Let's break down the three mathematical expressions from the image you uploaded.

1. First Expression:

$\frac{2}{3} \div \frac{4}{7} = ?$ To divide fractions, you multiply the first fraction by the reciprocal of the second: $\frac{2}{3} \div \frac{4}{7} = \frac{2}{3} \times \frac{7}{4} = \frac{2 \times 7}{3 \times 4} = \frac{14}{12}$ Simplify: $\frac{14}{12} = \frac{7}{6}$

2. Second Expression:

$\frac{4a}{7b}x + \frac{5b}{2a} = ?$ This is an algebraic expression that can only be simplified further if values of $a$, $b$, or $x$ are provided. For now, it remains in this form.

3. Third Expression:

$2\frac{3}{4}x + 3\frac{1}{2} = ?$ First, convert the mixed numbers to improper fractions: $2\frac{3}{4} = \frac{11}{4}, \quad 3\frac{1}{2} = \frac{7}{2}$ Now, the expression becomes: $\frac{11}{4}x + \frac{7}{2}$ To simplify further, we could combine like terms if more information is given about $x$.

Would you like more details or have any specific questions on these steps?

Five Related Questions:

1. How do you multiply and divide fractions?
2. What is the process for simplifying algebraic expressions with fractions?
3. How do you convert mixed numbers to improper fractions?
4. How can you combine algebraic terms if both terms involve variables?
5. When is it necessary to solve for a variable in an equation?

Tip:

When dividing fractions, remember to "flip and multiply"—this means multiplying by the reciprocal of the divisor.