Ta có:

\(\left(\right. \frac{13 \frac{2}{9} - 15 \frac{2}{3}}{18 \frac{3}{7} - 17 \frac{1}{4}} \cdot \frac{30^{2} - 5^{4}}{25 - 12 \cdot 5^{2}} \left.\right) \cdot x = \frac{\frac{2}{11} + \frac{3}{13} + \frac{4}{15} + \frac{5}{17}}{4 \frac{1}{11} + \frac{5}{13} + \frac{9}{15} + \frac{13}{17}}\)

Bước 1: Đổi hỗn số về phân số

• \(13 \frac{2}{9} = \frac{119}{9}\),
• \(15 \frac{2}{3} = \frac{47}{3}\),
• \(18 \frac{3}{7} = \frac{129}{7}\),
• \(17 \frac{1}{4} = \frac{69}{4}\)

Bước 2: Tính toán từng phần

Ta có:

\(\frac{119}{9} - \frac{47}{3} = \frac{119 - 141}{9} = \frac{- 22}{9}\) \(\frac{129}{7} - \frac{69}{4} = \frac{516 - 483}{28} = \frac{33}{28}\) \(30^{2} - 5^{4} = 900 - 625 = 275\) \(25 - 12 \cdot 25 = 25 - 300 = - 275\)

Khi đó:

\(\left(\right. \frac{- 22}{9} \div \frac{33}{28} \cdot \frac{275}{- 275} \left.\right) = \left(\right. \frac{- 22}{9} \cdot \frac{28}{33} \cdot \left(\right. - 1 \left.\right) \left.\right) = \frac{616}{297}\)

Bước 3: Tính vế phải

Tử số:

\(\frac{2}{11} + \frac{3}{13} + \frac{4}{15} + \frac{5}{17} = \frac{35494}{36465}\)

Mẫu số:

\(4 \frac{1}{11} + \frac{5}{13} + \frac{9}{15} + \frac{13}{17} = \frac{149645}{36465}\)

→ Vế phải:

\(\frac{35494}{36465} \div \frac{149645}{36465} = \frac{35494}{149645}\)

Bước 4: Giải phương trình

\(\frac{616}{297} \cdot x = \frac{35494}{149645} \Rightarrow x = \frac{35494}{149645} \cdot \frac{297}{616} = \frac{813}{7118}\)

Vậy:

\(\boxed{x = \frac{813}{7118}}\)

hỉu không =]]]

\(\left(1+2\frac{1}{4}-3\frac{1}{3}\right):\left(1+3\frac{1}{2}-4\frac{7}{12}\right)\)

\(=\left(1+2-3+\frac{1}{4}-\frac{1}{3}\right):\left(1+3-4+\frac{1}{2}-\frac{7}{12}\right)\)

\(=\frac{-1}{12}:\frac{-1}{12}=\frac{-1}{12}.\frac{12}{-1}=\frac{12}{12}=1\)

a. (1 + \(2\frac{1}{4}\) -  \(3\frac{1}{3}\)) : (1 + \(3\frac{1}{2}\) - \(4\frac{7}{12}\))

= \(-\frac{1}{12}\): ( \(-\frac{1}{12}\))

= 1

b. \(5\frac{1}{2}\)-  \(14\frac{3}{7}\) :  \(\frac{9}{13}\)-  \(3\frac{4}{7}\) :  \(\frac{9}{13}\)

= \(\frac{11}{2}\)+ (\(14\frac{3}{7}-3\frac{4}{7}\)) : \(\frac{9}{13}\)

= \(\frac{11}{2}\)- 26

= \(-\frac{41}{2}\)

A =

B =

C =

C =

C = (4.-12)/(13.17) +

C =

C =

C = 96/221

D = -1/12 - ( 2

D = -1/12 - ( 4

D = -1/12 - (-1

D = -1/12 + 1

-3/36 + 2

D = -1/36

):5/11

E = ):5/11

E = 0:5/11

E = 0

a)

