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Phương pháp giải:

Trừ nhẩm các số rồi điền kết quả thích hợp vào chỗ trống.

Lời giải chi tiết:

13 − 9 = 4            13 − 8 = 5

13 − 5 = 8            13 − 6 = 7

13 − 4 = 9            13 − 7 = 6

13 − 3 − 2 = 8      13 − 5 = 8

\(1,-\dfrac{4}{7}+\dfrac{2}{3}\times\dfrac{-9}{14}\)

\(=\dfrac{-4}{7}+\dfrac{-18}{42}\)

\(=\dfrac{-4\times6}{7\times6}+\dfrac{-18}{42}\)

\(=\dfrac{-20}{42}+\dfrac{-18}{42}\)

\(=-\dfrac{38}{42}\)

\(=-\dfrac{19}{21}\)

\(2,\dfrac{17}{13}-\left(\dfrac{4}{13}-11\right)\)

\(=\dfrac{17}{13}-\dfrac{4}{13}+11\)

\(=\dfrac{13}{13}+11\)

\(=1+11\)

\(=12\)

\(3,8\dfrac{2}{7}-\left(3\dfrac{4}{9}+4\dfrac{2}{7}\right)\)

\(=\dfrac{58}{7}-\left(\dfrac{31}{9}+\dfrac{30}{7}\right)\)

\(=\dfrac{58}{7}-\dfrac{31}{9}-\dfrac{30}{7}\)

\(=\dfrac{58}{7}-\dfrac{30}{7}-\dfrac{31}{9}\)

\(=\dfrac{28}{7}-\dfrac{31}{9}\)

\(=\dfrac{28\times9}{7\times9}-\dfrac{31\times7}{9\times7}\)

\(=\dfrac{252}{63}-\dfrac{217}{63}\)

\(=\dfrac{35}{63}\)

\(=\dfrac{5}{9}\)

\(5,\left(\dfrac{2}{3}-1\dfrac{1}{2}\right):\dfrac{4}{3}+\dfrac{1}{2}\)

\(=\left(\dfrac{2}{3}-\dfrac{3}{2}\right):\dfrac{4}{3}+\dfrac{1}{2}\)

\(=\left(\dfrac{2\times2}{3\times2}-\dfrac{3\times3}{2\times3}\right):\dfrac{4}{3}+\dfrac{1}{2}\)

\(=\left(\dfrac{4}{6}-\dfrac{9}{6}\right):\dfrac{4}{3}+\dfrac{1}{2}\)

\(=\dfrac{-5}{6}:\dfrac{4}{3}+\dfrac{1}{2}\)

\(=\dfrac{-5}{6}\times\dfrac{3}{4}+\dfrac{1}{2}\)

\(=\dfrac{-15}{24}+\dfrac{1}{2}\)

\(=\dfrac{-15}{24}+\dfrac{1\times12}{2\times12}\)

\(=\dfrac{-15}{24}+\dfrac{12}{24}\)

\(=\dfrac{-3}{24}\)

\(=-\dfrac{1}{8}\)

\(6,\dfrac{-5}{13}+\dfrac{2}{5}+\dfrac{-8}{13}+\dfrac{3}{5}-\dfrac{3}{7}\)

\(=\left(\dfrac{-5}{13}+\dfrac{-8}{13}\right)+\left(\dfrac{2}{5}+\dfrac{3}{5}\right)-\dfrac{3}{7}\)

\(=\dfrac{-13}{13}+\dfrac{5}{5}-\dfrac{3}{7}\)

\(=-1+1-\dfrac{3}{7}\)

\(=-\dfrac{3}{7}\)

\(7,\dfrac{6}{5}\times\dfrac{3}{7}+\dfrac{6}{5}:\dfrac{7}{10}+\dfrac{6}{5}\)

\(=\dfrac{6}{5}\times\dfrac{3}{7}+\dfrac{6}{5}\times\dfrac{10}{7}+\dfrac{6}{5}\)

\(=\dfrac{6}{5}\times\left(\dfrac{3}{7}+\dfrac{10}{7}+1\right)\)

\(=\dfrac{6}{5}\times\left(\dfrac{3}{7}+\dfrac{10}{7}+\dfrac{1\times7}{1\times7}\right)\)

\(=\dfrac{6}{5}\times\left(\dfrac{3}{7}+\dfrac{10}{7}+\dfrac{7}{7}\right)\)

\(=\dfrac{6}{5}\times\dfrac{20}{7}\)

\(=\dfrac{120}{35}\)

