Problem 90 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$3 \frac{2}{3}-2 \frac{1}{2}$$

Step-by-Step Solution

Answer

The answer is \(1 \frac{1}{6}\) or \(\frac{7}{6}\) as an improper fraction.

Step 1: Convert Mixed Numbers into Improper Fractions

A mixed number can be converted to an improper fraction using the formula: (whole number * denominator) + numerator.So, \(3 \frac{2}{3}\) becomes \(\frac{(3*3)+2}{3} = \frac{11}{3}\) and \(2 \frac{1}{2}\) becomes \(\frac{(2*2)+1}{2} = \frac{5}{2}\).

Step 2: Equalize the Denominators

Before subtracting the fractions, their denominators need to be equal. The least common multiple (LCM) of 3 and 2 is 6. To make the denominators the same, multiply the numerator and the denominator of the first fraction by 2 and the second one by 3: \(\frac{11}{3} * \frac{2}{2} = \frac{22}{6}\) and \(\frac{5}{2} * \frac{3}{3} = \frac{15}{6}\).

Step 3: Subtracting Fractions and Simplifying

Now, it's time to subtract the fractions: \(\frac{22}{6} - \frac{15}{6} = \frac{22 - 15}{6} = \frac{7}{6}\). This is an improper fraction and can be left as such or converted back to a mixed number. As a mixed number, it would be \(1 \frac{1}{6}\).