\(\begin{array}{l}\frac{3}{7}.\left( { - \frac{1}{9}} \right) + \frac{3}{7}.\left( { - \frac{2}{3}} \right)\\ = \frac{3}{7}.\left( { - \frac{1}{9} + \frac{-2}{3}} \right)\\ = \frac{3}{7}.\left( { - \frac{1}{9} - \frac{6}{9}} \right)\\ = \frac{3}{7}.\frac{{ - 7}}{9} = \frac{{ - 1}}{3}\end{array}\)                 

b)

\(\begin{array}{l}\left( {\frac{{ - 7}}{{13}}} \right).\frac{5}{{12}} + \left( {\frac{{ - 7}}{{13}}} \right).\frac{7}{{12}} + \left( {\frac{{ - 6}}{{13}}} \right)\\ = \frac{{ - 7}}{{13}}.\left( {\frac{5}{{12}} + \frac{7}{{12}}} \right) + \left( {\frac{{ - 6}}{{13}}} \right)\\ = \frac{{ - 7}}{{13}}.1 + \left( {\frac{{ - 6}}{{13}}} \right)\\ = \frac{{ - 7}}{{13}} + \left( {\frac{{ - 6}}{{13}}} \right)\\ = \frac{{ - 13}}{{13}}\\ = -1\end{array}\)

c)

\(\begin{array}{l}\left[ {\left( {\frac{{ - 2}}{3} + \frac{3}{7}} \right)} \right]:\frac{5}{9} + \left( {\frac{4}{7} - \frac{1}{3}} \right):\frac{5}{9}\\ = \left[ {\left( {\frac{{ - 2}}{3} + \frac{3}{7}} \right)} \right].\frac{9}{5} + \left( {\frac{4}{7} - \frac{1}{3}} \right).\frac{9}{5}\\ = \left( {\frac{{ - 2}}{3} + \frac{3}{7} + \frac{4}{7} - \frac{1}{3}} \right).\frac{9}{5}\\ = \left[ {\left( {\frac{{ - 2}}{3} - \frac{1}{3}} \right) + \left( {\frac{3}{7} + \frac{4}{7}} \right)} \right].\frac{9}{5}\\ = \left( { - 1 + 1} \right).\frac{9}{5}\\ = 0.\frac{9}{5} = 0\end{array}\)

d)

\(\begin{array}{l}\frac{5}{9}:\left( {\frac{1}{{11}} - \frac{5}{{22}}} \right) + \frac{5}{9}:\left( {\frac{1}{{15}} - \frac{2}{3}} \right)\\ = \frac{5}{9}:\left( {\frac{2}{{22}} - \frac{5}{{22}}} \right) + \frac{5}{9}:\left( {\frac{1}{{15}} - \frac{{10}}{{15}}} \right)\\ = \frac{5}{9}:\frac{{ - 3}}{{22}} + \frac{5}{9}:\frac{{ - 9}}{15}\\= \frac{5}{9}:\frac{{ - 3}}{{22}} + \frac{5}{9}:\frac{{ - 3}}{5}\\ = \frac{5}{9}.\frac{{ - 22}}{3} + \frac{5}{9}.\frac{{ - 5}}{3}\\ = \frac{5}{9}.\left( {\frac{{ - 22}}{3} - \frac{5}{3}} \right)\\ = \frac{5}{9}.\frac{-27}{3}= \frac{5}{9}.\left( { - 9} \right) =  - 5\end{array}\)

e)

\(\begin{array}{l}\frac{3}{5} + \frac{3}{{11}} - \left( {\frac{{ - 3}}{7}} \right) + \left( {\frac{{ - 2}}{{97}}} \right) - \frac{1}{{35}} - \frac{3}{4} + \left( {\frac{{ - 23}}{{44}}} \right)\\ = \frac{3}{5} + \frac{3}{{11}} + \frac{3}{7} - \frac{2}{{97}} - \frac{1}{{35}} - \frac{3}{4} - \frac{{23}}{{44}}\\ = \left( {\frac{3}{5} + \frac{3}{7} - \frac{1}{{35}}} \right) + \left( {\frac{3}{{11}} - \frac{3}{4} - \frac{{23}}{{44}}} \right) - \frac{2}{{97}}\\ = \left( {\frac{{21}}{{35}} + \frac{{15}}{{35}} - \frac{1}{{35}}} \right) + \left( {\frac{{12}}{{44}} - \frac{{33}}{{44}} - \frac{{23}}{{44}}} \right) - \frac{2}{{97}}\\ = \frac{35}{{35}}+ \frac{-44}{{44}}- \frac{2}{{97}}\\= 1 + \left( { - 1} \right) - \frac{2}{{97}}\\ =  - \frac{2}{{97}}\end{array}\)

