1. **State the problem:** Calculate the sum of $2\frac{2}{25} + \frac{56}{75}$. 2. **Convert the mixed number to an improper fraction:** $$2\frac{2}{25} = \frac{2 \times 25 + 2}{25} = \frac{50 + 2}{25} = \frac{52}{25}$$ 3. **Find a common denominator for the fractions:** The denominators are 25 and 75. The least common denominator (LCD) is 75. 4. **Convert $\frac{52}{25}$ to have denominator 75:** $$\frac{52}{25} = \frac{52 \times 3}{25 \times 3} = \frac{156}{75}$$ 5. **Add the fractions:** $$\frac{156}{75} + \frac{56}{75} = \frac{156 + 56}{75} = \frac{212}{75}$$ 6. **Simplify or convert to mixed number:** Divide 212 by 75: $$212 \div 75 = 2 \text{ remainder } 62$$ So, $$\frac{212}{75} = 2\frac{62}{75}$$ **Final answer:** $2\frac{62}{75}$