Here is the step-by-step solution to each part of the problem:

a)

$\frac{1}{100} \cdot 1 + \frac{1}{100} \cdot 0$

• $\frac{1}{100} \cdot 1 = \frac{1}{100}$
• $\frac{1}{100} \cdot 0 = 0$
• Result:
  $\frac{1}{100} + 0 = \frac{1}{100}$

b)

$-0.2 \cdot 10 + 0.1 \cdot 20$

• $-0.2 \cdot 10 = -2$
• $0.1 \cdot 20 = 2$
• Result:
  $-2 + 2 = 0$

c)

$-1.7 - 21.06 : (-5.2)$

• Division: $21.06 \div (-5.2) = -4.05$
• Subtraction:
  $-1.7 - (-4.05) = -1.7 + 4.05 = 2.35$

d)

$\left(-\frac{11}{12} + \frac{2}{3}\right) : \frac{3}{4}$

1. Simplify inside the parentheses:
   • $-\frac{11}{12} + \frac{2}{3} = -\frac{11}{12} + \frac{8}{12} = -\frac{3}{12} = -\frac{1}{4}$
2. Divide:
   $-\frac{1}{4} \div \frac{3}{4} = -\frac{1}{4} \cdot \frac{4}{3} = -\frac{1}{3}$

• Result:
  $-\frac{1}{3}$

e)

$\left(\frac{1}{6} - \frac{1}{5}\right) : \left(\frac{1}{6} + \frac{1}{7}\right)$

1. Subtraction:
   • $\frac{1}{6} - \frac{1}{5} = \frac{5}{30} - \frac{6}{30} = -\frac{1}{30}$
2. Addition:
   • $\frac{1}{6} + \frac{1}{7} = \frac{7}{42} + \frac{6}{42} = \frac{13}{42}$
3. Division:
   $-\frac{1}{30} \div \frac{13}{42} = -\frac{1}{30} \cdot \frac{42}{13} = -\frac{42}{390} = -\frac{7}{65}$

• Result:
  $-\frac{7}{65}$

f)

$-1.8 : \frac{1}{4} - \frac{2}{3} \cdot (-2.4)$

1. Division:
   • $-1.8 \div \frac{1}{4} = -1.8 \cdot 4 = -7.2$
2. Multiplication:
   • $\frac{2}{3} \cdot (-2.4) = -\frac{4.8}{3} = -1.6$
3. Subtraction:
   $-7.2 - (-1.6) = -7.2 + 1.6 = -5.6$

• Result:
  $-5.6$

g)

$\left(\frac{1}{6} + \frac{1}{5}\right) \cdot \left(\frac{1}{6} - \frac{1}{5}\right)$

1. Sum:
   • $\frac{1}{6} + \frac{1}{5} = \frac{5}{30} + \frac{6}{30} = \frac{11}{30}$
2. Difference:
   • $\frac{1}{6} - \frac{1}{5} = \frac{5}{30} - \frac{6}{30} = -\frac{1}{30}$
3. Multiplication:
   $\frac{11}{30} \cdot \left(-\frac{1}{30}\right) = -\frac{11}{900}$

• Result:
  $-\frac{11}{900}$

h)

$\left(3 \frac{2}{3} - 1 \frac{2}{7} \cdot \frac{5}{4}\right) : (-2.5)$

1. Convert mixed numbers to improper fractions:
   • $3 \frac{2}{3} = \frac{11}{3}$
   • $1 \frac{2}{7} = \frac{9}{7}$
2. Multiplication:
   • $\frac{9}{7} \cdot \frac{5}{4} = \frac{45}{28}$
3. Subtraction:
   $\frac{11}{3} - \frac{45}{28} = \frac{308}{84} - \frac{135}{84} = \frac{173}{84}$
4. Division:
   • $\frac{173}{84} \div -2.5 = \frac{173}{84} \cdot \frac{-1}{2.5} = \frac{173}{84} \cdot \frac{-1}{\frac{5}{2}} = \frac{173 \cdot -2}{84 \cdot 5} = -\frac{346}{420} = -\frac{173}{210}$

• Result:
  $-\frac{173}{210}$

Let me know if you would like clarification on any step or if you need additional assistance!

Questions to explore further:

1. How do you simplify fractions more efficiently?
2. What are the rules for dividing by a negative number?
3. How can mixed numbers be handled faster in arithmetic?
4. What is the significance of parentheses in these types of calculations?
5. How does the order of operations (PEMDAS/BODMAS) apply here?

Tip: Always double-check calculations involving negative signs, as they can easily be overlooked in