1. We are asked to find the sum of the fractions: $\frac{2}{10} + \frac{5}{15} + \frac{2}{3} + \frac{1}{5} + \frac{2}{4}$.\n\n2. To add fractions, we need a common denominator. The denominators are 10, 15, 3, 5, and 4.\n\n3. Find the least common denominator (LCD).\n- Prime factors:\n 10 = 2 \times 5\n 15 = 3 \times 5\n 3 = 3\n 5 = 5\n 4 = 2^2\n- LCD must include 2^2, 3, and 5, so LCD = 4 \times 3 \times 5 = 60.\n\n4. Convert each fraction to have denominator 60:\n$$\frac{2}{10} = \frac{2 \times 6}{10 \times 6} = \frac{12}{60}$$\n$$\frac{5}{15} = \frac{5 \times 4}{15 \times 4} = \frac{20}{60}$$\n$$\frac{2}{3} = \frac{2 \times 20}{3 \times 20} = \frac{40}{60}$$\n$$\frac{1}{5} = \frac{1 \times 12}{5 \times 12} = \frac{12}{60}$$\n$$\frac{2}{4} = \frac{2 \times 15}{4 \times 15} = \frac{30}{60}$$\n\n5. Add the numerators:\n$$12 + 20 + 40 + 12 + 30 = 114$$\nSo the sum is $$\frac{114}{60}$$.\n\n6. Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD).\n- GCD of 114 and 60 is 6.\n$$\frac{\cancel{6}19}{\cancel{6}10} = \frac{19}{10}$$\n\n7. The final answer is $$\frac{19}{10}$$ or as a mixed number $$1 \frac{9}{10}$$.