Câu 1 tính hợp lí

a,A=\(\frac{-9}{11}.\frac{3}{8}-\frac{9}{11}.\frac{5}{8}+\frac{17}{11}\)

b,B=\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{53.55}\)

Câu2 tìm x

a,\(x+5-\frac{1}{2}=3\frac{1}{2}\)

b,\(3^{x+1}=27\)

c,\(2016.\left[25-\left(3x+2\right)\right]=3^2.7\)

d,\(\frac{x}{6}+\frac{x}{10}+\frac{x}{15}+\frac{x}{21}+\frac{x}{28}+\frac{x}{36}+\frac{x}{45}+\frac{x}{60}+\frac{x}{78}=\frac{220}{39}\)

Ai giải nhanh tớ tick cho

Thank you

Bài 1 : Tính hợp lý 

a ) \(\frac{5}{7}.\frac{15}{11}+\frac{5}{7}.\frac{2}{11}-\frac{5}{7}.\frac{10}{11}\)

b) \(\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}.\frac{25}{4.6}.\frac{36}{5.7}\)

c) \(6\frac{4}{11}+\frac{8}{72}-\left(3\frac{8}{22}+\frac{1}{9}\right)\)

Bài 2 : tìm x 

a) 288 : ( 0,5 \(x\) - \(\frac{1}{3}\) ) - 1,8 = 10,2 

b) \(3\frac{1}{2}\)\(x\)- \(\frac{x}{2}+x\)= 3,5 : \(1\frac{1}{5}\)

c) \(\left(x-\frac{3}{1.2}\right)+\left(x-\frac{3}{2.3}\right)+...+\left(x-\frac{3}{99.100}\right)=1\)

Bài 3 : Hai vòi nước cùng chảy vào một bể . Vòi I chảy trong 10 h thì đầy bể . Vòi II chảy trong 6h thì đầy bể . 

a) Hỏi cả hai vòi cùng chảy vào bể thì sau bao lâu sẽ đầy bể 

b) Nếu có một vòi tháo ra trong 60h thì cạn một bể đầy nước . Vậy khi mở đồng thời cả 3 vòi thì sau bao lâu đầy bể ?

Bài 4 : So sánh \(A=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}vàB=\frac{1}{2}\)

Kiểm tra bài : Nhân, chia số hữu tỉ

Thực hiện phép tính :

(1) \(-\frac{3}{2}.\frac{7}{10}=\frac{-3.7}{2.10}=\frac{-21}{20}\)

(2) \(\frac{-5}{3}.\frac{6}{11}=\frac{-5.6}{3.11}=\frac{-30}{33}\)

(3) \(2\frac{1}{3}.\left(-1\frac{2}{3}\right)=\frac{7}{3}.\left(-\frac{5}{3}\right)=\frac{7.\left(-5\right)}{3.3}=-\frac{35}{9}\)

(4) \(\frac{9}{10}:\left(-\frac{15}{11}\right)=\frac{9}{10}.\left(\frac{-11}{15}\right)=\frac{9.\left(-11\right)}{10.15}=-\frac{99}{150}=-\frac{33}{50}\)

(5) \(\left(-1\right):\frac{3}{8}=\frac{\left(-1\right).8}{3}=-\frac{8}{3}\)

(6) \(\frac{1}{2}.\left(-\frac{5}{4}\right).\frac{8}{7}=\frac{1.\left(-5\right)}{2.4}.\frac{8}{7}=-\frac{5}{8}.\frac{8}{7}=-\frac{5.8}{8.7}=-\frac{5}{7}\)

(7) \(\frac{-9}{2}.\frac{2}{18}.\frac{1}{7}=\left(-\frac{9}{2}.\frac{2}{18}\right).\frac{1}{7}=\left(-\frac{9.2}{2.18}\right).\frac{1}{7}=-\frac{18}{36}.\frac{1}{7}=-\frac{18.1}{36.7}=-\frac{1}{14}\)

(8) \(\left(\frac{9}{2}-\frac{1}{3}\right).\frac{6}{17}=\left(\frac{27}{6}-\frac{2}{6}\right).\frac{6}{17}=\frac{27-2}{6}.\frac{6}{17}=\frac{25}{6}.\frac{6}{17}=\frac{25.6}{6.17}=\frac{25}{17}\)

