2 5/9:х=1 2/21: 2 1/7

To solve the proportion \( \frac{2 \frac{5}{9}}{x} = \frac{1 \frac{2}{21}}{2 \frac{1}{7}} \), we first convert the mixed numbers into improper fractions. 1. Convert \( 2 \frac{5}{9} \) into an improper fraction: \[ 2 \frac{5}{9} = \frac{2 \times 9 + 5}{9} = \frac{18 + 5}{9} = \frac{23}{9} \] 2. Convert \( 1 \frac{2}{21} \) into an improper fraction: \[ 1 \frac{2}{21} = \frac{1 \times 21 + 2}{21} = \frac{21 + 2}{21} = \frac{23}{21} \] 3. Convert \( 2 \frac{1}{7} \) into an improper fraction: \[ 2 \frac{1}{7} = \frac{2 \times 7 + 1}{7} = \frac{14 + 1}{7} = \frac{15}{7} \] Now, we rewrite the original equation with the improper fractions: \[ \frac{\frac{23}{9}}{x} = \frac{\frac{23}{21}}{\frac{15}{7}} \] Next, simplify the right side: \[ \frac{\frac{23}{21}}{\frac{15}{7}} = \frac{23}{21} \times \frac{7}{15} = \frac{23 \times 7}{21 \times 15} = \frac{161}{315} \] Now we can set up the equation: \[ \frac{\frac{23}{9}}{x} = \frac{161}{315} \] To solve for \( x \), we cross-multiply: \[ 23 \times 315 = 161 \times 9x \] Calculating \( 23 \times 315 \): \[ 23 \times 315 = 7245 \] Now, the equation is: \[ 7245 = 161 \times 9x \] Next, calculate \( 161 \times 9 \): \[ 161 \times 9 = 1449 \] Now we have: \[ 7245 = 1449x \] To solve for \( x \): \[ x = \frac{7245}{1449} \] Calculating \( \frac{7245}{1449} \): \[ x = 5 \] Thus, the value of \( x \) is: \[ \boxed{5} \]