Problem 35 - Introductory Algebra for College Students

Question

Divide as indicated. $$\frac{3}{x} \div \frac{12}{x}$$

Step-by-Step Solution

Answer

The solution to the problem \(\frac{3}{x} \div \frac{12}{x}\) is \(\frac{1}{4}\).

Step 1: Write the division as multiplication by the reciprocal.

Firstly, remember that dividing something is the same as multiplying by its reciprocal. So we rewrite the original equation \(\frac{3}{x} \div \frac{12}{x}\) to \(\frac{3}{x} \cdot \frac{x}{12}\).

Step 2: Simplify multiplication.

Multiplying fractions involves multiplying the numerators together and then the denominators together, hence, \(\frac{3}{x} \cdot \frac{x}{12} = \frac{3x}{x \cdot 12}\).

Step 3: Reduce the fraction.

The fraction can be simplified further by cancelling out the common x variable from the numerator and denominator. The simplified fraction becomes \(\frac{3}{12}\).

Step 4: Simplify the fraction.

The fraction \(\frac{3}{12}\) can be simplified by dividing the numerator and denominator by the greatest common divisor which is 3, yielding \(\frac{1}{4}\).