b. $$ \frac{3}{4}+5 \frac{2}{7}-\frac{28}{36} \div 4 \frac{2}{9} $$

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We start with the expression
$$
\frac{3}{4} + 5\frac{2}{7} - \frac{28}{36} \div 4\frac{2}{9}.
$$

**Step 1. Convert mixed numbers to improper fractions.**

For $$5\frac{2}{7}$$:
$$
5\frac{2}{7} = \frac{5 \times 7 + 2}{7} = \frac{35 + 2}{7} = \frac{37}{7}.
$$

For $$4\frac{2}{9}$$:
$$
4\frac{2}{9} = \frac{4 \times 9 + 2}{9} = \frac{36 + 2}{9} = \frac{38}{9}.
$$

The expression becomes
$$
\frac{3}{4} + \frac{37}{7} - \frac{28}{36} \div \frac{38}{9}.
$$

**Step 2. Simplify the division.**

Rewrite the division as multiplication by the reciprocal:
$$
\frac{28}{36} \div \frac{38}{9} = \frac{28}{36} \times \frac{9}{38}.
$$

First, simplify $$\frac{28}{36}$$. Both numerator and denominator are divisible by 4:
$$
\frac{28}{36} = \frac{7}{9}.
$$

Then multiply:
$$
\frac{7}{9} \times \frac{9}{38} = \frac{7 \times 9}{9 \times 38} = \frac{7}{38}.
$$

Now the expression is
$$
\frac{3}{4} + \frac{37}{7} - \frac{7}{38}.
$$

**Step 3. Find a common denominator and combine the fractions.**

The denominators are $$4$$, $$7$$, and $$38$$. We first factor them:
$$
4 = 2^2,\quad 7 \text{ is prime},\quad 38 = 2 \times 19.
$$
The least common multiple (LCM) is
$$
2^2 \times 7 \times 19 = 4 \times 7 \times 19 = 532.
$$

Convert each fraction to have the denominator $$532$$:

For $$\frac{3}{4}$$:
$$
\frac{3}{4} = \frac{3 \times 133}{4 \times 133} = \frac{399}{532}, \quad \text{since } 4 \times 133 = 532.
$$

For $$\frac{37}{7}$$:
$$
\frac{37}{7} = \frac{37 \times 76}{7 \times 76} = \frac{2812}{532}, \quad \text{since } 7 \times 76 = 532.
$$

For $$\frac{7}{38}$$:
$$
\frac{7}{38} = \frac{7 \times 14}{38 \times 14} = \frac{98}{532}, \quad \text{since } 38 \times 14 = 532.
$$

Now combine the fractions:
$$
\frac{399}{532} + \frac{2812}{532} - \frac{98}{532} = \frac{399 + 2812 - 98}{532}.
$$

Calculate the numerator:
$$
399 + 2812 = 3211,\quad 3211 - 98 = 3113.
$$

Thus, the result is
$$
\frac{3113}{532}.
$$

**Step 4. Final Answer.**

$$
\boxed{\frac{3113}{532}}
$$
$$ \frac{3113}{532} $$

b.

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