bài 1b)

\(8\frac{1}{14}-6\frac37\)

C1:\(\frac{113}{14}-\frac{45}{7}\) =\(\frac{113}{14}-\frac{90}{14}=\frac{23}{14}\)

C2:\(8\frac{1}{14}-6\frac37=\left(8-6\right)+\left(\frac{1}{14}-\frac37\right)=2+\left(\frac{1}{14}-\frac{6}{14}\right)\)

\(=2+\frac{-5}{14}=\frac{28}{14}-\frac{5}{14}=\frac{23}{14}\)

bài 1 c)\(7-3\frac67\)

C1:\(\) \(7-3\frac67=7-\frac{27}{7}=\frac{49}{7}-\frac{27}{7}=\frac{22}{7}\)

C2:\(7-3\frac67=\left(7-3\right)-\frac67=4-\frac67=\frac{28}{7}-\frac67=\frac{22}{7}\)

\(A=5+5^2+5^3+5^4+5^5+5^6+5^7+5^8+5^9\)

\(=\left(5+5^2+5^3\right)+\left(5^4+5^5+5^6\right)+\left(5^7+5^8+5^9\right)\)

\(=5\left(1+5+5^2\right)+5^4\left(1+5+5^2\right)+5^7\left(1+5+5^2\right)\)

\(=5.31+5^4.31+5^7.31=31.\left(5+5^4+5^7\right)\)chia hết cho 31

Vậy A chia 31 dư 0

\(S=1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+8}\)

\(=1+\frac{1}{\left(1+2\right).3.\frac{1}{2}}+\frac{1}{\left(1+3\right).3.\frac{1}{2}}+...+\frac{1}{\left(1+8\right).8.\frac{1}{2}}\)

\(=1+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{8.9}\)

\(=1+2.\left(\frac{3-2}{2+3}+\frac{4-3}{3.4}+...+\frac{9-8}{8.9}\right)\)

\(=1+2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\right)\)

\(=1+2\left(\frac{1}{2}-\frac{1}{9}\right)\)

\(=1+2.\frac{7}{18}=1+\frac{7}{9}=\frac{16}{9}\)

Bài 1a

- \(\frac45\) : \(\frac87\)

= - \(\frac45\) x \(\frac78\)

= - \(\frac{7}{10}\)

Bài 1b:

- \(\frac38\). \(\frac79\) + \(\frac{-3}{8}\).\(\frac29\) + 0,25

= - \(\frac38\).(\(\frac79+\frac29\)) + 0,25

= - \(\frac38\). 1 + 0,25

= - 0,375 + 0,25

= - 0,125

\(\frac{3}{7}+\frac{9}{7}+\frac{5}{7}=\frac{12}{7}+\frac{5}{7}=\frac{17}{7}\)

\(\frac{8}{9}\times\frac{1}{2}=\frac{4}{9}\)

\(\frac{9}{2}:\frac{8}{6}=\frac{9}{2}\times\frac{6}{8}=\frac{27}{8}\)

Ủng hộ ! 

\(\frac{3}{7}+\frac{9}{7}+\frac{5}{7}=\frac{17}{7}\)

\(\frac{8}{9}\times\frac{1}{2}=\frac{8}{18}=\frac{4}{9}\)

\(\frac{9}{2}:\frac{8}{6}=\frac{9}{6}\times\frac{6}{8}=\frac{54}{48}\)

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

Câu a:

(4 5/37 - 3 4/5 + 8 15/29) - (3 5/37 - 6 14/29)

= (4 5/37 - 3 5/37) + (8 15/29 + 6 14/29) - 3 4/5

= 1 + 15 - 3 4/5

= 16 - 3 - 4/5

= 13 - 4/5

= 61/5

Câu b:

(2\(\frac56\) + 1\(\frac49\)) : (10\(\frac{1}{12}\) - 9\(\frac12\))

= (17/6 + 13/9) :(121/12 - 19/2)

= (51/18 + 26/18) :(121/12 - 114/2)

= 77/18 : 7/12

= 77/18 x 12/7

= 22/3