\(a,-\frac{9}{12}=-\frac{9:3}{12:3}=-\frac{3}{4}\)

\(\frac{-18}{-24}=\frac{\left(-18\right):\left(-6\right)}{\left(-24\right):\left(-6\right)}=\frac{3}{4}\)

\(-\frac{35}{70}=-\frac{35:35}{70:35}=\frac{1}{2}\)

\(-\frac{9}{27}=-\frac{9:9}{27:9}=-\frac{1}{3}\)

\(b,\frac{1313}{4242}=\frac{1313:101}{4242:101}=\frac{13}{42}\)

\(\frac{-353535}{-424242}=\frac{\left(-353535\right):\left(-70707\right)}{\left(-424242\right):\left(-70707\right)}=\frac{5}{6}\)

\(c,\frac{2^3\times4^3\times5^4}{8^2\times25^3\times7}=\frac{2^3\times4^3\times25^2}{8\times8^2\times25^2\times25\times7}\)         ( 4^3 = 8^2 ; 5^4 = 25^2 )

\(=\frac{1}{25\times7}=\frac{1}{175}\)

\(a.\frac{-9}{-12}=\frac{-9:3}{-12:3}=\frac{-3}{-4}.\)

\(\frac{-18}{-24}=\frac{-18:6}{-24:6}=\frac{-3}{-4}\)

\(\frac{-35}{-70}=\frac{-35:35}{-70:35}=\frac{-1}{-2}\)

\(\frac{-9}{-27}=\frac{-9:9}{-27:9}=\frac{-1}{-3}\)

a) \(\frac{-9}{12}=\frac{-9\div3}{12\div3}=\frac{-3}{4}\)

\(\frac{-18}{-24}=\frac{-18\div\left(-6\right)}{-24\div\left(-6\right)}=\frac{3}{4}\)

\(\frac{-35}{70}=\frac{-35\div35}{70\div35}=\frac{-1}{2}\)

\(\frac{-9}{27}=\frac{-9\div9}{27\div9}=\frac{-1}{3}\)

b) \(\frac{1313}{4242}=\frac{1313\div101}{4242\div101}=\frac{13}{42}\)

\(\frac{-353535}{-424242}=\frac{-353535\div\left(-70707\right)}{-424242\div\left(-70707\right)}=\frac{5}{6}\)

c)\(\frac{2^3\times4^3\times5^4}{8^2\times25^3\times7}\)= \(\frac{2^3\times4^3\times5^4}{\left(2^3\right)^2\times\left(5^2\right)^3\times7}\)= \(\frac{2^3\times4^3\times5^4}{2^6\times5^6\times7}\)= \(\frac{2^3\times4^3\times5^4}{2^3\times2^3\times5^2\times5^4\times7}\)= \(\frac{2^3\times2^3}{2^3\times5^2\times7}\)= \(\frac{8}{25\times7}\)= \(\frac{8}{175}\)

\(S=\dfrac{2}{4\cdot7}+\dfrac{2}{7\cdot10}-\dfrac{3}{5\cdot9}-\dfrac{3}{9\cdot13}\)

\(=\dfrac{2}{3}\left(\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}\right)-\dfrac{3}{4}\left(\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}\right)\)

\(=\dfrac{2}{3}\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}\right)-\dfrac{3}{4}\cdot\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}\right)\)

\(=\dfrac{2}{5}\cdot\dfrac{3}{20}-\dfrac{3}{4}\cdot\dfrac{8}{65}=\dfrac{-21}{650}\)

Số số hạng là:

(85-5):2+1=41(số)

Tổng là 90x41:2=1845

\(a)\)\(6\frac{4}{5}-\left(1\frac{2}{3}+3\frac{4}{5}\right)\)

\(=6\frac{4}{5}-1\frac{2}{3}-3\frac{4}{5}\)

\(=\left(6\frac{4}{5}-3\frac{4}{5}\right)-1\frac{2}{3}\)

\(=\left(6+\frac{4}{5}-3-\frac{4}{5}\right)-\frac{5}{3}\)

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

\(=\frac{9}{3}-\frac{5}{3}\)

\(=\frac{4}{3}\)

\(b)\)\(6\frac{5}{7}-(1\frac{3}{4}+2\frac{5}{7})\)

\(=6\frac{5}{7}-1\frac{3}{4}-2\frac{5}{7}\)

\(=\left(6\frac{5}{7}-2\frac{5}{7}\right)-1\frac{3}{4}\)

\(=\left(6+\frac{5}{7}-2-\frac{5}{7}\right)-\frac{7}{4}\)

\(=4-\frac{7}{4}\)

\(=\frac{16}{4}-\frac{7}{4}\)

\(=\frac{9}{4}\)

\(c)\)\(7\frac{5}{9}-\left(2\frac{3}{4}+3\frac{5}{9}\right)\)

\(=7\frac{5}{9}-2\frac{3}{4}-3\frac{5}{9}\)

\(=\left(7\frac{5}{9}-3\frac{5}{9}\right)-2\frac{3}{4}\)

\(=\left(7+\frac{5}{9}-3-\frac{5}{9}\right)-\frac{11}{4}\)

\(=4-\frac{11}{4}\)

\(=\frac{16}{4}-\frac{11}{4}\)

\(=\frac{5}{4}\)

P/s: Câu b bạn thiếu ngoặc.