(9) \(\left(-\frac{12}{13}:\frac{36}{39}\right).\frac{3}{5}=\left(-\frac{12}{13}.\frac{39}{36}\right).\frac{3}{5}=\left(\frac{-12.39}{13.36}\right).\frac{3}{5}=-\frac{1.3}{5}=-\frac{3}{5}\)

(10) \(\left(-\frac{3}{7}+\frac{7}{9}\right):\frac{4}{7}+\left(-\frac{4}{7}+\frac{2}{9}\right):\frac{4}{7}=\left(\left(-\frac{3}{7}+\frac{7}{9}\right)+\left(-\frac{4}{7}+\frac{2}{9}\right)\right):\frac{4}{7}\)

\(=\left(\left(-\frac{27}{63}+\frac{49}{63}\right)+\left(-\frac{36}{63}+\frac{14}{63}\right)\right):\frac{4}{7}=\left(\left(-\frac{27+49}{63}\right)+\left(\frac{-36+14}{63}\right)\right):\frac{4}{7}\)

\(=\left(\left(\frac{22}{63}\right)+\left(-\frac{22}{63}\right)\right):\frac{4}{7}\)

\(=\frac{22+\left(-22\right)}{63}:\frac{4}{7}=\frac{0}{63}:\frac{4}{7}=0\)

Mình đăng các bài toán này lên thứ nhất là để kiểm tra năng lực thứ hai các bạn có thể xem đây và rút ra lời giải cho các bài khác và nếu mình sai chỗ nào các bạn chỉ mình sẽ chỉnh

bài 1 thực hiện phép tính, tính nhanh nếu có thể

a, \(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}\)

b,\(0,75.1\frac{7}{9}-1\frac{2}{5}:\frac{-21}{20}\)

c,\(2.\frac{3}{7}+\left(\frac{2}{9}-1\frac{3}{7}\right)-\frac{5}{3}:\frac{1}{9}\)

d,\(11\frac{1}{4}-\left(2\frac{5}{7}+5\frac{1}{4}\right)\)

e,\(\left(6-2\frac{4}{5}\right).3\frac{1}{8}-1\frac{3}{5}:25\%\)

g,\(0,2.\frac{15}{36}-\left(\frac{2}{5}+\frac{2}{3}\right):1\frac{1}{5}\)

h,\(2\frac{1}{3}-\frac{1}{3}.\left(\frac{-3}{2}+\left(\frac{2}{3}+0,4.5\right)\right)\)

i,\(\frac{1}{3}.\frac{5}{7}-\frac{7}{27}.\frac{36}{14}\)

k,\(\left(\frac{-5}{28}+1,75+\frac{8}{35}\right):\left(-3\frac{9}{20}\right)\)

l,\(\left(20+9\frac{1}{4}\right):2\frac{1}{4}\)

m,\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{12.13}\)

n,\(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{99.101}\)

Bài 1: Tính hợp lí (nếu có thể) Bài 2:Tìm x biết

a, \(\left(4\frac{2}{3}-1\frac{1}{6}\right):\left(1,75+1\frac{1}{2}\right)\) a, \(\frac{4}{9}+x=\frac{-5}{3}\)

b, \(\frac{11}{53}+\left(\frac{32}{47}+\frac{-10}{53}\right)+\frac{-64}{94}+\frac{1}{-53}+\frac{1}{3}\) b, 2,4:\(\left(\frac{1}{2}.x-\frac{3}{4}\right)=\frac{3}{10}\)

c, 125% -7\(\frac{1}{2}+0,5:\frac{4}{3}\) c, \(\frac{x+1}{-8}=\frac{-2}{x+1}\)

d, 1\(\frac{1}{20}.\left(\frac{-2}{3}\right)^2+\left(0,8-\frac{8}{15}\right):\frac{-4}{17}\) d, \(\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\right)-x=\frac{-100}{99}\)

