4 5/7х:2 1/13=2 8/9:2 4/11

To solve the equation \( 4 \frac{5}{7} \times 2 \frac{1}{13} = 2 \frac{8}{9} \div 2 \frac{4}{11} \), we first need to convert all mixed numbers to improper fractions and then simplify the equation step by step.

Step 1: Convert mixed numbers to improper fractions.

1. Convert \( 4 \frac{5}{7} \): \[ 4 \frac{5}{7} = \frac{4 \times 7 + 5}{7} = \frac{28 + 5}{7} = \frac{33}{7} \]

2. Convert \( 2 \frac{1}{13} \): \[ 2 \frac{1}{13} = \frac{2 \times 13 + 1}{13} = \frac{26 + 1}{13} = \frac{27}{13} \]

3. Convert \( 2 \frac{8}{9} \): \[ 2 \frac{8}{9} = \frac{2 \times 9 + 8}{9} = \frac{18 + 8}{9} = \frac{26}{9} \]

4. Convert \( 2 \frac{4}{11} \): \[ 2 \frac{4}{11} = \frac{2 \times 11 + 4}{11} = \frac{22 + 4}{11} = \frac{26}{11} \]

Step 2: Rewrite the equation using improper fractions.

\[ \frac{33}{7} \times \frac{27}{13} = \frac{26}{9} \div \frac{26}{11} \]

Step 3: Simplify both sides of the equation.

1. Left side: \[ \frac{33}{7} \times \frac{27}{13} = \frac{33 \times 27}{7 \times 13} = \frac{891}{91} \]

2. Right side: To divide by a fraction, we multiply by its reciprocal: \[ \frac{26}{9} \div \frac{26}{11} = \frac{26}{9} \times \frac{11}{26} = \frac{11}{9} \]

Step 4: Compare both sides of the equation.

So we have: \[ \frac{891}{91} = \frac{11}{9} \]

Step 5: Cross-multiply to check equality.

\[ 891 \times 9 \quad \text{and} \quad 11 \times 91 \]

Calculating both:

1. Left side: \[ 891 \times 9 = 8019 \]

2. Right side: \[ 11 \times 91 = 1001 \]

Since \( 8019 \neq 1001 \), the equation is not valid.

Conclusion

1. The left side yields \( \frac{891}{91} \).
2. The right side yields \( \frac{11}{9} \).
3. The two sides are not equal, which means the original equation does not hold true.