Guided Practice:
Simplify the expression.

[tex]\[ \frac{1}{3} - \frac{1}{2} \][/tex]

A. [tex]\(\frac{5}{6}\)[/tex]

B. [tex]\(\frac{1}{6}\)[/tex]

C. [tex]\(\frac{1}{6}\)[/tex]



Answer :

To simplify the expression [tex]\(\frac{1}{3} - \frac{1}{2}\)[/tex], let's break it down step-by-step.

1. Express each fraction with a common denominator:

The fractions [tex]\(\frac{1}{3}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex] have different denominators. The common denominator for 3 and 2 is 6.

2. Convert each fraction:

[tex]\[ \frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \][/tex]

[tex]\[ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \][/tex]

3. Subtraction of fractions with common denominators:

Now that both fractions have the same denominator, subtract the numerators:

[tex]\[ \frac{2}{6} - \frac{3}{6} = \frac{2 - 3}{6} = \frac{-1}{6} \][/tex]

4. Simplify the result:

The result, [tex]\(\frac{-1}{6}\)[/tex], is already in its simplest form.

So, [tex]\(\frac{1}{3} - \frac{1}{2} = \frac{-1}{6}\)[/tex].

The correct answer is:

C. [tex]\(\frac{1}{6}\)[/tex]