Rational Numbers and Operations：练习题

What is the value of the expression \(\frac{3}{5} + \left(-\frac{2}{3}\right) \times \frac{1}{4}\)?

Simplify the expression: \( \left( -\frac{3}{4} \times \frac{8}{9} \right) - \left( \frac{1}{2} \div \frac{3}{5} \right) \)

Simplify the following expression:
\(\frac{(-1.2) \times 0.5 - (-0.4)^2}{0.2}\).

Which of the following rational numbers is the smallest?

Calculate the value of \(\frac{-2.4 \times 0.5}{(-0.2)^2}\).

Consider the rational numbers \( A = 0.\overline{42} \) and \( B = 0.5\bar{6} \).
(a) Express \( A \) and \( B \) as fractions in their simplest form.
(b) Evaluate the expression \( E = \left( \frac{A}{B - \frac{1}{2}} \right) \times | -1.25 | \). Express your answer as an improper fraction in its simplest form.
(c) Convert your answer from part (b) into a recurring decimal.