Thực hiện phép tính (bằng cách hợp lí nếu có thể).
a)\(\dfrac{5}{23}\)+\(\dfrac{7}{17}\)+0,25−\(\dfrac{5}{23}\)+\(\dfrac{10}{17}\)
b)\(\dfrac{3}{7}\).2\(\dfrac{2}{3}\)−\(\dfrac{3}{7}\).1\(\dfrac{1}{2}\)
c)\(13\dfrac{1}{4}\):(−\(\dfrac{4}{7}\))−17\(\dfrac{1}{4}\):(−\(\dfrac{4}{7}\));
d)\(\dfrac{100}{123}\):(\(\dfrac{3}{4}\)+\(\dfrac{7}{12}\))+\(\dfrac{23}{123}\):(\(\dfrac{9}{5}\)−\(\dfrac{7}{15}\)).
a)
\(\dfrac{5}{23}+\dfrac{7}{17}+0,25-\dfrac{5}{23}+\dfrac{10}{17}\)
\(=\dfrac{5}{23}+\dfrac{7}{17}+\dfrac{1}{4}-\dfrac{5}{23}+\dfrac{10}{17}\)
\(=\left(\dfrac{5}{23}-\dfrac{5}{23}\right)+\left(\dfrac{7}{17}+\dfrac{10}{17}\right)+\dfrac{1}{4}\)
\(=0+1+\dfrac{1}{4}\)
\(=1+\dfrac{1}{4}\)
\(=\dfrac{5}{4}\)
b)
\(\dfrac{3}{7}.2\dfrac{2}{3}-\dfrac{3}{7}.1\dfrac{1}{2}\)
\(=\dfrac{3}{7}.\dfrac{8}{3}-\dfrac{3}{7}.\dfrac{3}{2}\)
\(=\dfrac{3}{7}.\left(\dfrac{8}{3}-\dfrac{3}{2}\right)\)
\(=\dfrac{3}{7}.\left(\dfrac{16}{6}-\dfrac{9}{6}\right)\)
\(=\dfrac{3}{7}.\dfrac{7}{6}\)
\(=\dfrac{1}{2}\)
c)
\(13\dfrac{1}{4}:\left(-\dfrac{4}{7}\right)-17\dfrac{1}{4}:\left(-\dfrac{4}{7}\right)\)
\(=\dfrac{53}{4}:\left(-\dfrac{4}{7}\right)-\dfrac{69}{4}:\left(-\dfrac{4}{7}\right)\)
\(=\dfrac{53}{4}.\dfrac{-7}{4}-\dfrac{69}{4}.\dfrac{-7}{4}\)
\(=\dfrac{-7}{4}.\left(\dfrac{53}{4}-\dfrac{69}{4}\right)\)
\(=\dfrac{-7}{4}.\left(-4\right)\)
\(=7\)
d)
\(\dfrac{100}{123}:\left(\dfrac{3}{4}+\dfrac{7}{12}\right)+\dfrac{23}{123}:\left(\dfrac{9}{5}-\dfrac{7}{15}\right)\)
\(=\dfrac{100}{123}:\left(\dfrac{9}{12}+\dfrac{7}{12}\right)+\dfrac{23}{123}:\left(\dfrac{27}{15}-\dfrac{7}{15}\right)\)
\(=\dfrac{100}{123}:\dfrac{4}{3}+\dfrac{23}{123}:\dfrac{4}{3}\)
\(=\dfrac{100}{123}.\dfrac{3}{4}+\dfrac{23}{123}.\dfrac{3}{4}\)
\(=\dfrac{3}{4}.\left(\dfrac{100}{123}+\dfrac{23}{123}\right)\)
\(=\dfrac{3}{4}.1\)
\(=\dfrac{3}{4}\)
`a) 5/23 + 7/17 + 0,25 - 5/23 + 10/17 `
`= ( 5/23 - 5/23 ) + ( 7/17 + 10/17 ) + 0,25 `
`= 0 + 17/17 + 1/4 `
`= 1 + 1/4 = 5/4 `
`b) 3/7 . 2 2/3 - 3/7 . 1 1/2 `
`= 3/7 . 8/3 - 3/7 . 3/2 `
`= 3/7 . ( 8/3 - 3/2 )`
`= 3/7 . ( 16/6 - 9/6 ) `
`= 3/7 . 7/6 = 1/2 `
c) `13 1/4 : ( - 4/7 ) - 17 1/4 : ( -4/7 ) `
`= 13 1/4 . ( -7/4 ) - 17 1/4 . ( -7/4 ) `
`= -4/7 . ( 53/4 - 69/4 ) `
`= -4/7 . (-4 ) = 7 . `
d) ` 100/123 : ( 3/4 + 7/12 ) + 23/123 : ( 9/5 - 7/15 ) `
`= 100/23 : ( 9/12 + 7/12 ) + 23/123 : ( 27/15 - 7/15 ) `
`= 100/23 : 4/3 + 23/123 : 4/3 `
`= 100/23 . 3/4 + 23/123 . 3/4 `
`= 3/4 . ( 100/23 + 23/123 ) `
`= 3/4 . 1 = 3/4 `
a)\(\dfrac{5}{23}\)+\(\dfrac{7}{17}\)+0,25-\(\dfrac{5}{23}\)+\(\dfrac{10}{17}\)
=(\(\dfrac{5}{23}\)-\(\dfrac{5}{23}\))+(\(\dfrac{7}{17}\)+\(\dfrac{10}{17}\))+0,25
=0+1+0,25
=1,25
b)
a)\(\dfrac{5}{23}\)+\(\dfrac{7}{17}\)+0,25-\(\dfrac{5}{23}\)+\(\dfrac{10}{17}\)
=(\(\dfrac{5}{23}\)-\(\dfrac{5}{23}\))+(\(\dfrac{7}{17}\)+\(\dfrac{10}{17}\))+0,25
=0+1+0,25
=1,25
b)\(\dfrac{3}{7}\).2\(\dfrac{2}{3}\)-\(\dfrac{3}{7}\).1\(\dfrac{1}{2}\)
=(\(\dfrac{3}{7}\)-\(\dfrac{3}{7}\)).(2\(\dfrac{2}{3}\).\(1\dfrac{1}{2}\))
=0.(2\(\dfrac{2}{3}\).\(1\dfrac{1}{2}\))
=(2\(\dfrac{2}{3}\).\(1\dfrac{1}{2}\))
=\(\dfrac{8}{3}\).\(\dfrac{3}{2}\)
=4