1. Stating the problem: Calculate the value of $0.1125 \div 0.45 + 0.2275 \div 0.65$.\n\n2. Use the division operation and addition: For any numbers $a$, $b$, and $c$, the expression is $\frac{a}{b} + \frac{c}{d}$.\n\n3. Calculate each division separately:\n$$0.1125 \div 0.45 = \frac{0.1125}{0.45}$$\nSimplify by multiplying numerator and denominator by 1000 to avoid decimals:\n$$\frac{0.1125}{0.45} = \frac{112.5}{450}$$\nDivide numerator and denominator by 112.5:\n$$\frac{\cancel{112.5}}{\cancel{450}} = \frac{1}{4} = 0.25$$\n\n4. Calculate the second division:\n$$0.2275 \div 0.65 = \frac{0.2275}{0.65}$$\nMultiply numerator and denominator by 1000:\n$$\frac{227.5}{650}$$\nDivide numerator and denominator by 32.5:\n$$\frac{\cancel{227.5}}{\cancel{650}} = \frac{7}{20} = 0.35$$\n\n5. Add the two results:\n$$0.25 + 0.35 = 0.6$$\n\nFinal answer: $0.6$