Problem 34 - Introductory Algebra for College Students

Question

Divide as indicated. $$\frac{x}{3} \div \frac{3}{8}$$

Step-by-Step Solution

Answer

The result is \(\frac{8x}{9}\).

Step 1: Identify the given fractions

The given fractions are \(\frac{x}{3}\) and \(\frac{3}{8}\).

Step 2: Change the division to multiplication

When you divide by a fraction, you actually multiply by its reciprocal. So the problem becomes \(\frac{x}{3} \times \frac{8}{3}\).

Step 3: Multiplication of fractions

Each fraction is then multiplied fraction by fraction. This results in the equation \(\frac{x \times 8}{3 \times 3}\).

Step 4: Simplify the fractions

Upon simplifying the fractions, it results in \(\frac{8x}{9}\).