Problem 5 - Introductory Algebra for College Students

Question

Multiply as indicated. $$\frac{3}{x} \cdot \frac{4 x}{15}$$

Step-by-Step Solution

Answer

The result of the multiplication \(\frac{3}{x} * \frac{4x}{15}\) simplifies to \(\frac{4}{5}\).

Step 1: Multiply The Numerators

Multiply the numerators of the fractions together. That is \(3 * 4x = 12x\). So the numerator of the answer is \(12x\).

Step 2: Multiply The Denominators

Multiply the denominators of the fractions together. That is \(x * 15 = 15x\). So the denominator of the answer is \(15x\).

Step 3: Write Down The Answer

The result from step 1 and step 2 gives us the answer to the multiplication of the fractions. So, \(\frac{3}{x} * \frac{4x}{15} = \frac{12x}{15x}\).

Step 4: Simplify The Answer

Notice that there is a common factor in the numerator and denominator which is \(x\), you can simplify by dividing both the numerator and denominator by \(x\). So, \(\frac{12x}{15x} = \frac{12}{15}\). This can further be simplified by dividing both the numerator and denominator by 3, resulting to \(\frac{4}{5}\).