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.
- Convert \( 2 \frac{5}{9} \) into an improper fraction:
\[ 2 \frac{5}{9} = \frac{2 \times 9 + 5}{9} = \frac{18 + 5}{9} = \frac{23}{9} \]
- Convert \( 1 \frac{2}{21} \) into an improper fraction:
\[ 1 \frac{2}{21} = \frac{1 \times 21 + 2}{21} = \frac{21 + 2}{21} = \frac{23}{21} \]
- 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:
\[ \boxed{5} \]
