{3}\\ 2,\\ a,\dfrac{13}{19}+\dfrac{18}{19}+\dfrac{17}{19}=\dfrac{13+18+17}{19}=\dfrac{48}{49}\\ b,\dfrac{3}{5}+\dfrac{3}{16}+13+16=\dfrac{48}{80}+\dfrac{15}{80}+\dfrac{1040}{80}+\dfrac{1280}{80}=\dfrac{2383}{80}\)

3, Chiều rộng hcn là:
`4:2- 5/6= 7/6`(m)

Đáp số: `7/6`m