Giải Bài 31 trang 21 sách bài tập toán 7 tập 1 - Cánh diều

Đề bài

Tính giá trị của mỗi biểu thức sau:

a) \(\dfrac{{45}}{4} - \left( {2\dfrac{5}{7} + 5,25} \right)\);

b) \(\dfrac{5}{9}:2,4 - \dfrac{{41}}{9}:2,4\);

c) \(\left( { - \dfrac{3}{4} + \dfrac{5}{{13}}} \right).\dfrac{7}{2} - \left( {\dfrac{9}{4} - \dfrac{8}{{13}}} \right).\dfrac{7}{2}\).

Lời giải chi tiết

a)

\(\begin{array}{l}\dfrac{{45}}{4} - \left( {2\dfrac{5}{7} + 5,25} \right)\\ = \dfrac{{45}}{4} - \left( {\dfrac{{19}}{7} + \dfrac{{525}}{100}} \right) \\= \dfrac{{45}}{4} - \left( {\dfrac{{19}}{7} + \dfrac{{21}}{4}} \right) \\= \dfrac{{45}}{4} - \left( {\dfrac{{76}}{{28}} + \dfrac{{147}}{{28}}} \right)\\ = \dfrac{{45}}{4} - \dfrac{{223}}{{28}}\\ = \dfrac{{315}}{{28}} - \dfrac{{223}}{{28}}\\ = \dfrac{{92}}{{28}}\\ = \dfrac{{23}}{7}\end{array}\)

b)

\(\dfrac{5}{9}:2,4 - \dfrac{{41}}{9}:2,4 \\= \left( {\dfrac{5}{9} - \dfrac{{41}}{9}} \right):2,4 \\= \dfrac{{ - 36}}{9}:\dfrac{{24}}{10} \\= (-4) :\dfrac{{12}}{5} \\= (-4).\dfrac{5}{{12}}\\ = \dfrac{{ - 5}}{3}\)

c)

\(\begin{array}{l}\left( { - \dfrac{3}{4} + \dfrac{5}{{13}}} \right).\dfrac{7}{2} - \left( {\dfrac{9}{4} - \dfrac{8}{{13}}} \right).\dfrac{7}{2}\\ = \left( {\dfrac{{ - 3}}{4} + \dfrac{5}{{13}} - \dfrac{9}{4} + \dfrac{8}{{13}}} \right).\dfrac{7}{2}\\ = \left( {\dfrac{{ - 12}}{4} + \dfrac{{13}}{{13}}} \right).\dfrac{7}{2} \\= \left( { - 3 + 1} \right).\dfrac{7}{2}\\ =  - 2.\dfrac{7}{2}\\ =  - 7\end{array}\)