a, \(\frac{1}{4}+\frac{5}{12}-\frac{1}{13}-\frac{7}{8}\)

\(=\left(\frac{1}{4}+\frac{5}{12}\right)-\left(\frac{1}{13}+\frac{7}{8}\right)\)

\(=\frac{2}{3}-\frac{99}{104}\)

\(=-\frac{89}{312}\)

b, \(11\frac{3}{13}-2\frac{4}{7}+5\frac{3}{13}\)

\(=\left(11\frac{3}{13}+5\frac{3}{13}\right)-2\frac{4}{7}\)

\(=\frac{214}{13}-\frac{18}{7}\)

\(=\frac{1264}{91}\)

c, \(\left(6\frac{4}{9}+3\frac{7}{11}\right)-4\frac{4}{9}\)

\(=6\frac{4}{9}+3\frac{7}{11}-4\frac{4}{9}\)

\(=\left(6\frac{4}{9}-4\frac{4}{9}\right)+3\frac{7}{11}\)

\(=2+3\frac{7}{11}\)

\(=5\frac{7}{11}\)

\(=\frac{62}{11}\)

d, \(\left(6,17+3\frac{5}{9}-2\frac{36}{97}\right)\left(\frac{1}{3}-0,25-\frac{1}{12}\right)\)

\(=\left(6,17+3\frac{5}{9}-2\frac{36}{97}\right)\left(\frac{1}{3}-\frac{1}{4}-\frac{1}{12}\right)\)

\(=\left(6,17+3\frac{5}{9}-2\frac{36}{97}\right)\cdot0\)

\(=0\)

e, \(-1,5\cdot\left(1+\frac{2}{3}\right)\)

\(=-\frac{3}{2}\cdot\frac{5}{3}\)

\(=-\frac{5}{2}\)

f, Đặt \(A=1^2+2^2+3^2+...+100^2\)

\(=1+2\left(3-1\right)+3\left(4-1\right)+...+100\left(101-1\right)\)

\(=1+2\cdot3-2+3\cdot4-3+...+100\cdot101-100\)

\(=\left(2\cdot3+3\cdot4+...+100\cdot101\right)-\left(1+2+3+...+100\right)\)

Đặt B = 2 . 3 + 3 . 4 + ... + 100 . 101 

3B = 2 . 3 ( 4 - 1 ) + 3 . 4 ( 5 - 2 ) + ... + 100 . 101 . ( 102 - 99 )

3B = 2 . 3 . 4 - 1 . 2 . 3 + 3 . 4 . 5 - 2 . 3 . 4 + ... + 100 . 101 . 102 - 99 . 100 . 101 

3B = 100 . 101 . 102

B = \(\frac{100\cdot101\cdot102}{3}\)

B = 343400

Thay B vào A. Ta được :

\(A=343400-\left(1+2+3+...+100\right)\)

Thay C = 1 + 2 + 3 + ... + 100

Dãy số 1; 2; 3; ...; 100 có số số hạng là:

( 100 - 1 ) : 1 + 1 = 100 ( số hạng )

Tổng của dãy số đó là :

( 100 + 1 ) . 100 : 2 = 5050

=> C = 5050

Thay C vào A. Ta được :

\(A=343400-5050\)

\(A=338350\)

Vậy A = 338350

câu 1 : là -4

câu 2 : là -1

nếu đúng hãy cho mình 1 k đúng nhé

GIẢI HẲN RA HỘ MK VỚI !!