Linz

 a) 6 và 4/5 - ( 1 và 2/3 + 3 và 4/5)

= 34/5- ( 5/3 + 19/5 )

= 34/5 - 5/3 - 19/5

= (34/5 - 9/5 ) - 5/3

=25/5 -5/3

= 5/1 - 5/3

= 15/3 - 5/3

=10/3

b) 6 và 5/7 - (1 và 3/4 + 2 và 5/7)

=47/7 - (7/4 + 19/7 )

= 47/7 -7/4 - 19/7

= (47/7 -19/7 ) - 7/4

= 28/7 -7/4

=4/1 - 7/4

= 16/4 - 7/4

= 9/4

c) 7 và 5/9 - ( 2 và 3/4 + 3 và 5/9 )

= 68/9 - ( 11/4 + 32/9 )

= 68/9 - 11/4 - 32/9

= (68/9 - 32/9 )- 11/4

= 36/9 -11/4

= 4/1 - 11/4

= 16/4 - 11/4

= 5/4

    Chúc bạn học tốt nha!!!!!

\(A=\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{8}+\dfrac{1}{9}\)

=1/3+1/2+2/5+1/3+2/7+1/4+1/9

=2789/1260

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

= \(\frac{6}{7}\) + (\(\frac{2}{9}\) . \(\frac{10}{7}\) ) -\(\frac{5}{3}\) . 9

=\(\frac{6}{7}\) +\(\frac{20}{63}\) - 15 = \(\frac{74}{63}\) -15 = \(\frac{-871}{63}\)

 nó có đẹp ko

1 3/7 là hỗn số nhé ko phải 1 nhân 3/7 đâu

\(x+x\cdot3:\dfrac{2}{9}+x:\dfrac{2}{7}=252\)

\(\Leftrightarrow x+x\cdot3\cdot\dfrac{9}{2}+x\cdot\dfrac{7}{2}=252\)

\(\Leftrightarrow x\cdot18=252\)

hay x=14

A=3.(1/1.2+1/2.3+1/3.4+.....+1/399.400)

A=3.(1/1-1/2+1/2-1/3+......+1/399-1/400)

A=3.(1-1/400)

A=3.399/400

A=1197/400

A=3.(1/1.2+1/2.3+1/3.4+.....+1/399.400)

A=3.(1/1-1/2+1/2-1/3+......+1/399-1/400)

A=3.(1-1/400)

A=3.399/400

A=1197/400

Bài 1: Tính nhanh:

A = 3/1*2 + 3/2*3 + 3/3*4 + ... + 3/399*400

=>3A = 1/1*2 + 1/2*3 + 1/3*4 + ... + 1/399*400

    3A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/399 - 1/400

    3A = 1 - 1/400

      3A = 400/400 - 1/400

      3A = 399/400

        A = 399/400 : 3

        A = 399/400 . 1/3

        A = 133/400.

Có gì ko hiểu bn ib mk nha.^^

\(A=\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+...+\frac{3}{399.400}\)

\(A=3.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{399.400}\right)\)

\(A=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{399}-\frac{1}{400}\right)\)

\(A=3.\left(1-\frac{1}{400}\right)\)

\(A=3.\frac{399}{400}\)

\(A=\frac{1197}{400}\)

\(B=\frac{5}{1.2}+\frac{5}{2.3}+\frac{5}{3.4}+...+\frac{5}{399.400}\)

\(B=5.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{399.400}\right)\)

\(B=5.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{399}-\frac{1}{400}\right)\)

\(B=5.\left(1-\frac{1}{400}\right)\)

\(B=5.\frac{399}{400}\)

\(B=\frac{399}{80}\)

\(C=\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{149.151}\)

\(C=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{149}-\frac{1}{151}\)

\(C=\frac{1}{5}-\frac{1}{151}\)

\(C=\frac{146}{755}\)

\(D=\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}+...+\frac{3}{149.151}\)

\(D=\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{149.151}\right)\)

\(D=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{149}-\frac{1}{151}\right)\)

\(D=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{151}\right)\)

\(D=\frac{3}{2}.\frac{146}{755}\)

\(D=\frac{219}{755}\)

\(E=\frac{11}{1.3}+\frac{11}{3.5}+\frac{11}{5.7}+...+\frac{11}{99.101}\)

\(E=\frac{11}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)

\(E=\frac{11}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(E=\frac{11}{2}.\left(1-\frac{1}{101}\right)\)

\(E=\frac{11}{2}.\frac{100}{101}\)

\(E=\frac{550}{101}\)

_Chúc bạn học tốt_