Problem 36 - Introductory Algebra for College Students

Question

Divide as indicated. $$\frac{x}{5} \div \frac{20}{x}$$

Step-by-Step Solution

Answer

\(\frac{x^2}{100}\)

Step 1: Write down the problem

The problem as given is \(\frac{x}{5} \div \frac{20}{x}\)

Step 2: Change the division to multiplication

To divide by a fraction, you multiply by its reciprocal. The reciprocal of \(\frac{20}{x}\) is \(\frac{x}{20}\). So now the problem becomes \(\frac{x}{5} * \frac{x}{20}\)

Step 3: Multiply the numerators and denominators

Now multiply the numerators together and put that product over the product of the denominators. That gives us \(\frac{x * x}{5 * 20}\)

Step 4: Simplify the result

This can be simplified to \(\frac{x^2}{100}\)