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`(2/3xx4/5)xx5/6`
`=2/3xx4/5xx5/6`
`=2/3xx4/6`
`=2/3xx2/3`
`=1`
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`(4/5+5/4)xx3/4`
`=(16/20+25/20)xx3/4`
`=41/20xx3/4`
`=123/80`
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`27/12+17/6-25/36-15/6`
`=(27/12-25/36)+(17/6-15/6)`
`=(81/36-25/36)+2/6`
`=56/36+2/6`
`=56/36+12/36`
`=68/36`
`=17/9`
\(4\cdot5\cdot\frac{6}{12}\cdot10\cdot8=\left(4\cdot5\right)\cdot\left(\frac{6}{12}\cdot8\right)\cdot10\)
\(=20\cdot4\cdot10=800\)
\(\frac{4\times5\times6}{12\times10\times8}=\frac{4\times5\times6}{2\times6\times5\times2\times2\times4}=\frac{1}{2\times2\times2}=\frac{1}{8}\)
\(\frac{4x5x6}{12x10x8}\)=\(\frac{1x1x1}{2x2x2}\)= \(\frac{1}{8}\)
A =\(\frac{2}{5}\times\frac{4}{7}+\frac{3}{5}\times\frac{4}{7}\) B = \(\frac{17}{13}\times\frac{12}{17}-\frac{4}{13}\times\frac{12}{17}\) C = \(\frac{9}{14}:\frac{6}{7}+\frac{5}{14}:\frac{6}{7}\) D =\(\frac{9}{12}:\frac{7}{9}\times\frac{12}{19}\)
= \(\frac{4}{7}\times\left(\frac{2}{5}+\frac{3}{5}\right)\) =\(\left(\frac{17}{13}-\frac{4}{13}\right)\times\frac{12}{17}\) = \((\frac{9}{14}+\frac{5}{14}):\frac{6}{7}\) = \(\frac{9}{12}\times\frac{9}{7}\times\frac{12}{19}\)
=\(\frac{4}{7}\times1\) = \(1\times\frac{12}{17}\) = \(1:\frac{6}{7}\) = \(\frac{9\times9\times12}{12\times7\times19}\)
=\(\frac{4}{7}\) = \(\frac{12}{17}\) =\(\frac{7}{6}\) = \(\frac{9\times9}{7\times19}=\frac{81}{133}\)
\(a.60\times\left(\frac{7}{12}+\frac{4}{15}\right)\)
\(=60\times\left(\frac{35}{60}+\frac{16}{60}\right)\)
\(=60\times\frac{51}{60}\)
\(=51\)
\(b.\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}\times\frac{8}{9}\)
\(=\frac{1\times2\times3\times4\times5\times6\times7\times8}{2\times3\times4\times5\times6\times7\times8\times9}\)
\(=\frac{1}{9}\)
\(\frac{1}{2}+\frac{2}{4}+\frac{3}{6}+\frac{4}{8}+\frac{5}{10}+\frac{6}{12}\)
\(=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\)
\(=6\times\frac{1}{2}=3\)
a) 8 × 5 × 9 = (8 × 5) × 9 = 40 × 9 = 360
b) 6 × 7 × 5 = (6 × 5) × 7= 30 × 7= 210
c) 6 × 4 × 25 = 6 × (4 × 25) = 6 × 100= 600