Đặt mỗi số số hạng của M là A;B

Ta quy đồng tử và mẫu của A bằng cách nhân cả tử và mẫu với 3.7.13;rồi dùng tính chất phân phối bỏ ngoặc ra.Tính toán bình thường.Khi đó A=1/7 

Tương tự với B ta quy đồng lên với 11.17.19;bỏ ngoặc đi và tính bình thường ;B=2/7

=>M=1/7+2/7-136/7=3/7-136/7=-19

\(\frac{7}{13}.\frac{5}{19}+\frac{7}{19}.\frac{8}{13}-\frac{37}{19}=\frac{1}{19}\left(\frac{5.7}{13}+\frac{7.8}{13}-37\right)=\frac{1}{19}\left(\frac{91}{13}-37\right)=\frac{1}{19}.\left(-30\right)=-\frac{30}{19}\)

\(=\frac{4x3x7x\left(-20\right)x\left(-11\right)}{7x5x4x12}=\frac{4x3x7x5x4x11}{7x5x4x3x4}=11\)

$=\frac{4x3x7x\left(-20\right)x\left(-11\right)}{7x5x4x12}=\frac{4x3x7x5x4x11}{7x5x4x3x4}=11$

\(\frac{7}{13}.\frac{5}{19}+\frac{7}{19}.\frac{8}{13}-3\frac{7}{19}\)

\(=\frac{7}{19}.\frac{5}{13}+\frac{7}{19}.\frac{8}{13}-3-\frac{7}{19}\)

\(=\frac{7}{19}\left(\frac{5}{13}+\frac{8}{13}\right)-3-\frac{7}{19}\)

\(=\frac{7}{19}-3-\frac{7}{19}\)

\(=-3\)

\(\frac{7}{13}.\frac{5}{19}+\frac{7}{19}.\frac{8}{13}-3\frac{7}{19}\)  

=\(\frac{7}{19}.\frac{5}{13}+\frac{7}{19}.\frac{8}{13}-3-\frac{7}{19}\)

= \(\frac{7}{19}.\left(\frac{5}{13}+\frac{8}{13}\right)-3-\frac{7}{19}\)

= \(\frac{7}{19}-3-\frac{7}{19}\) =  \(-3\)

a) \(-\frac{1}{4}.13\frac{9}{11}-0,25.6\frac{2}{11}\)

\(=-\frac{1}{4}.13\frac{9}{11}-\frac{1}{4}.6\frac{2}{11}\)

\(=-\frac{1}{4}\left(13\frac{9}{11}+6\frac{2}{11}\right)\)

\(=-\frac{1}{4}.20\)

\(=-5\)

b) \(B=\frac{-5}{6}.\frac{4}{19}+\frac{-7}{12}.\frac{4}{19}-\frac{40}{57}\)

\(=\frac{4}{19}\left(\frac{-5}{6}+\frac{-7}{12}\right)-\frac{40}{57}\)

\(=\frac{4}{19}.\frac{-17}{12}-\frac{40}{57}\)

\(=\frac{-17}{57}-\frac{40}{57}\)

\(=-1\)

c)  \(\frac{3}{7}.\frac{9}{26}-\frac{1}{14}.\frac{1}{13}-\frac{1}{7}\)

\(=\frac{3}{7}.\frac{9}{26}-\frac{1}{2}.\frac{1}{7}.\frac{1}{13}-\frac{1}{7}\)

\(=\frac{1}{7}\left(3.\frac{9}{26}-\frac{1}{2}.\frac{1}{13}-1\right)\)

\(=\frac{1}{7}.0\)

\(=0\)

d) \(\frac{4}{9}:\left(-\frac{1}{7}\right)+6\frac{5}{9}:\left(-\frac{1}{7}\right)\)

\(=\left(\frac{4}{9}+6\frac{5}{9}\right):\left(-\frac{1}{7}\right)\)

\(=7:\left(-\frac{1}{7}\right)\)

\(=-49\)

\(A=-\frac{1}{4}x3\frac{9}{11}-0,25x6\frac{2}{11}\)

\(A=-0,25x3\frac{9}{11}-0,25x6\frac{2}{11}\)

\(A=-0,25x\left(\frac{9}{11}+\frac{2}{11}\right)\)

\(A=-0,25x1\)

\(A=-0,25\)

\(B=-\frac{5}{6}x\frac{4}{19}+-\frac{7}{12}x\frac{4}{19}-\frac{40}{57}\)

\(B=-\frac{5}{6}x\frac{4}{19}+-\frac{7}{12}x\frac{4}{19}-\frac{4}{19}x190\)

\(B=\frac{4}{19}x\left(-\frac{5}{6}-\frac{7}{12}-190\right)\)

\(B=\frac{4}{19}x\left(-\frac{2297}{12}\right)\)

\(B=\frac{-2297}{57}\)

\(C=\frac{3}{7}x\frac{9}{26}-\frac{1}{14}x\frac{1}{13}-\frac{1}{7}\)

\(C=\frac{1}{7}x3x\frac{9}{26}-\frac{1}{7}x\frac{1}{2}x\frac{1}{13}-\frac{1}{7}\)

\(C=\frac{1}{7}x\left(3x\frac{9}{26}-\frac{1}{2}x\frac{1}{13}-1\right)\)

\(C=\frac{1}{7}x0\)

\(C=\frac{1}{7}\)

\(D=\frac{4}{9}:\left(-\frac{1}{7}\right)+6\frac{5}{9}:\left(-\frac{1}{7}\right)\)

\(D=\left(\frac{4}{9}+6\frac{5}{9}\right):\left(-\frac{1}{7}\right)\)

\(D=7:\left(-\frac{1}{7}\right)\)

\(D=-49\)

a) A = \(\frac{101}{19}.\) \(\frac{61}{218}-\frac{101}{218}.\frac{42}{19}+\frac{117}{218}\)

        = \(\frac{101}{218}.\frac{61}{19}-\frac{101}{218}.\frac{42}{19}+\frac{117}{218}\)

        =\(\frac{101}{218}.\left(\frac{61}{19}-\frac{42}{19}\right)+\frac{117}{218}\)

        =\(\frac{101}{218}.\frac{19}{19}+\frac{117}{218}\)

        =\(\frac{101}{218}.1+\frac{117}{218}\)

        =\(\frac{101}{218}+\frac{117}{218}\)

        =\(\frac{218}{218}\)\(=1\)

b) B = \(\left(\frac{5}{2011^2}+\frac{7}{2012^2}-\frac{9}{2013^2}\right).\left(\frac{4}{5}-\frac{3}{4}-\frac{1}{20}\right)\)

        =     \(\left(\frac{5}{2011^2}+\frac{7}{2012^2}-\frac{9}{2013^2}\right)\)\(.\left(\frac{1}{20}-\frac{1}{20}\right)\)

        = \(\left(\frac{5}{2011^2}+\frac{7}{2012^2}-\frac{9}{2013^2}\right).0\)

        = \(0\)

\(\frac{-3}{5}.\left(\frac{5}{7}+\frac{3}{7}+\frac{6}{7}\right)\)

=\(\frac{-3}{5}.\)\(\frac{14}{7}\)

=\(-\frac{3}{5}.2\)

=-6/5

=( 19/13+7/13) + ( 17/9+1/9) + ( 7/3 + 2/3)

= 26/13 + 18/9 + 9/3

= 2 + 2+3

= 7