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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) 145 + 86 + 14 + 55 = ( 145 + 55 ) + (86 + 14 )
= 200 + 100
= 300
b) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = ( 1+9 +2 + 8) + ( 3 + 7 + 4 + 6 ) + 5
= 20 + 20 + 5
= 45
3 x 7/10 + 7/10 x 5 + 2 x 14/20
=3x7/10+7/10x5+2x7/10
=7/10x(3+5+2)
=7/10x10
=7
10/7+9/27+8/14+5/3
=10/7+1/3+4/7+5/3
=(10/7+4/7)+(1/3+5/3)
=14/7+6/3
=2+2
=4
\(\frac{1}{2}\cdot\frac{18}{14}+\frac{1}{2}\cdot\frac{3}{14}-\frac{1}{2}\cdot\frac{7}{14}\)
\(=\frac{1}{2}\left(\frac{18}{14}+\frac{3}{14}-\frac{7}{14}\right)\)
\(=\frac{1}{2}\cdot1=\frac{1}{2}\)
\(\dfrac{9}{14}\cdot\dfrac{3}{7}+\dfrac{3}{7}+\dfrac{5}{14}-\dfrac{2}{7}\)
\(=\dfrac{3}{7}\left(\dfrac{9}{14}+1\right)+\dfrac{5}{14}-\dfrac{4}{14}\)
\(=\dfrac{3}{7}\cdot\dfrac{23}{14}+\dfrac{1}{14}\)
\(=\dfrac{69}{98}+\dfrac{7}{98}=\dfrac{76}{98}=\dfrac{38}{49}\)