1) \( \left(3 \frac{1}{4}+0,2,5-1 \frac{5}{4}\right):\left(2 \frac{1}{4}-4 \frac{1}{2}\right. \). \( -0,75):\left(-4 \frac{1}{2}\right)=\frac{1}{3} \) 1)

To solve this problem, we need to perform the operations inside the parentheses first and then divide the results. Let's start with the left side of the equation: \( \left(3 \frac{1}{4}+0,2,5-1 \frac{5}{4}\right) \) First, convert the mixed numbers to improper fractions: \( 3 \frac{1}{4} = \frac{13}{4} \) \( 1 \frac{5}{4} = \frac{9}{4} \) Now, perform the addition and subtraction: \( \frac{13}{4} + 0.25 - \frac{9}{4} \) Since 0.25 is the same as \( \frac{1}{4} \), we can rewrite the equation as: \( \frac{13}{4} + \frac{1}{4} - \frac{9}{4} \) Combine the fractions: \( \frac{13 + 1 - 9}{4} = \frac{5}{4} \) Now, let's solve the right side of the equation: \( \left(2 \frac{1}{4}-4 \frac{1}{2}\right) \) Convert the mixed numbers to improper fractions: \( 2 \frac{1}{4} = \frac{9}{4} \) \( 4 \frac{1}{2} = \frac{9}{2} \) Now, perform the subtraction: \( \frac{9}{4} - \frac{9}{2} \) To subtract these fractions, we need a common denominator. The least common denominator for 4 and 2 is 4, so we can rewrite \( \frac{9}{2} \) as \( \frac{18}{4} \): \( \frac{9}{4} - \frac{18}{4} \) Now, subtract the fractions: \( \frac{9 - 18}{4} = \frac{-9}{4} \) Finally, divide the results of the left side by the right side: \( \frac{5}{4} \div \frac{-9}{4} \) To divide by a fraction, we multiply by its reciprocal: \( \frac{5}{4} \times \frac{-4}{9} \) Now, multiply the numerators and the denominators: \( \frac{5 \times -4}{4 \times 9} = \frac{-20}{36} \) Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4: \( \frac{-20 \div 4}{36 \div 4} = \frac{-5}{9} \) So, the final answer is: \( \frac{-5}{9} \)