\(a)9+\frac{24}{25}=\frac{9\cdot25+24}{25}=\frac{249}{25}\)

\(b)\frac{1}{20}+\frac{1}{4}+\frac{2}{5}=\frac{1}{20}+\frac{5}{20}+\frac{8}{20}=\frac{1+5+8}{20}=\frac{14}{20}=\frac{7}{10}\)

\(c)\frac{7}{12}+4=\frac{7}{12}+\frac{4}{1}=\frac{7+48}{12}=\frac{55}{12}\)

\(d)10+\frac{9}{8}=\frac{10}{1}+\frac{9}{8}=\frac{80+9}{8}=\frac{89}{8}\)

\(e)\frac{1}{4}+\frac{2}{25}+\frac{9}{100}=\frac{25}{100}+\frac{8}{100}+\frac{9}{100}=\frac{25+8+9}{100}=\frac{42}{100}=\frac{21}{50}\)

Còn 3 câu làm tương tự

Ba câu còn lại mình làm luôn :D

\(f)\frac{28}{90}+6=\frac{14}{45}+6=\frac{14}{45}+\frac{6}{1}=\frac{14+270}{45}=\frac{284}{45}\)

\(g)\frac{3}{7}+\frac{4}{9}+\frac{4}{7}+\frac{7}{11}=(\frac{3}{7}+\frac{4}{7})+\frac{4}{9}+\frac{4}{11}=1+\frac{4}{9}+\frac{4}{11}\)

\(=\frac{7}{7}+\frac{4}{9}+\frac{4}{11}=\frac{693+308+252}{693}=\frac{1253}{693}=\frac{179}{99}\)

\(h)\frac{1}{8}+\frac{1}{12}+\frac{3}{8}+\frac{5}{12}=(\frac{1}{8}+\frac{3}{8})+(\frac{1}{12}+\frac{5}{12})=\frac{4}{8}+\frac{6}{12}=\frac{1}{2}+\frac{1}{2}=1\)

ta gọi \(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{90}\)là A

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)

\(\Leftrightarrow1.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{9}-\frac{1}{10}\right)\)

\(\Rightarrow A=1-\frac{1}{10}=\frac{9}{10}\)

ta gọi B là biểu thức thứ2

\(B=\frac{2.2}{3}\times\frac{3.3}{2.4}\times\frac{4.4}{3.5}\times...\times\frac{10.10}{9.11}\)

\(\Rightarrow\)2 x \(\frac{10}{11}\)\(=\frac{20}{11}\)

\(\Rightarrow\)\(x+\frac{9}{10}=\frac{20}{11}+\frac{9}{110}\)

\(\Rightarrow x=1\)

mk nghĩ vậy bạn ạ, mk mong nó đúng

giúp

=> (1/1.2 + 1/2.3 + 1/3.4 + ... + 1/8.9 + 1/9.10) : x = 9/20

=> (1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/8 - 1/9 + 1/9 - 1/10) : x = 9/20

=> (1 - 1/10) : x = 9/20

=> 9/10 : x = 9/20

X = 9/10 : 9/20 = 2

D.9/10

k minh nha!

B.91/90

chuan 100%

a) \(\left(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{90}\right)\cdot100-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right]:\dfrac{1}{2}=89\)

\(\Rightarrow\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{9\cdot10}\right)\cdot100-\left[\dfrac{5}{2}:\left(x+\dfrac{103}{50}\right)\right]:\dfrac{1}{2}=89\)

\(\Rightarrow\left(1-\dfrac{1}{2}+\dfrac{1}{2}-...+\dfrac{1}{9}-\dfrac{1}{10}\right)\cdot100-\left[\dfrac{5}{2}:\left(x+\dfrac{103}{50}\right)\right]:\dfrac{1}{2}=89\)

\(\Rightarrow\left(1-\dfrac{1}{10}\right)\cdot100-\left[\dfrac{5}{2}:\left(x+\dfrac{103}{50}\right)\right]:\dfrac{1}{2}=89\)

\(\Rightarrow\dfrac{9}{10}\cdot100-\left[\dfrac{5}{2}:\left(x+\dfrac{103}{50}\right)\right]:\dfrac{1}{2}=89\)

\(\Rightarrow90-\left[\dfrac{5}{2}:\left(x+\dfrac{103}{50}\right)\right]:\dfrac{1}{2}=89\)

\(\Rightarrow\dfrac{5}{2}:\left(x+\dfrac{103}{50}\right)=90-89\)

\(\Rightarrow\dfrac{5}{2}:\left(x+\dfrac{103}{50}\right)=1\)

\(\Rightarrow x+\dfrac{103}{50}=\dfrac{5}{2}\)

\(\Rightarrow x=\dfrac{11}{25}\)

b) \(x\cdot9,85+x\cdot0,15=0,1\)

\(\Rightarrow x\cdot\left(9,85+0,15\right)=0,1\)

\(\Rightarrow x\cdot10=0,1\)

\(\Rightarrow x=\dfrac{0,1}{10}\)

\(\Rightarrow x=0,01\)

c) \(\dfrac{2}{5}+2022x=\dfrac{4}{10}\)

\(\Rightarrow\dfrac{2}{5}+2022x=\dfrac{2}{5}\)

\(\Rightarrow2022x=\dfrac{2}{5}-\dfrac{2}{5}\)

\(\Rightarrow2022x=0\)

\(\Rightarrow x=\dfrac{0}{2022}\)

\(\Rightarrow x=0\)

a) \(\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{90}\right).100-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right]:\dfrac{1}{2}=89\left(1\right)\)

Ta có :

\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{90}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\)

\(=1-\dfrac{1}{10}=\dfrac{9}{10}\)

\(\left(1\right)\Rightarrow\dfrac{9}{10}.100-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right]:\dfrac{1}{2}=89\)

\(\Rightarrow90-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right].2=89\)

\(\Rightarrow\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right].2=90-89\)

\(\Rightarrow\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)=\dfrac{1}{2}\)

\(\Rightarrow x+\dfrac{206}{100}=\dfrac{5}{2}:\dfrac{1}{2}\)

\(\Rightarrow x+\dfrac{103}{50}=\dfrac{5}{2}.\dfrac{2}{1}\)

\(\Rightarrow x+\dfrac{103}{50}=5\)

\(\Rightarrow x=5-\dfrac{103}{50}\)

\(\Rightarrow x=\dfrac{250}{50}-\dfrac{103}{50}\)

\(\Rightarrow x=\dfrac{147}{50}\)

a. 10/13 + 9/16         
=160/208+117/208
=277/208
7/90 + 123/270
=7/90+41/90
=48/90
=8/15

b. 19/21 - 5/12                 
=76/84-35/84
=41/84
 90/100 - 25/40
=9/10-25/40
=36/40-25/40
=11/40

thank

cứu

a) 10; 13; 18; 26; 36; 52...

c) 0; 1; 4; 9; 16; 25...

m) 1; 4; 9; 16; 25; 36; 49; 64...

p) 1; 3; 9; 27; 81; 243...

\(B=\frac{1.2+2.4+3.6+4.8+5.10}{3.4+6.8+9.12+12.16+15.20}\)

\(B=\frac{1.2+2^2.1.2+3^21.2+4^2.1.2+5^2.1.2}{3.4+2^23.4+3^23.4+4^23.4+5^23.4}\)

\(B=\frac{2.\left(1+2^2+3^2+4^2+5^2\right)}{12\left(1+2^2+3^2+4^2+5^2\right)}\)\(\Rightarrow B=\frac{2}{12}=\frac{1}{6}\)