a. $$ \quad 2 \frac{2}{3}+1 \frac{1}{2}+3 \frac{3}{4}= $$ c. $$ \quad 6 \frac{2}{2}+1 \frac{7}{25}+2 \frac{2}{2}= $$

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Let's solve each of the problems step by step.

### Part a: $$ 2 \frac{2}{3} + 1 \frac{1}{2} + 3 \frac{3}{4} $$

1. **Convert mixed numbers to improper fractions:**
   - $$ 2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} $$
   - $$ 1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} $$
   - $$ 3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} $$

2. **Find a common denominator:**
   - The denominators are 3, 2, and 4. The least common multiple (LCM) of these numbers is 12.

3. **Convert each fraction to have a denominator of 12:**
   - $$ \frac{8}{3} = \frac{8 \times 4}{3 \times 4} = \frac{32}{12} $$
   - $$ \frac{3}{2} = \frac{3 \times 6}{2 \times 6} = \frac{18}{12} $$
   - $$ \frac{15}{4} = \frac{15 \times 3}{4 \times 3} = \frac{45}{12} $$

4. **Add the fractions:**
   $$
   \frac{32}{12} + \frac{18}{12} + \frac{45}{12} = \frac{32 + 18 + 45}{12} = \frac{95}{12}
   $$

5. **Convert back to a mixed number:**
   - $$ \frac{95}{12} = 7 \frac{11}{12} $$

So, the answer for part a is:
$$
2 \frac{2}{3} + 1 \frac{1}{2} + 3 \frac{3}{4} = 7 \frac{11}{12}
$$

### Part c: $$ 6 \frac{2}{2} + 1 \frac{7}{25} + 2 \frac{2}{2} $$

1. **Convert mixed numbers to improper fractions:**
   - $$ 6 \frac{2}{2} = 6 + 1 = 7 $$ (since $$ \frac{2}{2} = 1 $$)
   - $$ 1 \frac{7}{25} = \frac{1 \times 25 + 7}{25} = \frac{25 + 7}{25} = \frac{32}{25} $$
   - $$ 2 \frac{2}{2} = 2 + 1 = 3 $$ (since $$ \frac{2}{2} = 1 $$)

2. **Convert whole numbers to fractions:**
   - $$ 7 = \frac{7 \times 25}{25} = \frac{175}{25} $$
   - $$ 3 = \frac{3 \times 25}{25} = \frac{75}{25} $$

3. **Add the fractions:**
   $$
   \frac{175}{25} + \frac{32}{25} + \frac{75}{25} = \frac{175 + 32 + 75}{25} = \frac{282}{25}
   $$

4. **Convert back to a mixed number:**
   - $$ \frac{282}{25} = 11 \frac{7}{25} $$ (since $$ 282 \div 25 = 11 $$ remainder $$ 7 $$)

So, the answer for part c is:
$$
6 \frac{2}{2} + 1 \frac{7}{25} + 2 \frac{2}{2} = 11 \frac{7}{25}
$$

### Final Answers:
- Part a: $$ 7 \frac{11}{12} $$
- Part c: $$ 11 \frac{7}{25} $$
Part a: $$ 7 \frac{11}{12} $$ Part c: $$ 11 \frac{7}{25} $$

a. \( \quad 2 \frac{2}{3}+1 \frac{1}{2}+3 \frac{3}{4}= \) c. \( \quad 6 \frac{2}{2}+1 \frac{7}{25}+2 \frac{2}{2}= \)

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