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a. 6 và 5/3 + 7 và 13/8 +3 và 1/3- 4 và 5/8
=23/3+69/8+4/3-37/8
=391/24+4/3+37/8=141/8-37/8=103/8
b.=(27/5+69/11)-(17/5-52/11)
=642/55+73/55=13

5/6x1/3+1/2x3/4x5/3
=5/18+3/8x5/3
=5/18+15/24
=5/18+5/8
=130/144=65/72

7/8 . 1/8 . 6/ 11 + 1/8 . 5/11
= 1/8( 7/8 . 6/11+ 5/11 )
= 1/8 . 41/44 = 41/352

\(\frac{2}{1}\cdot3\cdot\frac{2}{3}\cdot5\cdot\frac{2}{5}\cdot7\cdot\frac{2}{7}\cdot9\cdot\frac{2}{9}\cdot11\)
\(=2\cdot\left(3\cdot\frac{2}{3}\right)\cdot\left(5\cdot\frac{2}{5}\right)\cdot\left(7\cdot\frac{2}{7}\right)\cdot\left(9\cdot\frac{2}{9}\right)\cdot11\)
\(=2\cdot2\cdot2\cdot2\cdot2\cdot11\)
\(=352\)

a) \(\frac{3}{2}-\frac{5}{6}:x=\frac{5}{15}-\frac{3}{15}\)
\(\Leftrightarrow\frac{3}{2}-\frac{5}{6}:x=\frac{2}{15}\)
\(\Leftrightarrow\frac{5}{6}:x=\frac{3}{2}-\frac{2}{15}\)
\(\Leftrightarrow\frac{5}{6}:x=\frac{41}{30}\)
\(\Leftrightarrow x=\frac{5}{6}:\frac{41}{30}\)
\(\Leftrightarrow x=\frac{25}{41}\)
b) \(x-\frac{6}{7}.\frac{14}{8}=\frac{1}{2}-\frac{2}{5}\)
\(\Leftrightarrow x-\frac{3}{2}=\frac{1}{10}\)
\(\Leftrightarrow x=\frac{1}{10}+\frac{3}{2}\)
\(\Leftrightarrow x=\frac{8}{5}\)
c) \(x:\frac{6}{5}+\frac{2}{3}=\frac{7}{3}\)
\(\Leftrightarrow x:\frac{6}{5}=\frac{7}{3}-\frac{2}{3}\)
\(\Leftrightarrow x:\frac{6}{5}=\frac{5}{3}\)
\(\Leftrightarrow x=\frac{5}{3}.\frac{6}{5}\)
\(\Leftrightarrow x=2\)
A = \(\frac{2}{5\times6}\) + \(\frac{2}{6\times7}\) + ... + \(\frac{2}{2024\times2025}\)
A = \(\) 2 x (\(\frac{1}{5\times6}\) + \(\frac{1}{6\times7}\) + ... + \(\frac{1}{2024\times2025}\))
A = 2 x (\(\frac15\) - \(\frac16\) + \(\frac16\) - \(\frac17\) + ... + \(\frac{1}{2024}\) - \(\frac{1}{2025}\))
A = 2 x (\(\frac15\) - \(\frac{1}{2025}\))
A = 2 x (\(\frac{405}{2025}-\frac{1}{2025}\))
A = 2 x \(\frac{404}{2025}\)
A = \(\frac{808}{2025}\)