Let's solve the problems from the image step by step.

Problem 3:

$\frac{1}{5} + \frac{12}{20} = \frac{1}{5} + \frac{1}{5}$

Step 1: Make like units (common denominators).

Convert $\frac{12}{20}$ to a fraction with denominator 5: $\frac{12}{20} = \frac{1}{5}$ Now the expression is: $\frac{1}{5} + \frac{1}{5}$

Step 2: Add the fractions.

$\frac{1}{5} + \frac{1}{5} = \frac{2}{5}$ Thus, the final result is: $\boxed{\frac{2}{5}}$

Problem 4:

$\frac{5}{9} - \frac{9}{27}$

Step 1: Make like units (common denominators).

Convert $\frac{9}{27}$ to a fraction with denominator 9: $\frac{9}{27} = \frac{1}{3}$ Now, convert $\frac{1}{3}$ to a fraction with denominator 9: $\frac{1}{3} = \frac{3}{9}$ So the new expression is: $\frac{5}{9} - \frac{3}{9}$

Step 2: Subtract the fractions.

$\frac{5}{9} - \frac{3}{9} = \frac{2}{9}$ Thus, the final result is: $\boxed{\frac{2}{9}}$

Problem 5:

$\frac{7}{30} + \frac{3}{6}$

Step 1: Make like units (common denominators).

Convert $\frac{3}{6}$ to a fraction with denominator 30: $\frac{3}{6} = \frac{15}{30}$ Now the expression is: $\frac{7}{30} + \frac{15}{30}$

Step 2: Add the fractions.

$\frac{7}{30} + \frac{15}{30} = \frac{22}{30}$

Step 3: Simplify.

$\frac{22}{30} = \frac{11}{15}$ Thus, the final result is: $\boxed{\frac{11}{15}}$

Problem 6:

$\frac{5}{6} - \frac{20}{36}$

Step 1: Make like units (common denominators).

Convert $\frac{5}{6}$ to a fraction with denominator 36: $\frac{5}{6} = \frac{30}{36}$ Now the expression is: $\frac{30}{36} - \frac{20}{36}$

Step 2: Subtract the fractions.

$\frac{30}{36} - \frac{20}{36} = \frac{10}{36}$

Step 3: Simplify.

$\frac{10}{36} = \frac{5}{18}$ Thus, the final result is: $\boxed{\frac{5}{18}}$

Would you like any further details or explanations for these problems?

Here are five related questions to help deepen your understanding:

1. How do you convert fractions to have the same denominator?
2. What is the process for simplifying fractions after performing addition or subtraction?
3. How can you quickly check if fractions are equivalent?
4. Can you explain how to simplify complex fractions into their simplest forms?
5. What are the steps to find the least common denominator in fraction problems?

Tip: When adding or subtracting fractions, always ensure you have a common denominator before performing the operation.