Simplify:

$$
\frac{3}{4} + \frac{2}{3} \div \frac{4}{9} \div \frac{5}{2} - \frac{1}{4} imes \frac{2}{5}
$$

Question

Simplify:

$$
\frac{3}{4} + \frac{2}{3} \div \frac{4}{9} \div \frac{5}{2} - \frac{1}{4} 	imes \frac{2}{5}
$$

Accepted Answer

**Solution:**
Given expression:
$$ \frac{3}{4} + \frac{2}{3} \div \frac{4}{9} \div \frac{5}{2} - \frac{1}{4} \times \frac{2}{5} $$
First, solve the division and multiplication parts.
$$ \frac{2}{3} \div \frac{4}{9} = \frac{2}{3} \times \frac{9}{4} = \frac{18}{12} = \frac{3}{2} $$
Now divide by $\frac{5}{2}$:
$$ \frac{3}{2} \div \frac{5}{2} = \frac{3}{2} \times \frac{2}{5} = \frac{3}{5} $$
Now solve the multiplication part:
$$ \frac{1}{4} \times \frac{2}{5} = \frac{2}{20} = \frac{1}{10} $$
So the expression becomes:
$$ \frac{3}{4} + \frac{3}{5} - \frac{1}{10} $$
Taking LCM of 4, 5, and 10 as 20:
$$ \frac{3}{4} = \frac{15}{20} $$
$$ \frac{3}{5} = \frac{12}{20} $$
$$ \frac{1}{10} = \frac{2}{20} $$
Now,
$$ \frac{15}{20} + \frac{12}{20} - \frac{2}{20} = \frac{25}{20} $$
$$ \frac{25}{20} = \frac{50}{40} $$
Therefore, the correct answer is:
$$ \boxed{\frac{50}{40}} $$

Answer

Answer

Answer