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a; \(\dfrac{2}{5}\) x \(\dfrac{3}{4}\) + \(\dfrac{6}{15}\) : \(\dfrac{4}{9}\) x 5
= \(\dfrac{3}{10}\) + \(\dfrac{2}{5}\) x \(\dfrac{9}{4}\) x 5
= \(\dfrac{3}{10}\) + \(\dfrac{9}{10}\) x 5
= \(\dfrac{3}{10}\) + \(\dfrac{45}{10}\)
= \(\dfrac{48}{10}\)
= \(\dfrac{24}{5}\)
b; \(\dfrac{25}{12}\) x \(\dfrac{18}{35}\) x \(\dfrac{63}{24}\)
= \(\dfrac{15}{14}\) x \(\dfrac{63}{24}\)
= \(\dfrac{45}{16}\)
c; 4\(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) : 5\(\dfrac{1}{2}\)
= \(\dfrac{9}{2}\) + \(\dfrac{1}{2}\) : \(\dfrac{11}{2}\)
= \(\dfrac{9}{2}\) + \(\dfrac{1}{11}\)
= \(\dfrac{99}{22}\) + \(\dfrac{2}{22}\)
= \(\dfrac{101}{22}\)
Gọi tổng là A ta có :
A x 2 = 2/2.4 + 2/4.6 + 2/6.8 + ... + 2/18.20
A x 2 = 1/2 - 1/4 - 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/18 - 1/20
A x 2 = 1/2 - 1/20
A x 2 = 9/20
A = 9/20 : 2
A = 9/40
\(a,\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+....+\frac{4}{16.18}+\frac{4}{18.20}\)
\(=\frac{4}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{18}-\frac{1}{20}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{20}\right)\)
\(=2.\frac{9}{20}\)
\(=\frac{9}{10}\)
\(b,\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}\)
\(=\frac{9}{10}\)
5h17p+6h57p*5
=317p+417p*5
=2402p
14p15s:5=855s:5=171s
3h56'+5h15'=236p+315p=551p
7 ngày 13h*7=49 ngày 91h
=52 ngày 19h
17h5p:5=1025p:5=205p
2h18'*8=16h144'=18h24'
8h-3h26p=480p-206p=274p
52p6s:6=3126s:6=521s
Ta có 1/3x4= 1/3- 1/4
2/4x6= 1/4-1/6
..............................
5/13x18= 1/13 - 1/18
=> 1/3 -1/4 + 1/4 -1/6 +......+ 1/13 -1/18
= 1/3 - 1/18
= 5/18
TA có
4-2/2*4+6-4/4*6+8-6/6*8+...+2016-2014/2014*2016
=1/2-1/4+1/4-1/6+...+1/2014-1/2016
=1/2+1/4-1/4+1/6-1/6+...+1/2014-1/2014-1/2016
=1/2-1/2016
=1007/2016
2/2×4 + 2/4×6 + ... + 2/16×18 + 2/18×20
= 1/2 - 1/4 + 1/4 - 1/6 + ... + 1/16 - 1/18 + 1/18 - 1/20
= 1/2 - 1/20
= 10/20 - 9/20
= 9/20
2/2x4+2/4x6+...+2/16x18+2/18x20
=1/2=1/4+1/4-1/6+...+1/16-1/18+1/18-1/20
=1/2-1/20
=10/20-9/20
=1/20
\(\frac{2}{5}\times\frac{3}{4}\times\frac{6}{15}:\frac{4}{9}\times5=\frac{2\times3\times6\times9\times5}{5\times4\times15\times4}=\frac{27}{20}\)
2/5 x 3/4 x 6/15 : 4/9 x 5 = 6/20 x 6/15 : 4/9 x 5 = 36/300 : 4/9 x 5 = 324/1200 x 5 = 1620/1200