Đề bài

1) Thực hiện phép tính:

a) \(\frac{1}{4} + \frac{3}{4} \cdot \left( {\frac{2}{3} - 0,5} \right)\)

b) \(1\frac{3}{{25}} - \frac{{17}}{{19}} - \frac{3}{{25}} + \frac{{2022}}{{2023}} - \frac{2}{{19}}\)

2) Tìm \(x\) biết:

a) \(\frac{2}{3}x - \frac{1}{2} = \frac{1}{{10}}\)

b) \(5,16 - 2x = (5,7 + 2,3) \cdot ( - 0,3)\)

Phương pháp giải

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Lời giải của GV Loigiaihay.com

1)

a) \(\frac{1}{4} + \frac{3}{4} \cdot \left( {\frac{2}{3} - 0,5} \right)\)\( = \frac{1}{4} + \frac{3}{4} \cdot \left( {\frac{2}{3} - \frac{1}{2}} \right)\)\( = \frac{1}{4} + \frac{3}{4} \cdot \frac{1}{6}\)\( = \frac{1}{4} + \frac{1}{8}\)\( = \frac{3}{8}\)

b) \(1\frac{3}{{25}} - \frac{{17}}{{19}} - \frac{3}{{25}} + \frac{{2022}}{{2023}} - \frac{2}{{19}}\)\( = \left( {1\frac{3}{{25}} - \frac{3}{{25}}} \right) + \left( {\frac{{ - 17}}{{19}} + \frac{{ - 2}}{{19}}} \right) + \frac{{2022}}{{2023}}\) \( = 1 + ( - 1) + \frac{{2022}}{{2023}}\) \( = \frac{{2022}}{{2023}}.\)

2)

a) \(\frac{2}{3}x - \frac{1}{2} = \frac{1}{{10}}\)

\(\frac{2}{3}x = \frac{1}{{10}} + \frac{1}{2}\)

\(\frac{2}{3}x = \frac{3}{5}\)

\(x = \frac{3}{5}:\frac{2}{3}\)

\(x = \frac{3}{5}.\frac{3}{2}\)

\(x = \frac{9}{{10}}\)

Vậy \(x = \frac{9}{{10}}\).

b) \(5,16 - 2x = (5,7 + 2,3) \cdot ( - 0,3)\)

\(5,16 - 2x =  - 2,4\)

\(2x = 5,16 - ( - 2,4)\)

\(2x = 7,56\)

\(x = 7,56:2\)

\(x = 3,78\)

Vậy \(x = 3,78\)