Problem 56 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

The result of the operation \( \frac{12}{7} \div 3 \) is \( \frac{12}{21} \).

Step 1: Understand Mathematical Operation

The problem is asking for the result of dividing the fraction \( \frac{12}{7} \) by 3. This translates to \(\frac{12}{7} \div 3\).

Step 2: Convert Division to Multiplication

The division of fractions can be converted to a multiplication problem by multiplying the first fraction by the reciprocal (or 'flip') of the second fraction. In this case, the number 3 is also a fraction (i.e., \(\frac{3}{1}\)). Its reciprocal is \(\frac{1}{3}\). So, the problem becomes \(\frac{12}{7} \times \frac{1}{3}\).

Step 3: Perform The Multiplication

When multiplying fractions, the numerators are multiplied together and the denominators are multiplied together: \( \frac{12 \times 1}{7 \times 3} = \frac{12}{21}\)

Step 4: Simplify The Result

The fraction \( \frac{12}{21} \) cannot be simplified further, since 12 and 21 do not share any common factors apart from 1. Therefore, the simplest form of the fraction is \( \frac{12}{21} \).