Tính tỉ số \(\frac{A}{B}\) biết:

\(\frac{1}{2} + \frac{1}{3} + ... + \frac{1}{{2023}} + \frac{1}{{2024}}\) và \(B = \frac{{2023}}{1} + \frac{{2022}}{2} + \frac{{2021}}{3} + ... + \frac{2}{{2022}} + \frac{1}{{2023}}\).

a) \(1,56 + 8,44:4,22\)

\( = 1,56 + 2\)

\( = 3,56\)

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

\( = \frac{2}{7} + \frac{5}{7}.\frac{7}{{20}}.4\)

\[ = \frac{2}{7} + 1\]\[ = \frac{9}{7}\].

b) \[\frac{5}{7} + \frac{4}{{ - 14}}\]

\[ = \frac{5}{7} + \frac{{ - 2}}{7}\]\[ = \frac{3}{7}\].

d) \(\frac{3}{4}.26\frac{2}{9} - 38\frac{2}{9}.\frac{3}{4}\)

\( = \frac{3}{4}.\left( {26\frac{2}{9} - 38\frac{2}{9}} \right)\)

\( = \frac{3}{4}.\left( {26 + \frac{2}{9} - 38 - \frac{2}{9}} \right)\)

\( = \frac{3}{4}.\left( { - 12} \right) =  - 9\).

a) \(\frac{1}{2}:x = 0,6\)

\(x = 0,5:0,6\)

\(x = \frac{5}{6}\)

Vậy \(x = \frac{5}{6}\).

b) \(x - \frac{5}{6} =  - \frac{2}{3}\)

\(x =  - \frac{2}{3} + \frac{5}{6}\)

\(x =  - \frac{4}{6} + \frac{5}{6}\)

\(x = \frac{1}{6}\)

Vậy \(x = \frac{1}{6}\).

c) \[\left( {\frac{2}{3} - 2x} \right)\left( {x + \frac{4}{5}} \right) = 0\]

Suy ra \[\frac{2}{3} - 2x = 0\] hoặc \[x + \frac{4}{5} = 0\]

Trường hợp 1:

\[\frac{2}{3} - 2x = 0\]

\(2x = \frac{2}{3}\)

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

Vậy \[x \in \left\{ {\frac{1}{3};\frac{{ - 4}}{5}} \right\}\].

Trường hợp 2:

\[x + \frac{4}{5} = 0\]

\[x = \frac{{ - 4}}{5}\]