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Chapter 1: Problem 86

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

Short Answer

Expert verified
\frac{5}{6}

Step by step solution

01

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.
02

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.
03

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 \( \frac{3*3}{2*3} - \frac{2*2}{3*2} = \frac{9}{6} - \frac{4}{6}\).
04

Perform the Subtraction Operation

Now, subtract the two fractions. Since they now have the same denominator, subtract the numerators to get \( \frac{9-4}{6} = \frac{5}{6}\).
05

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.

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