Problem 58 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$3 \div \frac{12}{7}$$

Step-by-Step Solution

Answer

The answer to the operation is \(\frac{7}{4}\).

Step 1: Write the problem

The given problem is \(3 \div \frac{12}{7}\)

Step 2: Finding the Reciprocal of the Fraction

Reciprocal of \(\frac{12}{7}\) is \(\frac{7}{12}\)

Step 3: Multiplying by the Reciprocal

This operation is equivalent to \(3 \times \frac{7}{12}\), which equals \(\frac{21}{12}\)

Step 4: Reducing to Lowest Terms

The fraction \(\frac{21}{12}\) can be simplified by dividing both the numerator and the denominator by their common factor. The common factor of 21 and 12 is 3, and when we divide both by 3 we get \(\frac{7}{4}\)