Bài 41 trang 23 SGK Toán 7 tập 1

Đề bài

Tính:

a) \(\left( {1 + \frac{2}{3} - \frac{1}{4}} \right).{\left( {\frac{4}{5} - \frac{3}{4}} \right)^2}\)

b) \(2:{\left( {\frac{1}{2} - \frac{2}{3}} \right)^3}\)

Hướng dẫn giải

a)

\(\begin{array}{l}
\left( {1 + \frac{2}{3} - \frac{1}{4}} \right).{\left( {\frac{4}{5} - \frac{3}{4}} \right)^2} \\= \left( {\frac{{12}}{{12}} + \frac{8}{{12}} - \frac{3}{{12}}} \right).{\left( {\frac{{16}}{{20}} - \frac{{15}}{{20}}} \right)^2}\\
 = \frac{{17}}{{12}}.{\left( {\frac{1}{{20}}} \right)^2} =\frac{{17}}{{12}}.\frac{{{1^2}}}{{{{20}^2}}}\\ = \frac{{17}}{{12}}.\frac{1}{{400}} = \frac{{17}}{{4800}}
\end{array}\)

b)   \(2:{\left( {\frac{1}{2} - \frac{2}{3}} \right)^3} = 2:{\left( {\frac{3}{6} - \frac{4}{6}} \right)^3}\)

\(= 2:{\left( { - \frac{1}{6}} \right)^3} = 2:\left( { - \frac{1}{{216}}} \right) \)

\(=  - 2.216 =  - 432\)