6. \( 2 \frac{2}{3}+1 \frac{4}{9}=2-1 \frac{4}{9}= \)

Let's solve the expression step by step. 1. **Convert mixed numbers to improper fractions:** - For \( 2 \frac{2}{3} \): \[ 2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} \] - For \( 1 \frac{4}{9} \): \[ 1 \frac{4}{9} = \frac{1 \times 9 + 4}{9} = \frac{9 + 4}{9} = \frac{13}{9} \] - For \( 1 \frac{4}{9} \) again in the second part: \[ 1 \frac{4}{9} = \frac{13}{9} \] 2. **Now, substitute these values into the expression:** \[ 2 \frac{2}{3} + 1 \frac{4}{9} = \frac{8}{3} + \frac{13}{9} \] 3. **Find a common denominator to add the fractions:** - The least common multiple of 3 and 9 is 9. - Convert \( \frac{8}{3} \) to have a denominator of 9: \[ \frac{8}{3} = \frac{8 \times 3}{3 \times 3} = \frac{24}{9} \] 4. **Now add the fractions:** \[ \frac{24}{9} + \frac{13}{9} = \frac{24 + 13}{9} = \frac{37}{9} \] 5. **Now, calculate \( 2 - 1 \frac{4}{9} \):** - Convert \( 2 \) to a fraction: \[ 2 = \frac{2 \times 9}{9} = \frac{18}{9} \] - Now subtract: \[ 2 - 1 \frac{4}{9} = \frac{18}{9} - \frac{13}{9} = \frac{18 - 13}{9} = \frac{5}{9} \] 6. **Now we have:** \[ 2 \frac{2}{3} + 1 \frac{4}{9} = \frac{37}{9} \] \[ 2 - 1 \frac{4}{9} = \frac{5}{9} \] 7. **Final expression:** \[ 2 \frac{2}{3} + 1 \frac{4}{9} = 2 - 1 \frac{4}{9} \implies \frac{37}{9} = \frac{5}{9} \] The final answer is: \[ \frac{37}{9} \neq \frac{5}{9} \] Thus, the two sides of the equation are not equal.