Divide:frac(5x,8)÷frac(15sup(x,2),4)

(Assume all denominators are nonzero)

To solve the division of two fractions, \(\frac{5x}{8} \div \frac{15x^2}{4}\), you can follow these steps:

### Step 1: Rewrite the Division as Multiplication
Dividing by a fraction is the same as multiplying by its reciprocal. So, the expression becomes:
\[
\frac{5x}{8} \times \frac{4}{15x^2}
\]

### Step 2: Multiply the Numerators and Denominators
Now, multiply the numerators together and the denominators together:
\[
\frac{5x \times 4}{8 \times 15x^2} = \frac{20x}{120x^2}
\]

### Step 3: Simplify the Expression
Next, simplify the fraction. Both the numerator and the denominator have a common factor of \(20x\):
\[
\frac{20x}{120x^2} = \frac{1}{6x}
\]

### Final Answer
Thus, the simplified result of the division is:
\[
\frac{1}{6x}
\]

Would you like more details on any step or have any questions?

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Here are some follow-up questions you might find helpful:

1. What is the general rule for dividing fractions?
2. How do you find the reciprocal of a fraction?
3. How can you simplify algebraic expressions?
4. Why is it important to check for nonzero denominators?
5. How would the expression change if the exponents were different?

**Tip:** When dividing fractions, always remember to multiply by the reciprocal of the second fraction.

Learn how to divide fractions \(\frac{5x}{8} \div \frac{15x^2}{4}\) step-by-step with a detailed solution. This problem involves fractions, algebraic manipulation, and division of fractions using reciprocals. Suitable for Grades 7-9.

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