Bài 1 thực hiện phép tính 

a)\(\frac{45}{19}-\left(\frac{1}{2}+\left(\frac{1}{3}+\left(\frac{1}{4}\right)^{-1}\right)^{-1}\right)^{-1}.\)

b) \(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^{10}.6^{19}-7.2^{29}.27^6}.\)

Bài 2. tìm x, biết:

 a) 2(x-1) - 3(2x+2) - 4(2x+3) =16

 b) \(3\frac{1}{2}:\left|2x-1\right|=\frac{21}{22}\)

 c)  |x²+|x-1|| = x²+2

Bài 3. Chứng minh rằng số có dạng abcabc luôn chia hết cho 11

Bài 4.tính:

a)   A = \(\left(\frac{0,4-\frac{2}{9}+\frac{2}{11}}{1,4-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-0,25+\frac{1}{5}}{1\frac{1}{6}-0,875+0,7}\right):\frac{2012}{2013}\)

b)   B =\(4.\left(-\frac{1}{2}\right)^2-2.\left(-\frac{1}{2}\right)^2+3.\left(-\frac{1}{2}\right)+1\)

c)   C =\(\frac{1}{2}:\left(-1\frac{1}{2}\right):1\frac{1}{3}:\left(-1\frac{1}{4}\right):1\frac{1}{5}:\left(-1\frac{1}{6}\right):...:\left(-1\frac{1}{100}\right)\)

d)   D =\(\frac{4^6.9^5+6^9.120}{-8^4.3^{12}+6^{11}}\)

Tính giá trị biểu thức :

1. \(A=\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{9}-\frac{4}{11}}\) 

2. \(B=\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.\frac{4^2}{4.5}\)

3. \(C=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.\frac{5^2}{4.6}\)

4. \(D=(\frac {150}{1111}+\frac{5}{75}-\frac{14}{77})(\frac{1}{5}-\frac{1}{6}-\frac{1}{30}) \)

5. Cho \(M=8\frac{2}{7}-\left(3\frac{4}{9}+3\frac{9}{7}\right);N=\left(10\frac{2}{9}+2\frac{3}{5}\right)-6\frac{2}{9}\). Tính \(P=M-N\)

6. \(E=10101\left(\frac{5}{111111}+\frac{5}{222222}-\frac{4}{3.7.11.13.37}\right)\)

7. \(F=\frac{\frac{1}{3}+\frac{1}{7}-\frac{1}{13}}{\frac{2}{3}+\frac{2}{7}-\frac{2}{13}}.\frac{\frac{3}{4}-\frac{3}{16}-\frac{3}{256}+\frac{3}{64}}{1-\frac{1}{4}+\frac{1}{16}-\frac{1}{64}}+\frac{5}{8}\)

8. \(G=\left[\frac{\left(6-4\frac{1}{2}\right):0,03}{\left(3\frac{1}{20}-2,65\right).4+\frac{2}{5}}-\frac{\left(0,3-\frac{3}{20}\right).1\frac{1}{2}}{\left(1,88+2\frac{3}{25}\right).\frac{1}{80}}\right]:\frac{49}{60}\)

9. \(H=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{4.5.6}+...+\frac{1}{98.99.100}\)

10. \(I=\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.....\frac{2499}{2500}\)

11. \(k=\left(-1\frac{1}{2}\right)\left(-1\frac{1}{3}\right)\left(-1\frac{1}{4}\right)...\left(-1\frac{1}{999}\right)\)

12. \(L=1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}...\)(98 thừa số)

13. \(M=-2+\frac{1}{-2+\frac{1}{-2+\frac{1}{-2+\frac{1}{3}}}}\)

14. \(N=\frac{155-\frac{10}{7}-\frac{5}{11}+\frac{5}{23}}{403-\frac{26}{7}-\frac{13}{11}+\frac{13}{23}}\)

15. \(P=\left(\frac{1}{4}-1\right)\left(\frac{1}{5}-1\right)...\left(\frac{1}{2000}-1\right)\left(\frac{1}{2001}-1\right)\)

16. \(Q=\left(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{2005.2006}\right):\left(\frac{1}{1004.2006}+\frac{1}{1005.2005}+...+\frac{1}{2006.1004}\right)\)