Tính bằng cách thuận tiện nhất:
1/3 + 2/3 + 5/12 + 4/3 + 1/12
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A = (2 + 22) + (23 + 24 ) +…(2199 + 2200)
A = 6 + 22 (2 + 22 ) +… + 2198 (2 + 22)
A = 6 + 22 (6 ) +… + 2198 (6)
A = 6(1 + 22 +… + 2198)
Vậy A chia hết cho 6
a) \(\left(\frac{2}{7}+\frac{3}{8}+\frac{12}{7}+\frac{5}{8}\right).\frac{19}{36}\)
\(=\left\{\left(\frac{2}{7}+\frac{12}{7}\right)+\left(\frac{3}{8}+\frac{5}{8}\right)\right\}.\frac{19}{36}\)
\(=\left(\frac{14}{7}+\frac{8}{8}\right).\frac{19}{36}\)
\(=\left(2+1\right).\frac{19}{36}\)
\(3.\frac{19}{36}=\frac{19}{12}\)
\(\frac{1}{2}+\frac{2}{4}+\frac{3}{6}+\frac{4}{8}+\frac{5}{10}+\frac{6}{12}\)
\(=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\)
\(=6\times\frac{1}{2}=3\)
`3/4+2/5+3/12`
`=3/4+3/12+2/5`
`=9/12+3/12+2/5`
`=12/12+2/5`
`=1+2/5`
`=7/5`
\(=\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{4}{5}+\dfrac{2}{3}+\dfrac{1}{4}\)
=(1/3+2/3)+(1/4+1/4)+(1/5+4/5)
=1+1+1/2
=5/2
\(a,\\ =\left(\dfrac{4}{9}+\dfrac{5}{9}\right)+\left(\dfrac{1}{8}+\dfrac{7}{8}\right)=1+1=2\\ b,\\ =\left(\dfrac{1}{3}+\dfrac{4}{3}+\dfrac{2}{3}\right)\left(\dfrac{5}{12}+\dfrac{1}{12}\right)\\ =\dfrac{7\times2}{3\times2}+\dfrac{1\times3}{2\times3}=\dfrac{14+3}{6}=\dfrac{17}{6}\)
\(a,\dfrac{4}{9}+\dfrac{1}{8}+\dfrac{5}{9}+\dfrac{7}{8}=\left(\dfrac{4}{9}+\dfrac{5}{9}\right)+\left(\dfrac{1}{8}+\dfrac{7}{8}\right)=\dfrac{9}{9}+\dfrac{8}{8}=1+1=2\\ b,\dfrac{1}{3}+\dfrac{2}{3}+\dfrac{5}{12}+\dfrac{4}{3}+\dfrac{1}{12}=\left(\dfrac{1}{3}+\dfrac{2}{3}+\dfrac{4}{3}\right)+\left(\dfrac{5}{12}+\dfrac{1}{12}\right)=\dfrac{7}{3}+\dfrac{6}{12}=\dfrac{7}{3}+\dfrac{1}{2}=\dfrac{14}{6}+\dfrac{3}{6}=\dfrac{17}{6}\)
\((\frac{1}{2}+\frac{1}{4}+\frac{1}{6}) \)x \((\frac{36}{9}-\frac{12}{9}:\frac{1}{3}) \)
\(= (\frac{1}{2}+\frac{1}{4}+\frac{1}{6}) \) x \((\frac{36}{9}-\frac{36}{9})\)
\( = (\frac{1}{2}+\frac{1}{4}+\frac{1}{6}) \) x \(0\)
\(= 0\)
= { 1/3 + 2/3 + 4/3 } + { 5/12 + 1/12 }
=7/3 + 6/12 = 102/36
Rút gọn = 51/18
= ( 1/3 + 2/3 + 4/3 ) + ( 5/12 + 1/12 )
= 7/3 + 6/12
= 28/12 + 6/12
= 34/12 = 17/6