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

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UpStudy AI · Accepted Answer

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.
The two sides of the equation are not equal.

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