Tính một cách hợp lí:
\(\begin{array}{l}a)A = \frac{{10}}{{11}} + \frac{1}{{11}}.\frac{3}{{11}} + \frac{1}{{11}}.\frac{8}{{11}}\\b)B = \frac{5}{7}.\frac{{40}}{{11}} - \frac{5}{11}.\frac{{117}}{7}\end{array}\)
Sử dụng tính chất phân phối giữa phép nhân với phép cộng và trừ:
a.b - a.c = a.(b-c)
\(\begin{array}{l}a)A = \frac{{10}}{{11}} + \frac{1}{{11}}.\frac{3}{{11}} + \frac{1}{{11}}.\frac{8}{{11}}\\ = \frac{{10}}{{11}} + \frac{1}{{11}}.(\frac{3}{{11}} + \frac{8}{{11}})\\ = \frac{{10}}{{11}} + \frac{1}{{11}}.\frac{{11}}{{11}}\\ = \frac{{10}}{{11}} + \frac{1}{{11}}.1\\= \frac{{10}}{{11}} + \frac{1}{{11}}\\ = \frac{{11}}{{11}}\\ = 1\\b)B = \frac{5}{7}.\frac{{40}}{{11}} - \frac{5}{11}.\frac{{117}}{7}\\ = \frac{5}{7}.\frac{{40}}{{11}} - \frac{5}{7}.\frac{{117}}{11}\\ = \frac{5}{7}.(\frac{{40}}{{11}} - \frac{{117}}{{11}})\\ = \frac{5}{7}.\frac{{ - 77}}{{11}}\\ = \frac{{5}}{{7}}. (-7)\\= ( - 5)\end{array}\)