Bài 49 trang 51 Vở bài tập toán 6 tập 2

Đề bài

Tính giá trị biểu thức sau một cách hợp lí:

\(A=\dfrac{7}{19}.\dfrac{8}{11}+\dfrac{7}{19}.\dfrac{3}{11}+\dfrac{12}{19}\) ;

\(B= \dfrac{5}{9}.\dfrac{7}{13}+\dfrac{5}{9}.\dfrac{9}{13}-\dfrac{5}{9}.\dfrac{3}{13}\) ;

\(C=\left (\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117} \right )\\.\left (\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{12} \right )\)

Lời giải chi tiết

\(A=\dfrac{7}{19}.\dfrac{8}{11}+\dfrac{7}{19}.\dfrac{3}{11}+\dfrac{12}{19}\)

\(= \dfrac{7}{19}.\left (\dfrac{8}{11}+\dfrac{3}{11} \right )+\dfrac{12}{19}\)

\( = \dfrac{7}{{19}}.\dfrac{{11}}{{11}} + \dfrac{{12}}{{19}}\)

\(=\dfrac{7}{19} +\dfrac{12}{19}=\dfrac{19}{19}=1\).

\(B= \dfrac{5}{9}.\dfrac{7}{13}+\dfrac{5}{9}.\dfrac{9}{13}-\dfrac{5}{9}.\dfrac{3}{13}\)

\(=\dfrac{5}{9}.\left (\dfrac{7}{13}+\dfrac{9}{13}-\dfrac{3}{13} \right )\)

\(=\dfrac{5}{9}.\dfrac{7+9-3}{13}\)\(=\dfrac{5}{9}.\dfrac{13}{13}=\dfrac{5}{9}\)

\(C=\left (\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117} \right )\)\(.\left (\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{12} \right )\)

\(=\left (\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117} \right )\)\(.\left (\dfrac{4}{12}-\dfrac{3}{12}-\dfrac{1}{12} \right )\)

\(=\left (\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117} \right ).0=0\)

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