\(A=\frac{21}{31}+\frac{-16}{7}+\frac{44}{53}+\frac{10}{21}+\frac{9}{53} \)

\(A=\left(\frac{16}{7}+\frac{10}{21}\right)+\left(\frac{44}{53}+\frac{9}{53}\right)+\frac{21}{31}\)

\(A=\frac{58}{21}+1+\frac{21}{31}\)

\(A=\frac{100}{21}\)

\(B=6\left(\frac{1}{15.18}+\frac{1}{18.21}+...+\frac{1}{87.90}\right)\)

\(B=6\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)

\(B=6\left(\frac{1}{15}-\frac{1}{90}\right)\)

\(B=6.\frac{1}{18}\)

\(B=\frac{1}{3}\)

\(\left(\frac{3}{4}+\frac{2}{11}-\frac{8}{13}\right)+\left(\frac{1}{4}-\frac{5}{13}\right)\)

\(=\frac{3}{4}+\frac{2}{11}-\frac{8}{13}+\frac{1}{4}-\frac{5}{13}\)

\(=\left(\frac{3}{4}+\frac{1}{4}\right)+\frac{2}{11}-\left(\frac{8}{13}+\frac{5}{13}\right)\)

\(=1+\frac{2}{11}-1\)

\(=\frac{2}{11}\)

\(\left(\frac{9}{53}+\frac{21}{31}\right)+\left(\frac{44}{53}-\frac{16}{7}\right)+\frac{10}{31}\)

\(=\frac{9}{53}+\frac{21}{31}+\frac{44}{53}-\frac{16}{7}+\frac{10}{31}\)

\(=\left(\frac{9}{53}+\frac{44}{53}\right)+\left(\frac{21}{31}+\frac{10}{31}\right)-\frac{16}{7}\)

\(=1+1-\frac{16}{7}\)

\(=2-\frac{16}{7}\)

\(=\frac{14}{7}-\frac{16}{7}\)

\(=\frac{-2}{7}\)

\(\left(\dfrac{21}{31}+\dfrac{-16}{7}\right)+\left(\dfrac{44}{53}+\dfrac{10}{31}\right)+\dfrac{9}{53}.\)

\(\dfrac{21}{31}-\dfrac{16}{7}+\dfrac{44}{53}+\dfrac{10}{31}+\dfrac{9}{53}=\left(\dfrac{21}{31}+\dfrac{10}{31}\right)+\left(\dfrac{44}{53}+\dfrac{9}{53}\right)-\dfrac{16}{7}=1+1-\dfrac{16}{7}=\dfrac{-2}{7}.\)

\(\left(\frac{21}{31}+\frac{2013}{6039}\right)-\left(\frac{44}{53}-\frac{10}{31}\right)-\frac{9}{53}\)

\(=\frac{21}{31}+\frac{1}{3}-\frac{44}{53}+\frac{10}{31}-\frac{9}{53}\)

\(=\left(\frac{21}{31}+\frac{10}{31}\right)+\left(\frac{-44}{53}-\frac{9}{53}\right)+\frac{1}{3}\)

\(=1+\left(-1\right)+\frac{1}{3}\)

\(=\frac{1}{3}\)

a) 1 - 3 + 5 - 7 + 9 - 11

= (1 - 3) + (5 - 7) + (9 - 11)

= (-2) + (-2) + (-2)

= -6

b) -14 - 16 - 18 - ... - 92

= - (14 + 16 + 18 + .... + 92)

Áp dụng công thức tính dãy số ta có :

14 + 16 + 18 + .... + 92 = 2120

= -2120

c) 15 + 18 + 21 + .... + 63 + 66 + 70

= (15 + 18 + 21 + ..... + 66) + 70

Áp dụng công thức tính dãy số ta có :

15 + 18 + ..... + 66 = 729

= 729 + 70

= 8799

d) 2 - 3 + 4 - 5 + 6 - 7 + 8 - 9 + 10

= (2 - 3) + (4 - 5) + (6 - 7) + (8 - 9) + 10

= (-1) + (-1) + (-1) + (-1) + 10

= 6

a)1-3+5-7+9-11=-6

nhớ k cho mk nha,mk đầu tiên đấy nha bn

Câu 1:

\(=\dfrac{21}{31}+\dfrac{1}{3}-\dfrac{44}{53}+\dfrac{10}{31}-\dfrac{9}{53}=\dfrac{1}{3}\)

Câu 2:

1: =>1,3x=-1,31

=>130x=-131

=>x=-131/130

2: =>(4,5-2x)=11/14:(-11/7)=-7/14=-1/2=-0,5

=>2x=5

=>x=5/2

Bài 1: Ta chỉ cần bỏ ngoặc rồi cộng hai phân số để ra kết quả là số tự nhiên là xong

Bài 2:

A = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+............+\frac{1}{2003.2004}\)

A = \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-.............-\frac{1}{2003}+\frac{1}{2003}-\frac{1}{2004}\)

A = \(1-\frac{1}{2004}\)

A = \(\frac{2004}{2004}-\frac{1}{2004}=\frac{2003}{2004}\)

Mk làm mẫu 1 bài nha 

Bài 1 :

a, = (1/4+3/4) - (5/13+8/13)+2/11

    = 1 - 1 + 2/11

    = 2/11

Tk mk nha

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2003.2004}\)

\(\Leftrightarrow A=1\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2003}-\frac{1}{2004}\right)\)

\(\Leftrightarrow A=1\left(1-\frac{1}{2004}\right)\)

\(\Leftrightarrow A=\frac{2003}{2004}\)

\(D=\frac{6}{15\times18}+\frac{6}{18\times21}+\frac{6}{21\times24}+...+\frac{6}{87\times90}\)

\(=2\times\left(\frac{3}{15\times18}+\frac{3}{18\times21}+...+\frac{3}{87\times90}\right)\)

\(=2\times\left(\frac{18-15}{15\times18}+\frac{21-18}{18\times21}+...+\frac{90-87}{87\times90}\right)\)

\(=2\times\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)

\(=2\times\left(\frac{1}{15}-\frac{1}{90}\right)=\frac{1}{9}\)