https://file.aiquickdraw.com/mathbot/file/1726009758868r7sg2jjf.jpg

Let's simplify both parts of the question.

### a) Simplify:  
\[
\frac{3x}{8} \times \frac{4}{3x}
\]

1. Multiply the numerators:  
   \[
   3x \times 4 = 12x
   \]
2. Multiply the denominators:  
   \[
   8 \times 3x = 24x
   \]
   
Now, the expression becomes:  
\[
\frac{12x}{24x}
\]

3. Cancel out the common factor \(x\) (assuming \(x \neq 0\)) and simplify:  
\[
\frac{12}{24} = \frac{1}{2}
\]

So, the simplified answer for part **a** is:  
\[
\frac{1}{2}
\]

### b) Simplify:  
\[
\frac{x}{5} \div \frac{x}{15}
\]

1. Dividing fractions is the same as multiplying by the reciprocal:  
   \[
   \frac{x}{5} \times \frac{15}{x}
   \]
2. Multiply the numerators:  
   \[
   x \times 15 = 15x
   \]
3. Multiply the denominators:  
   \[
   5 \times x = 5x
   \]

Now, the expression becomes:  
\[
\frac{15x}{5x}
\]

4. Cancel out the common factor \(x\) (assuming \(x \neq 0\)) and simplify:  
\[
\frac{15}{5} = 3
\]

So, the simplified answer for part **b** is:  
\[
3
\]

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

Here are 5 related questions you can explore:

1. How do you multiply and divide algebraic fractions?
2. What happens when the variable in the fraction is zero?
3. How do you simplify fractions involving variables and constants?
4. What are the general rules for multiplying and dividing rational expressions?
5. How do you deal with complex rational expressions with multiple terms?

**Tip:** Always check for common factors before multiplying or dividing fractions to simplify the process.

Simplify the following: a) (3x/8) * (4/3x), b) (x/5) ÷ (x/15)

Learn how to simplify algebraic fractions involving multiplication and division with variables. This step-by-step solution explains how to solve expressions such as (3x/8) * (4/3x) and (x/5) ÷ (x/15). Perfect for students in Grades 6-8.

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