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Chapter 7: Problem 35

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

Short Answer

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

Step by step solution

01

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 \(\frac{3}{x} \cdot \frac{x}{12}\).
02

Simplify multiplication.

Multiplying fractions involves multiplying the numerators together and then the denominators together, hence, \(\frac{3}{x} \cdot \frac{x}{12} = \frac{3x}{x \cdot 12}\).
03

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 \(\frac{3}{12}\).
04

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 \(\frac{1}{4}\).

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Most popular questions from this chapter

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