Problem 86 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

\frac{5}{6}

Step 1: Identify the Denominators

First identify the denominators of the two fractions, which in this case are 2 and 3. The denominators are different, so it is necessary to find a common denominator before performing the subtraction.

Step 2: Find the Least Common Denominator (LCD)

The least common denominator can be found by multiplying the two denominators together. In this case, \(2 \times 3 = 6\). So, the least common denominator is 6.

Step 3: Convert the Fractions

Now, convert the fractions so that they both have the denominator of 6. Multiply the numerator and denominator of the first fraction by 3 and the second fraction by 2. The fractions then become \( \frac{3*3}{2*3} - \frac{2*2}{3*2} = \frac{9}{6} - \frac{4}{6}\).

Step 4: Perform the Subtraction Operation

Now, subtract the two fractions. Since they now have the same denominator, subtract the numerators to get \( \frac{9-4}{6} = \frac{5}{6}\).

Step 5: Reduce to Lowest Terms

The fraction \( \frac{5}{6} \) is already at its lowest terms as 5 and 6 have no common divisors other than 1. Therefore, \(\frac{5}{6}\) is the answer.