\(=\dfrac{24}{7}\)

a) (x-9,25.4) : (x-9,25.4) = 1

=> x-9,5.4 = x-9,25.4 = 1

=> x-9,25.4 = 1

x-9,25 = 1:4

x-9,25 = 0,25

x = 0,25 + 9,25

x = 9,5

b) 42-36:[2.(2.x+1)+4] = 40

36:[2.(2.x+1)+4] = 42 - 40

36:[2.(2.x+1)+4] = 2

2.(2.x+1)+4 = 36 : 2

2.(2.x+1)+4 = 18

2.(2x+1) = 18 - 4

2.(2x+1) = 14

2x+1 = 14 : 2

2x+1 = 7

2x = 7 - 1

2x = 6

x = 6 : 2

x = 3

=>125(3x+2):13=1000:13

=>125(3x+2)=1000

=>3x+2=8

=>x=2

`@` `\text {Ans}`

`\downarrow`

`a.`

`A=(1/2-7/13-1/3)+(-6/13+1/2+1 1/3)`

`= 1/2 - 7/13 - 1/3 - 6/13 + 1/2 + 1 1/3`

`= (1/2 + 1/2) + (-7/13 - 6/13) + (-1/3 + 1 1/3) `

`= 1 - 1 + 1`

`= 1`

`b.`

`B=0,75+2/5+(1/9-1 1/2+5/4)`

`= 3/4 + 2/5 + 1/9 - 3/2 + 5/4`

`= (3/4+5/4)+ 1/9 + 2/5 - 3/2`

`= 2 + 1/9 - 11/10`

`= 19/9 - 11/10`

`= 91/90`

`c.`

`(-5/9).3/11+(-13/18).3/11`

`= 3/11*[(-5/9) + (-13/18)]`

`= 3/11*(-23/18)`

`= -23/66`

`d.`

`(-2/3).3/11+(-16/9).3/11`

`= 3/11* [(-2/3) + (-16/9)]`

`= 3/11*(-22/9)`

`= -2/3`

`e.`

`(-1/4).(-2/13)-7/24.(-2/13)`

`= (-2/13)*(-1/4-7/24)`

`= (-2/13)*(-13/24)`

`= 1/12`

`f.`

`(-1/27).3/7+(5/9).(-3/7)`

`= 3/7*(-1/27 - 5/9)`

`= 3/7*(-16/27)`

`= -16/63`

`g.`

`(-1/5+3/7):2/11+(-4/5+4/7):2/11`

`=[(-1/5+3/7)+(-4/5+4/7)] \div 2/11`

`= (-1/5+3/7 - 4/5 + 4/7) \div 2/11`

`= [(-1/5-4/5)+(3/7+4/7)] \div 2/11`

`= (-1+1) \div 2/11`

`= 0 \div 2/11 = 0`

\(5^3\left(3x+2\right)\div13=10^3\div\left(13^5\div13^4\right)\)

\(\Rightarrow125\left(3x+2\right)\div13=1000\div13\)

\(\Rightarrow125\left(3x+2\right)=1000\)

\(\Rightarrow3x+2=1000\div125\)

\(\Rightarrow3x+2=8\)

\(\Rightarrow3x=8-2\)

\(\Rightarrow3x=6\Rightarrow x=6\div3\Rightarrow x=2\)

Vậy : x = 2

 2/2023 / 4/3 ?

A = \(\dfrac{\dfrac{2}{3}-\dfrac{2}{13}+\dfrac{2}{2023}}{\dfrac{4}{3}-\dfrac{4}{13}+\dfrac{4}{2023}}\)

A = \(\dfrac{2.\left(\dfrac{1}{3}-\dfrac{1}{13}+\dfrac{1}{2023}\right)}{4.\left(\dfrac{1}{3}-\dfrac{1}{13}+\dfrac{1}{2023}\right)}\)

A = \(\dfrac{1}{2}\)

a: =-5/9-4/9+8/15+7/15-2/11=-2/11

b: =10/17+7/17-5/13-8/13+11/25

=11/25

c: =(9/12-2/12)*3/2=7/12*3/2=21/24=7/8

d: =(31/10-25/10)*3-2

=3/5*3-2

=9/5-2

=-1/5

A=(13+13²)+(13³+13⁴)+.......................+(13⁹⁹+13¹⁰⁰)

A=1.(13+13²)+13².(13+13²)+..............+13⁹⁸.(13+13²)

A=1.182+13².182+..........................+13⁹⁸.182

A+182.(1+13²+..............+13⁹⁸) Chia hết cho 182

--> A chia hết cho 182