Bộ 5 đề thi giữa kì 1 Toán 7 Cánh diều cấu trúc mới có đáp án - Đề 2

B. TỰ LUẬN (3,0 điểm)

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(1,5 điểm) Thực hiện phép tính:

a) \(\frac{{13}}{{25}} - \frac{{11}}{4} - \frac{{28}}{{25}} + \frac{{15}}{4}\);

b) \({\left( { - \frac{1}{2}} \right)^2} - \frac{5}{8}:{\left( {0,5} \right)^3} - \frac{5}{3}.\left( { - 6} \right)\);

c) \({\left( {\frac{2}{3} - \frac{1}{6}} \right)^2} + 1\frac{2}{3}.\left| { - 0,25} \right| - 3.\sqrt {\frac{1}{{16}}} \).

 

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Hướng dẫn giải

a) \(\frac{{13}}{{25}} - \frac{{11}}{4} - \frac{{28}}{{25}} + \frac{{15}}{4}\)

\( = \left( {\frac{{13}}{{25}} - \frac{{28}}{{25}}} \right) + \left( {\frac{{15}}{4} - \frac{{11}}{4}} \right)\)

\( = \frac{{ - 15}}{{25}} + \frac{4}{4}\)

\( = \frac{{ - 3}}{5} + 1\)

\( = \frac{2}{5}\).

b) \({\left( { - \frac{1}{2}} \right)^2} - \frac{5}{8}:{\left( {0,5} \right)^3} - \frac{5}{3}.\left( { - 6} \right)\)

\( = \frac{1}{4} - \frac{5}{8}:0,125 + 10\)

\( = \frac{1}{4} - \frac{5}{8}:\frac{1}{8} + 10\)

\( = \frac{1}{4} - \frac{5}{8}.8 + 10\)

\( = \frac{1}{4} - 5 + 10\)

\( = \frac{1}{4} + 5\)

\( = \frac{{21}}{4}\).

c) \({\left( {\frac{2}{3} - \frac{1}{6}} \right)^2} + 1\frac{2}{3}.\left| { - 0,25} \right| - 3.\sqrt {\frac{1}{{16}}} \)

\( = {\left( {\frac{1}{2}} \right)^2} + \frac{5}{3}.0,25 - 3.\sqrt {{{\left( {\frac{1}{4}} \right)}^2}} \)

\( = \frac{1}{4} + \frac{5}{3}.\frac{1}{4} - 3.\frac{1}{4}\)

\( = \frac{1}{4} \cdot \left( {1 + \frac{5}{3} - 3} \right)\)

\( = \frac{1}{4}.\left( {\frac{5}{3} - 2} \right)\)

\( = \frac{1}{4}.\left( { - \frac{1}{3}} \right)\)

\( = - \frac{1}{{12}}.\)