Question

Tính giá trị biểu thức bằng cách hợp lý nhất:

P=\(\dfrac{2}{3}-\left(-\dfrac{1}{4}\right)+\dfrac{3}{5}-\dfrac{7}{45}-\left(-\dfrac{5}{9}\right)+\dfrac{1}{2}+\dfrac{1}{35}\)

Answer 1

\(P=\dfrac{2}{3}-\left(-\dfrac{1}{4}\right)+\dfrac{3}{5}-\dfrac{7}{45}-\left(-\dfrac{5}{9}\right)+\dfrac{1}{2}+\dfrac{1}{35}\)

\(P=\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{3}{5}-\dfrac{7}{45}+\dfrac{5}{9}+\dfrac{1}{2}+\dfrac{1}{35}\)
\(P=\left(\dfrac{1}{2}+\dfrac{1}{4}\right)+\left(\dfrac{-7}{45}+\dfrac{2}{3}+\dfrac{5}{9}\right)+\left(\dfrac{3}{5}+\dfrac{1}{35}\right)\)

\(P=\dfrac{3}{4}+\)\(\dfrac{16}{5}\)\(+\dfrac{22}{35}\)

\(P=\dfrac{641}{140}\)

Answer 2

\(P=\dfrac{2}{3}-\left(-\dfrac{1}{4}\right)+\dfrac{3}{5}-\dfrac{7}{45}-\left(-\dfrac{5}{9}\right)+\dfrac{1}{2}+\dfrac{1}{35}\)

\(P=\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{3}{5}-\dfrac{7}{45}+\dfrac{5}{9}+\dfrac{1}{2}+\dfrac{1}{35}\)

\(P=\left(-\dfrac{7}{45}+\dfrac{2}{3}+\dfrac{5}{9}\right)+\left(\dfrac{1}{35}+\dfrac{3}{5}\right)+\left(\dfrac{1}{4}+\dfrac{1}{2}\right)\)

\(P=\left(-\dfrac{7}{45}+\dfrac{30}{45}+\dfrac{25}{45}\right)+\left(\dfrac{1}{35}+\dfrac{21}{35}\right)+\left(\dfrac{1}{4}+\dfrac{2}{4}\right)\)

\(P=\dfrac{48}{45}+\dfrac{22}{35}+\dfrac{3}{4}\)

\(P=\dfrac{1027}{420}\)