Question

Tính giá trị của các biểu thức sau

a) M= \(2\frac{1}{315}\cdot\frac{1}{651}-\frac{1}{105}\cdot3\frac{650}{651}-\frac{4}{315\cdot651}+\frac{4}{105}\)

b) N= \(2\frac{1}{547}\cdot\frac{3}{211}-\frac{546}{547}\cdot\frac{1}{211}-\frac{4}{547\cdot211}\)

Answer 1

a: \(M=\dfrac{631}{315}\cdot\dfrac{1}{651}-\dfrac{1}{105}\cdot\dfrac{2603}{651}-\dfrac{4}{315\cdot651}+\dfrac{4}{105}\)

\(=\dfrac{1}{315\cdot651}\cdot\left(631-4\right)-\dfrac{1}{105}\left(\dfrac{2603}{651}-4\right)\)

\(=\dfrac{1}{105}\cdot\dfrac{1}{1953}\cdot627+\dfrac{1}{105\cdot651}\)

\(=\dfrac{1}{105\cdot651}\left(\dfrac{1}{3}\cdot627+1\right)=\dfrac{1}{105\cdot651}\cdot210=\dfrac{2}{651}\)

b: \(N=\dfrac{1095}{547}\cdot\dfrac{3}{211}-\dfrac{546}{547\cdot211}-\dfrac{4}{547\cdot211}\)

\(=\dfrac{1}{547\cdot211}\left(1095\cdot3-546-4\right)\)

\(=\dfrac{1}{547\cdot211}\cdot2735=\dfrac{5}{211}\)