Bài tập cuối chương 1

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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)\(\dfrac{100}{123}\):(\(\dfrac{3}{4}\)+\(\dfrac{7}{12}\))+\(\dfrac{23}{123}\):(\(\dfrac{9}{5}\)\(\dfrac{7}{15}\)).


 

Vanh Nek
21 tháng 11 2022 lúc 18:03

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)

\(\dfrac{100}{123}:\left(\dfrac{3}{4}+\dfrac{7}{12}\right)+\dfrac{23}{123}:\left(\dfrac{9}{5}-\dfrac{7}{15}\right)\)

\(=\dfrac{100}{123}:\left(\dfrac{9}{12}+\dfrac{7}{12}\right)+\dfrac{23}{123}:\left(\dfrac{27}{15}-\dfrac{7}{15}\right)\)

\(=\dfrac{100}{123}:\dfrac{4}{3}+\dfrac{23}{123}:\dfrac{4}{3}\)

\(=\dfrac{100}{123}.\dfrac{3}{4}+\dfrac{23}{123}.\dfrac{3}{4}\)

\(=\dfrac{3}{4}.\left(\dfrac{100}{123}+\dfrac{23}{123}\right)\)

\(=\dfrac{3}{4}.1\)

\(=\dfrac{3}{4}\)

animepham
21 tháng 11 2022 lúc 18:16

`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 `

le phong
21 tháng 6 2023 lúc 11:36

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)

le phong
22 tháng 6 2023 lúc 10:36

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