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76. Tính giá trị biểu thức sau một cách hợp lí:
\(A=\frac{7}{19}.\frac{8}{11}+\frac{7}{19}.\frac{3}{11}+\frac{12}{19}\) ;
\(B= \frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}\) ;
\(C=\left (\frac{67}{111}+\frac{2}{33}-\frac{15}{117} \right ).\left (\frac{1}{3}-\frac{1}{4}-\frac{1}{12} \right )\).
Hướng dẫn giải.
\(A= \frac{7}{19}.\left (\frac{8}{11}+\frac{3}{11} \right )+\frac{12}{19}=\frac{7}{19}.1 +\frac{12}{19}=1\).
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\(B=\frac{5}{9}.\left (\frac{7}{13}+\frac{9}{13}-\frac{3}{13} \right )=\frac{5}{9}.\frac{7+9-3}{13}=\frac{5}{9}.\frac{13}{13}=\frac{5}{9}.\)
\(C=\left (\frac{67}{111}+\frac{2}{33}-\frac{15}{117} \right ).\left (\frac{1}{3}-\frac{1}{4}-\frac{1}{12} \right )\)
\(=\left (\frac{67}{111}+\frac{2}{33}-\frac{15}{117} \right ).\frac{4-3-1}{12}=\left (\frac{67}{111}+\frac{2}{33}-\frac{15}{117} \right ).0=0\)